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SigmaPlot® 8.0 Programming Guide

1. 99 9 1 1 0 10 0 100 0 1000 0 SHEAR STRESS week Transform for the User Defined Y Axis Scale NKKKKKKKKKKEK KK y log log 100 y KKEKKKKKKKKKKEKK This transform is an example of how to transform your data to fit a custom axis scale and to compute the grid line intervals for that scale Place your y data in y_col and the y tick mark L cations in tick coL or change the column number to suit your data Results are placed beginning in column res y Cols tick col 3 res 4 y_data col y_col Original y data NKKKKKKKKKKHK FUNCTION FOR Y AXIS SCALE KKKKKKKKKKK f y log log 100 y YTLaNnstorm for axis scale PR Te ey ie ONE OUTE a Tees INTERVAL DATA RENARE EN ea Viet Col eack col y tick intervals PRE PLACE Y DATA AND Y AX LS GRIDIN WORKSHEET FAX col res f y_data transformed y data Col rest y yi y values for y grid Graphing Transform Examples 133 Example Transforms Vector Plot TheVECTOR XFM transform creates a field of vectors lines with arrow heads from data which specifiesthe X and Y position length and angle of each vector T he data is entered into four columns Executing the transform produces six columns of three XY pairs which describe the arrow body and the upper and lower components of the arrow head O ther settings are gt thelength of the ar
2. Graphing Transform Examples 125 Example Transforms Shade Between xxxxx x Shading Between Curves Curves Transform This transform fills the area between two x y SHADE_2 XFM line curves with vertical lines The x data tor both curves MUST be in strictly increasing order Create a new line and scatter plot select result_x and result_y columns for the x and y axes Turn symbols off in the Symbols panel of the Plot tab in the Graph Properties dialog box For a solid color between the curves use a large density about 500 For a nicely spaced WrerewGal ally tery wt densiry Or BU N KAKKKKKKKKKK Papat KAKKKKKKKKKKHK cxl 1 column for first curve x data gyl 2 eo Lunn for first curve y data Cx2 3 column for second curve x data cy2 4 column for second curve y data density 50 line density of fill N KAKKKKK KKK RESULTS KAKKKKKKKKKHK result_x 5 column for x fill results result_y 6 column for y fill results N KAKKKKIK IKK KK Program KAKKKKKKKKKHK XL col cxl1 x data Lor first curve i icoltcy 1 yv Gata fOr LL rset curve X2 col cxzZ x data for second curve Xa COLCCYZ y data for second curve xl min min X1 xZ2 min min XZ xl max max X1 x2_max max X2 Take the largest x_min and the smallest x_max x min AES mi lt OZ as 7 mMin XL MIn x_max if xl_max gt x2_max x2_max xl_max dx
3. results and constructs an ANOVA table Required INPUT y data fitted y data function parameters coefficients RESULTS sum of squares degrees of freedom mean squared F value R squared amp R values standard error of fit INPUT to be placed in specify source columns y_col 2 y data column number Lite Cols fitted y data column number param_col 4 parameter column number ANOVA to be placed in column anova 5 ANOVA table starting column 5 columns x 10 rows V Co Liy Cc L define y values f col fit_col define fitted y values p col param_col define function parameters n count y number of y data points tdof n 1 total degrees of freedom r count 1f p lt gt 0 p the number of nonzero parameters Tee BRE ROIS ANOVA TABLE CALCULATION 28 ae Re A Regression Degrees of Freedom FOOT LOOT VE PR COUN D 7 7 2 count p 1 Error Degrees of Freedom edof tdof rdof Sum of Squares of Residuals SSE total y 2 Sum of Squares of Error about the Mean SSM total y mean y 2 Sum of Squares of Error due to Regression SSR SSM SSE Standard Error of Ert 72 Data Transform Examples OT ee Example Transforms se sqrt SSE rdof F value f1 SSM SSE edof SSE rdof F if n lt 2 n lt 2 I f1 R squared R2 1 SSE SSM xx xx x x PLACE ANOVA TABLE IN WORKSHEET vce ree eS col anova 0 0 REGRESSION E
4. T hex range argument specifies the x variable and the y range argument specifies the y variable Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must have the same size and the number of valid data points must be greater than or equal to 3 T he optional f argument defines the amount of Lowess smoothing and corresponds to the fraction of data points used for each regression f must be greater than or equal to 0 and less than or equal to 1 0 lt f lt 1 If fis omitted no smoothing is used For x 0 1 2 y 0 1 4 the operation col 1 xwtr x y places the x75 x25 as double 1 00 into column 1 X25 x50 x75 xatymax User defined Functions You can create any user defined function consisting of any expression in the transform language and then refer to it by name For example the following transform defines the function dist2pts which returns the distance between two points dist2pts x1 y1 x2 y2 sqrt x2 x1 2 y2 y1 2 You can then use this custom defined function instead of the expression to the right of the equal sign in subsequent equations For example to plot the distances User defined Functions 69 Transform Function Reference between two sets of XY coordinates with the first points stored in columns 1 and 2 and the second in columns 3 and 4 enter col 5 dist2pts col 1 col 2 col 3 col 4 T he resulti
5. You can add optional comments to describe a macro command or function and how it interacts in the script W hen the macro is running comment lines are ignored Indicate a comment by beginning a line with an apostrophe Comments always must end the line they re on T he next program line must go on anew line By default comment lines appear as green text Editing Macros 249 Automating Routine Tasks Scrolling and Moving When you usethe scroll bars the insertion point does not change To edit the macro the Insertion Point code that you are viewing in the macro window you must move the insertion point manually To edit macro code manually 1 IntheM acro window click where you want to edit 2 You can also use arrows and key combinations to move the insertion point when you do this the window scrolls automatically Editing Macro Code You can edit macro code in the same way you edit text in most word processing and text editing programs You add select and delete text type over code or insert text by moving the insertion point and then typing in new text As with other programming languages you can also add comments to code To edit macro code gt Open the macro code window and select the text to edit Adding Comments to Adding comments to code is an excellent way to identify the purpose of the various Code parts of amacro and to map locations as you edit a complex macro Comments can be inserted that fully document how to
6. 158 199 200 entering equation settings 188 192 Equation Library 148 error status messages 182 183 examples 205 219 240 executing 205 208 214 fit statements 220 generating a regression equation 189 190 influencing operation 200 202 introduction 1 2 iterations 145 159 160 201 linear regression 205 211 local maximum 222 local minimum 222 logistic function regression 212 217 M arquardt Levenberg algorithm 145 multiple function 234 237 options 200 202 overview 1 2 parameters 198 199 229 231 plotting results 209 211 quitting 165 report 167 175 results 163 166 205 208 211 214 results messages 181 183 running a regression again 164 saving results 165 166 209 211 scaling x variable 238 solving equations 232 233 step size 160 201 straight line 205 211 tips 219 240 308 tolerance 161 201 222 transform functions 196 tutorial 205 217 variables 190 198 225 weight variables 194 197 198 225 weighted regression 225 227 see also linear regression and regression examples Regression Equation library 148 285 3 Dimensional 300 Gaussian 300 Lorentzian 300 Paraboloid 300 Plane 300 Exponential D ecay 290 1 Parameter Single 292 2 Parameter Simple Exponent 291 293 2 Parameter Single 291 292 2 Parameter Single Exponential D ecay 290 3 Parameter Simple Exponent 291 293 3 Parameter Single 291 292 3 Parameter Single Exponential D ecay 290 4 Parameter D ouble 291 292
7. Gell ers Ul f2 celliterd x cel litera IVa else for jl 1 ton do start search loop if jgl gt 1 then if u lt x jl then ater A oe Se ieee dt Neen lt a dxl u x xa Vax Cel er wl f CSLL Cera sc Cel CrS TLE Celi ere7 lt 1 5 cCelLlitcy xI 40x celler rul HE cell er4 a Celery lt 2 y Cell CerG lt 7 Lox cellier 01 f2 cel liera x 71 Coda Cer 57 och yx CEVI CrO 9 L end if end if end if end for end search loop end if else XJ2 X AX2 0 X X72 GelL eri uler eel era 42 Cel L Cera x24 4 CELL CrO XTZ CELIC 62 paz 92 Graphing Transform Examples ee Example Transforms Cell er Uk Ht iteeiei erd xX r Cel L er 57 XJA Cel erG lt 2 ax Celliors uly t2 cel 6rd lt jZ gt CeL LOES Z rax end if end for Fast Fourier Transform T he Fast Fourier Transform converts data from the time domain to the frequency domain It can be used to remove noise from or smooth data using frequency based filtering Use the fft function to find the frequency domain representation of your data then edit the results to remove any frequency which may adversely affect the original data T he Fast Fourier Transform uses the following transform functions gt fft invfft real img complex mulcpx gt Invcpx VVVVYV T he Fast Fourier Transform operates on arange of real values or a block of complex values For complex values there are two columns of data T he first colu
8. Predicted Values T hisis the value for the dependent variable predicted by the regression model for each observation Regression T he confidence interval for the regression gives the range of variable values computed for the region containing the true relationship between the dependent and independent variables for the specified level of confidence The 5 values are lower limits and the 95 values are the upper limits Population T he confidence interval for the population gives the range of variable values computed for the region containing the population from which the 174 Interpreting Regression Reports Regression Wizard observations were drawn for the specified level of confidence The5 values are lower limits and the 95 values are the upper limits Regression Equation Libraries and Notebooks Figure 8 29 The Standard Regression Equation Library Regression equations are stored in notebook files just as other SigmaPlot documents N otebooks that are used to organize and contain only regression equations are referred to as libraries and distinguished from ordinary notebooks with a file extension of JFL T hese library notebooks can be opened and modified like any other notebook file You can also use ordinary SigmaPlot notebooks JN B as equation libraries as well as save any notebook asa JFL file Regression equations within notebooks are indicated with a icon that appears next to the equation name T he equation
9. R ion untitled x The Regression Dialog a Ea Equati Vanabl i quations anables Initial Parameters Constraints Options Iterations fioo Step Size fioo Tolerance fo oo07 O0 Trigonometric Units f Degrees i Radians f Grads T his section covers the minimum steps required to enter the code for a regression equation For more information on entering the code for each section see Equations on page 193 Variables on page 194 Weight Variables on page 197 Initial Parameters on page 198 Constraints on page 199 Other O ptions on page 200 VVVVVY Adding Comments are placed in the edit box by preceding them with an apostrophe Comments _ or asemicolon You can also use apostrophes or semicolons to comment out equations instead of deleting them 188 Entering Regression Equation Settings Entering Equations Figure 9 5 Entering the Regression Equation and the Regression Statement Editing Code To enter the code for the Equation section 1 Click in the Equation window and type the regression equation model using the transform language operators and functions T he equation should contain all of the variables you plan to use as independent variables as well as the name for the predicted dependent variable which is not your y variable You can use any valid variable name for your equation variables and parameters but short single letter names are recommende
10. Regression Equation Library To see the library currently in use click the Back button from the Regression W izard equation panel Previously selected libraries and open notebooks can be selected from the Library D rop D own list A regression equation library can be opened viewed and modified as any ordinary notebook To open a regression library gt Click the O pen toolbar button select JFL as the file type from the File Type drop down list then select the library to open or gt Click the O pen button in the Regression W izard library panel to open the current library T he library panel can be reached by clicking Back from the Equations panel You can copy paste rename and delete regression equations as any other notebook item O pening aregression equation directly from anotebook automatically launches the Regression W izard with the variables panel selected You can also select another notebook or library as the source for the equations in the Regression W izard Selecting a different equation library changes the categories and equations listed Regression W izard equations panel SigmaPlot Fit Library CSP AS Borin jb LSPS hy Fits JFL Template JNT k Notebook Open _ Help Cancel Back f Net cinish 176 Regression Equation Libraries and Notebooks pS Regression Wizard To change the library 1 Start the Regression W izard by pressing F5 or choosing the Statistics menu Regr
11. Transforms use operators to define variables and apply functions A complete set of arithmetic relational and logical operators are provided Order of Operation T he order of precedence is consistent with P E M A Parentheses Exponentiation Multiplication and Addition and proceeds as follows except that parentheses override any other rule Exponentiation associating from right to left Unary minus M ultiplication and division associating from left to right Addition and subtraction associating from left to right Relational operators Logical negation Logical and associating from left to right Logical or associating from left to right VVVVVVYV y T his list permits complicated expressions to be written without requiring too many parentheses Example T he statement a lt 10 and b lt 5 groups to a lt 10 and b lt 5 not to a lt 10 and b lt 5 Order of Operation 17 Transform Operators 5 N ote that only parentheses can group terms for processing Curly and square brackets are reserved for other uses Figure 4 1 i User Defined Transform untitled Examples of Transform Operators Edit Transform a 10 col 1 col 2 b col 1 1 if a 0 and b 10 c col 3 Trigonometric Units i Degrees Radians Grads Operations on Ranges T he standard arithmetic operators addition subtraction multiplication division and exponentiation follow basic rules when used with scalars For ope
12. then click OK Click Finish The curve fitter goes through many more iterations W hen it is completed view the Weighted graph page T he graph shows the nonlinear regression results with and without weighting T he weighted results fit the very small recirculation data represented by the 226 Example 2 Weighted Regression Figure 11 15 Comparing the Function Results of Weighted and Unweighted Nonlinear Regression Fits Advanced Regression Examples third exponential quite well H owever when weighting is not used the curve fitter ignored the relatively small values in the recirculation portion of the data resulting in a poor fit B Weighted Graph Weighted Worksheet OY x Time Sec a Example 3 Piecewise Continuous Function T he data obtained from the wash in of a volatile liquid into amixing chamber is modeled by three separate equations reoresenting three line segments joined at their endpoints E 20 1 ty fit x T t T f t T X4U 4 where fi ift lt t lt T f 5f 0 fT lt t lt T f t if T lt t lt t Example 3 Piecewise Continuous Function 227 Advanced Regression Examples Figure 11 16 The Weighted Triple Exponential Equation Figure 11 17 The Data in the Piecewise Continuous Graph Fitted with the Equations for Three Lines 3 O pen the Piecewise C ontinuous worksheet and graph by double clicking the graph page icon in the Piecewise C
13. x a b H owever you may find it necessary to conserve space by omitting spaces Blank lines are ignored so that you can use them to separate or group equations for easier reading If the equation requires more than one line you may want to begin the second and any subsequent lines indented a couple of spaces press the space bar before typing the line Although this is not necessary indenting helps distinguish a continuing equation from anew one You can resize the transform dialog box to enlarge the edit box You can press Ctrl X Ctrl C and Ctrl V to cut copy and paste text in the edit window Transforms are limited to a maximum of 100 lines N ote that you can enter more than one transform statement on a line however this is only recommended if space iS a premium U se only parentheses to enclose expressions Curly brackets and square brackets are reserved for other uses To enter a comment type an apostrophe or a semicolon then type the comment to the right of the apostrophe or semicolon If the comment requires more than one line repeat the apostrophe or semicolon on each line before continuing the comment SigmaPlot and SigmaStat generally solve equations regardless of their sequence in the transform edit box H owever the col function which returns the values in a worksheet column depends on the sequence of the equations as shown In the following example Example T he sequence of the equations col 1
14. 214 217 regression results 169 Standard error of the estimate regression results 168 Standardized residuals regression diagnostic results 172 Statements IF function 20 Statistical functions 25 Statistical summary table results 168 Statistics bivariate 74 75 D urbin W atson 171 F statistic 170 PRESS 171 t statistic 169 STDDEV function 63 74 STDERR function 64 Step graph transform 84 86 Step size 160 default value 160 entering 160 201 Stepwise regression results adjusted R2 168 Strings 12 in transforms 7 Studentized deleted residuals regression results 173 Studentized residuals regression diagnostic results 173 SUBBLOCK function 64 SUM function 65 Sum of squares absolute minimum 223 local maximum 223 regression results 169 Survival Curve transform gee K aplan M eier survival curve transform T t statistic regression results 169 TAN function 65 TANH function 66 Tolerance 161 default setting 161 entering 161 201 reducing 222 satisfying 181 182 TOTAL function 66 71 74 Transform components 6 9 Index scalars amp ranges 18 20 user defined functions 6 variables 19 20 Transform components scalars and ranges gee also transform operators 18 Transform components variables see also transform operators relational operators 19 Transform examples 11 14 71 140 analysis of variance table 71 73 anova table 71 73 bivariate statistics 74 75 coefficient of determ
15. 3 Parameter Sigmoid 4 Parameter Sigma 5 Parameter Hew Logistic 3 Parameter Logistic 4 Parameter Edit Code Weibull 4 Parameter Lr eer APARA EN ga ey ey ee x Hep Cancel Back Next Einish 142 The Regression Wizard Feature Highlights Introduction To The Regression Wizard T he Regression W izard offers notable improvements over the previous SigmaPlot curve fitters T hese include gt A built in Equation Library that can be extended limitlessly with your own user defined functions and libraries Graphical display of built in equations Graphical selection of variables from worksheets or graphs Automatic parameter estimation for widely varied datasets Automatic plotting of results Automatic generation of textual reports Inclusion of fit equations into notebooks VVVVY y T he Regression W izard is also one hundred percent compatible with older FIT files as described below Opening FIT Files Adding FIT Files to a Library or Notebook Use the File menu O pen command to open old curve fit FIT files selecting SigmaPlot Curve Fit as the file type FIT files are opened as a single equation in a notebook FIT files can also be opened from the library panel of the Regression W izard You can add these equations to other notebooks by copying and pasting To add them to your regression library open the library notebook STAN D ARD JFL for SigmaPlot s built in libr
16. Bivariate statistics transform 74 75 BLOCK function 32 Fast Fourier transform 94 BLOCKHEIGHT function 32 BLOCKWIDTH function 32 C Cancelling aregession 162 CELL function 33 CHOOSE function 34 Coefficient of determination stepwise regression results 163 168 Coefficient of determination R2 transform 82 83 Coefficient of variation parameters 164 207 214 217 Coefficients regression results 168 COL function 21 34 Color smooth color transition transform 127 129 Comments entering regression 188 Completion status messages regression results 181 182 COM PLEX function 35 Components s transform components 6 9 Computing derivatives 87 93 Confidence interval linear regressions 113 116 regression results 174 301 Index Constant variance test regression results 172 Constraints parameter badly formed 182 defining 158 entering 156 158 199 200 208 209 viewing 164 Constructor notation example of use 71 regression example 196 square bracket 8 Convergence 145 Cook s D istance test results 173 Correlation coefficient regression results 163 168 COS function 35 COSH function 36 COUNT function 36 71 Curly brackets 5 Curve fitter functions 25 introduction 144 Curve fitting pitfalls 219 240 Curves coefficient of determination 82 83 curves of constant damping and natural frequency 137 140 Kaplan M eier survival curve transform 129 131 transform for integrating under a curve 73 74
17. If fis omitted no smoothing is used For x 0 1 2 y 0 1 4 the operation col 1 x75 x y 3 places the x atypin ne as 2 00 into column 1 X25 x50 xatymax xwtr T he xatymax function returns the x value at the maximum y value found with optional Lowess smoothing xatymax x range y range f T hex range argument specifies the x variable and the y range argument specifies the y variable Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must have the same size and the number of valid data points must be greater than or equal to 3 T he optional f argument defines the amount of Lowess smoothing and corresponds to the fraction of data points used for each regression f must be greater than or equal to 0 and less than or equal to 1 0 lt f lt 1 If fis not defined no smoothing is used If duplicate y maximums are found xatymax will return the average value of all the x at y maximums 68 Transform Function Descriptions OT ee Example Related Functions xwtr summary syntax Example Related Functions Transform Function Reference For x 0 1 2 y 0 1 4 the operation col 1 xatymax x y places the x at the y maximum as 2 00 into column 1 x25 X50 x75 xwtr T he xwtr function returns value of x75 x25 in the ranges of coordinates provided with optional Lowess smoothing xwtr x range y range f
18. and then click Stop Recording TheM acro Recorder stops recording and the M acro O ptions dialog box appears Hacro Options Name OF Create 2D Graphs ok e Cancel Description SigmaPlot macro script Help E Assign To I Command Name Create 2D Graphs Menu Name My Macrog saved In C Program Files SPY 6 SigmaPlot Macro Libr Type a name for the macro in the N ame text box Give the macro a descriptive name You can use a combination of upper and lowercase letters numbers and underscores For example a macro that formats all of your graph legends to match a certain report might be called ReoortlAddFormatT oLegend Enter a more detailed description in the D escription text box Click OK After you have finished recording the macro save it globally for use in all of Sig maPlot or locally for use in a particular notebook file Figure 12 3 Macros associated with notebooks appear in the notebook Double click a macro icon to open the Macros dialog box Creating Macros as Menu Commands Figure 12 4 Macros Dialog Box Automating Routine Tasks W hen you return to the N otebook window your macro appears in the N otebook E SigmaP lot Macro Library jnb OF 5 u Section 1 Open Survival Worksheet z 2 Survival Curve Maco ies a a Section 2 nit Grouped Column Avera u Section 3 ummary ang Vector Plat B You can place your macro as a menu command on th
19. col 4 alpha col 2 col 1 theta must occur as shown T he second equation depends on the data produced by the first Reversing the order produces different results To avoid this sequence problem assign variables to the results of the computation then equate the variables to columns x col 4 y x alpha z y theta col 1 y col 2 z T he sequence of the equations is now unimportant Transform Syntax and Structure 5 Using Transforms Transform Components Variables Functions Constructs Operators Numbers 6 Transform Components Transform equations consist of variables and functions O perators are used to define variables or apply functions to scalars and ranges A scalar is a single worksheet cell number missing value or text string A range is a worksheet column or group of scalars You can define variables for use in other equations within a transform Variable definition uses the following form variable expression Variable names must begin with a letter after that they can include any letter or number or the underscore character _ Variable names are case sensitive an A is not the equivalent of an a O nce a variable has been defined by means of an expression that variable cannot be redefined within the same transform A function is similar to a variable except that it refers to a general expression not a specific one and thus requires arguments T he syntax for a functi
20. fied numbers T he factorial function returns the factorial for each specified number The mod function returns the modulus or remainder of division for specified numerators and divisors T heln function returns the natural logarithm for the specified numbers T he log function returns the base 10 logarithm for the specified numbers T he sqrt function returns the square root for the specified numbers Range Functions The following functions give information on ranges eum a E e PEE E EE count function returns the number of numeric values in a range T he missing function returns the number of missing values and text strings in a range Transform Function Descriptions 23 Transform Function Reference T he size function returns the number of data pointsin a range including all numbers missing values and text strings Accumulation Functions he accumulation functions return values equal to the accumulated operation of the function T he diff function returns the differences of the numbers in a range T he sum function returns the cumulative sum of a range of numbers T he total function returns the value of the total sum of a range Random Generation Thetwo random number generating functions can be used to create a series of Functions normally or uniformly distributed numbers gaussian T he gaussian function is used to generate a series of nor mally Gaussian or bell shaped dis
21. is satisfied N ote that this result may still be false caused by a local minimum in the sum of squares Converged zero parameter changes T he changes in all parameters between the last two iterations are less than the computer s precision D id not converge exceeded maximum number of iterations M ore iterations were required to satisfy the convergence criteria Select M ore Iterations to continue for the Same number of iterations or increase the number of iterations specified in the O ptions dialog box and rerun the regression D id not converge inner loop failure T here are two nested iterative loops in the M arquardt algorithm T his diagnostic occurs after 50 sequential iterations in the inner loop T he use of constraints may cause this to happen due to alack of convergence In some cases the parameter values obtained with constraints are still valid in the sense that they result in good estimates of the regression parameters Terminated by user You pressed Esc or selected the C ancel button and terminated the regression process Function overflow using initial parameter values T he regression iteration process could not get started since the first function evaluation resulted in a math error For example if you used f sqrt axx and the initial a value and all x values are positive amath error occurs Examine your equation parameter values and independent variable values and make the appropriate changes Parameters
22. like this sigmoidal fit but unlike a linear fit have CV values that are not absolutely correct H owever they still can be used to compare the relative variability of parameters For example b 3 9 is more than eight times as variable as c 0 45 N one of the dependencies shown in the last column are close to 1 0 suggesting that the model is not over parameterized 214 Lesson 2 Sigmoidal Function Fit Regression Lessons 5 To save the regression results and graph the curve click Finish A report along with worksheet data and a fitted curve are added to your notebook worksheet and graph Figure 10 18 T r l z Thane Carve torthe B Tutorial 2 Graph Tutonal 2 Worksheet Sigmoidal Data Catoid Sinus Reflex Response E amp g E p u f Fitting with A Morethan a single regression can be run and plotted on a graph Typically this is Different Equation doneto gauge the effects of changes to parameter values or to compare the effect of a different fit equation In this case try a five parameter logistic function instead of the four parameter version 1 PressF5 The Regression W izard appears Select Sigmoid 5 Parameter as your equation 2 Click Next then click the O ptions button Enter a value of 5 into the Iterations box Lesson 2 Sigmoidal Function Fit 215 Regression Lessons Figure 10 19 The Regression Options dialog box Figure 10 20 Results of the Five Parameter Logistic Equatio
23. second or third order conditions If you have only a few data points you should try different orders to see which one you like the most See the example for the effect of too low an order on the first and second derivatives Graphing Transform Examples 87 Example Transforms 1 end spline segments approach straight lines asymptotically 2 end spline segments approach parabolas asymptotically 3 end spline segments approach cubics asymptotically 7 Moveto the RESULTS heading and enter the first column number for the results cr This column for the beginning of the results block is specified in both transforms 8 Click Run to run the transform W hen it finishes press F10 then open the CBESPLN 2 XFM transform file in the XFM S directory M ake sure that the er variable is identical to the previous value then click Run 9 If you opened the Cubic Spline graph view the page T he first graph plots the original XY data as a scatter plot and the interpolated data as a second line plot by picking the cr column asthe X column and cr l asthe Y column T he sec ond graph plots the derivatives as line plots using the cr column versus the cr 2 column and the cr column versus the cr 3 column 10 To create your own graphs using SigmaPlot create a Scatter Plot using a Simple Scatter style which plots the original data in columns 1 and 2 as XY pairs Add an additional Line Plot using a Simple Spline Curve then plot the cr column as the
24. straight linefor X2 1 f If x lt 1 constant x line x constant x C line x a bxx You can enter and define up to 25 parameters but a large number of parameters will slow down the regression process You can determine if you are using too many parameters by examining the parameter dependencies of your regression results D ependencies near 1 0 0 999 for example indicate that the equation is overparameterized and that you can probably remove one or more dependent Equations 193 Editing Code parameters For more information on parameter dependencies see Interpreting Initial Results on page 163 Defining the Fit The mos general form of the fit statement is Statement fit f to y with weight w f identifies the predicted dependent variable to be fit to the data in the set of equations as defined by the model y isthe observed dependent variable later defined in the Variables section whose value is generally determined from a worksheet column w isthe optional weight variable also defined in the Variables section Any valid variable name can be used in place of f y and w If the optional weighting variable is not used the fit statement has the form fit f to y Defining Constants Constants are simply defined by setting one of the parameters of the equation model to a value using the form constant value For example one commonly used constant is pi defined as 01 3 14159265359 Defining Alternate F
25. tae ce Six Parameter Triple Exponential Decay i y ae e 00 Seven Parameter Triple Exponential Decay K y y tae ce ge Modified Three Parameter Single Exponential Decay C7 y ae 290 Regression Equation Library Exponential Linear Combination y y tae x Exponential Rise to Two Parameter Single Exponential Rise to Maximum Maximum y a 1 e Three Parameter Single Exponential Rise to Maximum y yy a 1 e s Four Parameter Double Exponential Rise to Maximum y a 1 e 1 6 Five Parameter Double Exponential Rise to Maximum yay tale iae Two Parameter Simple Exponent Rise to Maximum y a 1 b s Three Parameter Simple Exponent Rise to Maximum y y a 1 b s 291 G Regression Equation Library Exponential Growth One Parameter Single Exponential Growth y e Two Parameter Single Exponential Growth y ae Three Parameter Single Exponential Growth b yY Yo a Four Parameter Double Exponential Growth bx d y ae e Five Parameter Double Exponential Growth y yg tae c Modified One Parameter Single Exponential Growth Modified Two Parameter Single Exponential Growth J Aa m 292 ee Regression Equation
26. 0 of a Simplified Lorentzian Distribution Figure 11 2 The Regression Options dialog box Showing Step Size Set to 0 00001 220 Curve Fitting Pitfalls To find Xo the curve fitter computes the sum of squares function 3 F yl i l as a function of the parameter Xo T he graph of this result using the x and y data is provided in Figure 11 1 T he curve fitter then searches this parameter space for any Xg value where a relative minimum exists T he sum of squares for X has two minima an absolute minimum at xp 0 and a relative minimum at Xp 4 03 and a maximum at 2 5 As the curve fitter searches for a minimum it may stumble upon the local minimum and return an incorrect result If you start exactly at a maximum the curve fitter may also remain there Sum of Squares False convergence caused by a small step size Click the O ptions button N ote that the value of x0 is set to 1000 and the Step Size option is set to 0 000001 Regression Options Initial Parameters Parameter Constraints Values fiona Parameters Constants i Iterations fioo Step Size 0 000001 Tolerance n 000 Fit With weight none k Advanced Regression Examples Click OK then click N ext Using the large initial value of X and a small step size the curve fitter takes one small step finds that there is no change in the sum of squares using the default value for tolerance 0 000
27. 227 228 solving equations 232 233 weighted regression 225 227 Regression functions multiple function regression 234 237 Regression results ANOVA table 169 coefficients 168 confidence interval 174 confidence interval for the regression 174 constant variance test 172 constants 168 Cook s Distance test 173 DFFITS 174 diagnostics 172 D urbin W atson statistic 171 F statistic 170 influence diagnostics 173 leverage 173 normality test 171 P value 169 170 309 Index power 172 predicted values 174 PRESS statistic 171 standard error 169 standard error of the estimate 168 statistics 168 sum of squares 169 t statistic 169 Regression statements bad or missing 182 containing unknown function 183 editing 222 entering 205 209 unknown variable 183 Regression Wizard 142 143 147 cancelling a regression 162 constraints 156 158 creating new equations 152 default results 151 equation options 155 finish button 151 fit with weight 158 interpreting initial results 163 introduction 141 145 iterations 159 multiple independent variables 154 opening FIT files 143 parameters 156 running regression from anotebook 151 saving equation changes 162 Selecting data 147 Selecting equations 147 Selecting variables 148 Setting graph options 150 Setting results options 149 step size 160 tolerance 161 using 147 175 variable options 154 viewing and editing code 153 viewing Initial results 149 watching t
28. 4 Parameter D ouble Exponential D ecay 290 5 Parameter D ouble 291 292 5 Parameter D ouble Exponential D ecay 290 6 Parameter T riple Exponential D ecay 290 7 Parameter T riple Exponential D ecay 290 Exponential Linear Combination 291 M odified 1 Parameter Single 292 M odified 2 Parameter Simple Exponent 293 M odified 2 Parameter Single 292 M odified 3 Parameter Single Exponential D ecay 290 Stirling M odel 293 Exponential Growth 292 Exponential Riseto M aximum 291 H yperbola 293 2 Parameter H yperbolic D ecay 294 2 Parameter Rectangular H yperbola 293 3 Parameter H yperbolal 293 3 Parameter H yperbolic D ecay 294 3 Parameter Rectangular H yperbolal 293 4 Parameter D ouble Rectangular H yperbola 294 5 Parameter D ouble Rectangular H yperbola 294 M odified H yperbola 294 M odified H yperbolall 294 M odified H yperbola III 294 Logarithm 299 2 Parameter 299 2 Parameter 299 2 Parameter 300 2nd Order 300 3rd Order 300 Peak 286 3 Parameter Gaussian 286 3 Parameter Log N ormal 287 3 Parameter Lorentzian 286 3 Parameter M odified Gaussian 286 4 Parameter Gaussian 286 4 Parameter Log N ormal 287 4 Parameter Lorentzian 286 4 Parameter M odified Gaussian 286 4 Parameter Pseudo V oigt 287 4 Parameter W eibul 287 5 Parameter Pseudo V oigt 287 5 Parameter W elbul 287 Polynomials 285 Cubic 285 Inverse 2nd Order 285 Inverse 3rd Order 286 Inverse First O rder 285 Linear 285 Quadratic 285 Power 296 2 Parameter 296 3 Parameter
29. 8 0 Programming Guide Copyright 2002 by SPSS Inc All rights reserved Printed in the United States of America No part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording or otherwise without the prior written permission of the publisher 1234567890 05 04 03 02 01 00 ISBN 1 56827 233 2 Contents MOUCH ON sarae E E E outed nota uit it cuiieatess 1 Tans TONIS siea E O E OR 1 FOC FOS SIONS nrsumsdisn dans mumeiedheromedade A tonya btdnet saesad neste snchleat 1 AUOMAUON sasusssarr isc aitevauceyetay a Meataadcnest 2 USING UhAnSIONMNS siise EEE SN ENA 3 Using the Transform Dialog BOX vsce eeeiic akin eee oe 3 Transform Syntax and Structure s ssesensenensnrnssrnsnrnnsnennrrrrnrnenrnnrnsnennnrnnsrnnnernrnsennnnnnnt 4 Transtorm Component arsana A 6 Tra sioim TUONA ircccsniano aa O 11 Stanna a WGN SIONNY aridan mipien a A i aar a 11 Saving and Executing Transform S onricuroi nan n hele a 14 Graphing the Transform Results s ssssnnseennrssennrssnrrrssnnrnsnnnrrsnnnrsnnrrrssnrrnssnrrrssnrrnsnna 14 Recoding Exam pie orasuri a a a eur dl hcl Waal 15 Transform ODEratOi S cedure 17 ORGS Ol OD SIAN o sssneroimepnison ra e aaae 17 Operations on Ranges scscrcsonssuneinen ton o a enn a a a 18 PAVING Operators annann a E R 19 Relational Operators cessi iaaa Ea N a iE a 19 Logical OD CFALONS srine r E E T 20 Transf
30. DIFFEQN XFM Yi dt dy T Ves 1 T56Y gt 65 075 lg5 Y1 P5gV2 P5793 dy GE 175 1 s57 3 dy T lg5Y1 Data Transform Examples 77 Example Transforms YAR SOlUCLOM Of Coupled Frrse Order Ditrerentiaal x Equations by Fourth Order Runge Kutta Method wees NUMDST OF Hewett obs en Enter the number of differential equations negn the number of differential equations less than or equal to 4 neqn 4 number of differential equations SEKAR Differential Bove ton Sees xx Set the functions fpl fp2 fp3 fp4 to be equal to coupled first order ordinary differential equations where x is the independent variable and yl y2 y3 and y4 are the dependent variables The number of equations must be equal to the negn value set above T neqn lt 4 then use zeros 0 for the unused equations LPL ay LEY rY Sra S OSTE lotro os Myr oo Vy ZFS TOZ XYL YZ Vo 74 LOo Vl 1564 72 PRO Ae Vly V2 rY oe Vo SS Eory IAr Tay fp4 x yl y2 y3 y4 r85 yl KERET R TTEA Value SEREEN Enter the maximum number of integration steps nstep nstep 25 number of integration steps Enter the initial and final x values followed by the initial values of yl and y2 y3 and y4 if they are used If neqn lt 4 then use zeros 0 for the unused initial yi values x0 0 initial x x1 1 final x cell 2 1 100 yl initia
31. Graph command or select the Graph W izard from the toolbar C reate a Line Plot with a Simple Straight Line style plotting your original data versus row numbers by choosing Single Y data format If you set the frequency sampling value fs to nonzero create a Line Plot with a Simple Straight Line style graphing columns 2 and 3 using XY Pair data format O therwise create a Line Plot with a Simple Straight Line style plotting column 3 power spectral density versus row num bers by choosing Single Y data format T he power spectral density plot of the signal f t shows two major peaks at the two frequencies of the sine waves 10cps and 100cps and a more or less con stant noise level in between Graphing Transform Examples 95 Example Transforms For more information on how to create graphs in SigmaPlot see the SigmaPlot U s s M anual Figure 6 5 5 Power Spectral Density Example Graph ER xe E a 0 The top graph shows f t data E generated by the sum of two ii i sine waves plus Gaussian i random noise The bottom graph is the power spectral 2 l density of the signal f t 0 100 200 300 400 500 X Axis gt 1e 6 e 1e4 5 0b Q T 1e 4 4 F 1e 3 Qa 09 1e 2 7 5 lt 1e 1 4 NN 1e 0 0 50 100 150 200 250 Frequency cps The Power Spectral This transform computes the power spectral density Density Transform psd Of data in column ci and places It PO
32. If x 1 0 0 75 3 1 and y 1 2 2 1 1 1 the operation complex x y returns 1 0 0 75 3 1 1 2 2 1 1 1 fft invfft real imaginary mulcpx invcpx T his function returns ranges consisting of the cosine of each value in the argument given This and other trigonometric functions can take values in radians degrees or grads This is determined by the Trigonometric U nits selected in the U ser D efined Transform dialog box Transform Function Descriptions 35 Transform Function Reference syntax Example Related Functions cosh summary syntax Example Related Functions count summary syntax cos number s T he numbers argument can be a scalar or range If you regularly use values outside of the usual 27 to 27 or equivalent range use the mod function to prevent loss of precision Any missing value or text string contained within a range is ignored and returned as the string or missing value If you choose D egrees as your Trigonometric Units in the U ser D efined Transform dialog box the operation cos 0 60 90 120 180 returns values of 1 0 5 0 0 5 1 acos asin atan sin tan T his function returns the hyperbolic cosine of the specified argument cosh numbers T he numbers argument can be a scalar or range Like the circular trig functions this function also accepts numbers in degrees radians or grads depending on the units selected in the U ser D efined Transform dialo
33. Library Stirling Model bx p y yore n Two Parameter Simple Exponent y ab Three Parameter Simple Exponent yY Yo ab Modified Two Parameter Simple Exponent J y Yo loga a Hyperbola Two Parameter Rectangular Hyperbola _aX o b X Three Parameter Rectangular Hyperbola aX o y T tx Three Parameter Rectangular Hyperbola Il ax x y bD x 293 Regression Equation Library Four Parameter Double Rectangular Hyperbola ee cere X X Five Parameter Double Rectangular Hyperbola a Two Parameter Hyperbolic Decay y Oh T b x d x _ ab yb x Three Parameter Hyperbolic Decay y oe T Modified Hyperbola Modified Hyperbola Il a p a av Modified Hyperbola III y og Qim 1 cx 294 Waveform Regression Equation Library Three Parameter Sine WA y asin 2m c Four Parameter Sine Three Parameter Sine Squared WM e Four Parameter Sine Squared MN veeg Four Parameter Damped Sine Five Parameter Damped Sine x Www y y ae ge c Modified Sine y asin b 295 Regression Equation Library Modified Sine Squared MU veee Modified Damped Sine ye ae an aca Power Two Parameter ral _
34. M anual Vector Transform VECTOR PLOT TRANSFORM VECTOR XFM Given a field of vector x y positions angles and lengths in four columns this transform will generate six columns of data that can be plotted to display the original data as vectors with arrow heads The input data is located in columns xc to xct3 with x y in columns xc and xct l vector angles a COLUMMm Xet and vector Lengths T column Xet The results are placed in columns xc 4 to xct9 To generate the vector plot make a Line Plot with Multiple Straight Lines using XYpairs of these columns xc t4 vs xc 5 xc t6 vs XxC 7 0 KOFO VS Rot This transform may be used in conjunction with the MESH XFM transform which generates x y pairs and corresponding z values pi 314159265359 Graphing Transform Examples 135 S E Example Transforms T KKKKKKKKKKKK Input KKKKKKKKKKKK xc 1 column for start of data block L 1 length of arrow head Angle pi 6 angle of arrow head radians T KKKKKKKKKK Constant Vector Length KKAKKKKKKKK To specify a constant vector length uncomment the two lines below and specify the vector length 1 5 length of vector used only for constant length vectors Uncomment the two statements below to use this value to specify vectors with constant length l This will overwrite any data in column xct3 nm size col xc col xc 3 data l 1 nm T KAKAKKKKKKKKKK Results KKKKKKKKKKK
35. Plot Object Plot properties and methods are mainly used to return the Plot child objects Return specific Plot child objects using different Plot properties gt Linereturns the Line plot object Symbols returns the Symbol plot object Fill returns the Solid plot object e g bars D ropLines returns a collection of the drop line Line objects Functions returns collection of the Function objects e g regression and reference lines VVVY Use ChildO bjects 0 to return the Tuple GraphO bjects collection Tuples represent the individual plot curves M any Plot attributes and attribute values can only be returned or set using the G eAttribute and SetAttribute methods Use the Plot Attribute constants to specify these attributes Axes GraphObjects T he Axes collection corresponds to all the sets of axes available for a graph Collection To use the Axes Collection Use the index to return specific x y or z axes from an Axes collection Axis Object TheAxis objects represents a SigmaPlot axis Axes have an O bjectT ype value of 4 or GPT AXIS To use the Axis Object An axis has several Line and Text objects associated with it including the axis line itself grid lines tick marks and labels and the axis title Use the LineAttributes property to return the collection of axis lines and the AxisT itles and TickLabelAttributes property to return collection of axis text objects M ost other Axis attributes such as range scale breaks
36. SigmaPlot or you will lose access to the application IsCurrentBrowser Returns whether or not the specified item is the currently selected item in the Entry Property notebook tree T hisis particularly useful when adding new objects to a notebook in s specific notebook location IsCurrentltem Returns whether or not the specified item is the currently selected item T his Property property is particularly useful when used in conjunction with the Currentltem property IsOpen Property A property common to all N otebookltems objects Returns a Boolean indicating whether or not the specified document or section is open O pen and close notebook items using the O pen and Close methods ItemType Property A property common to all N otebookl tems objects Returns an integer denoting the item object type Reportltem SigmasStat Reportlten SigmaP lot es 270 SigmaPlot Properties Keywords Property Left Property Line Property LineAttributes Property Name Property NamedRanges Property NameObject Property SigmaPlot Automation Reference A standard property of notebook files and all N otebookltems objects Sets the K eywords field under the Summary tab of the W indows 95 98 file Properties dialog box N ote that the keywords for notebook items are not currently displayed or used The default keywords used by SigmaPlot notebooks are SigmaPlot and SigmasStat Sets or returns the left coordinate of the application w
37. Solving Nonlinear Equations Advanced Regression Examples 2 Doubleclick the Solving N onlinear Equation and click the Edit Code button Figure 11 26 The Solving Nonlinear Equations Statements Used to Solve Four Parameter Logistic Equation with Known Parameters p4 1 2080 f o1 71 exp p2 4 p3 p4 50 fit F toy Regression Solving Nonlinear Equation Options Iterations fioo Step Size fioo Tolerance 0 000 oo Initial Parameters Constraints Trigonometric Unite f Degrees i Radians f Grads 3 Examine the regression statements N ote that x is a parameter y 0 and the fit equation is modified f p1 1 exp p2 x p3 p4 50 Since you are fitting f to y 0 these statements effectively solve the original problem for x when y 50 T he values for parameters a b c and d were obtained by fitting the four parameter logistic equation to a given set of dose response data 4 Click Run to execute the regression T he parameter solution isthe unknown x For this example x is approximately 149 5 Figure 11 27 The Results the Solving Nonlinear Equations Example Converged zero parameter changes Ror E Req 0 Norm 7 105427358e 15 View Constraints Parameter Value StdErr Cy re Dependencies 1 495e 2 5620e 15 3 758e 15 C O000000 Regression Wizard Help Cancel Back Hert Example 5 Solving Nonlinear Equations 233 Advanced Regression Examples Exa
38. Three Parameter y Yo ax Pareto Function me eee i l y 7 1 xa Three Parameter Symmetric w y a x xg Four Parameter Symmetric w y E 296 Regression Equation Library Modified Two Parameter ee Modified Two Parameter ee ee y a 1 x lt Modified Pareto lt lI m m m o f gt lt lt og Rational One Parameter Rational lt lI x lt l One Parameter Rational 1 ax Two Parameter Rational i a bx Two Parameter Rational Il a y Oo 1 bx 297 Regression Equation Library Three Parameter Rational a _ at bx y 1 cx Three Parameter Rational a y 1 dx b CX Three Parameter Rational III P y a bx C xX Three Parameter Rational IV a X pe eee a b CX Four Parameter Rational KO Five Parameter Rational Six Parameter Rational C 298 a bx 2 1 cx dx 2 a bx cx 2 1 dx ex 2 a bx cx 2 3 14 dx ex fx Regression Equation Library Seven Parameter Rational N y a bx ox dx 1 ex fx 9x Eight Parameter Rational ye a bx cx dx 1 ext fx gx hx Nine Parameter Rational o y a bx cx dx ex 1 FX gx hx ix Ten Parameter Ratio
39. WORKSHEET es 2 725 col res R SQUARE r2 Standard Deviation of Linear Regression Parameters Standard Deviation Regression Transform STDV_REG XFM T his transform computes linear 1st order regression parameter values slope and intercept and their standard deviations using X and Y data sets of equal length To calculate 1st order regression parameters and their standard deviations for XY data points 1 PlacetheX datain column 1 of the worksheet and the Y data in column 2 If your data isin other columns you can specify these columns after you open the STDV_REG XFM transform file You can enter data into an existing worksheet or a new worksheet 2 PressF10 to open the User D efined Transform dialog box then click the O pen button and open the STDV_REG XFM transform filein the XFM S directory If necessary change the x_col y_col and res variables to the correct column numbers 3 Click Run T he results are placed in columns 3 and 4 or in the columns speci fied by the res variable xe TYANSLOrm tO Compute Standard Deviations Of ENRERE Tair ReOOvesS Lom COSCkELeCLeniS Axes eran at Place your x data In x col and y data imn y Col or change the column numbers to suit your data Results are placed in columns res and res 1 xX col 1 column number for x data y_col 2 column number for y data res 3 first results column Xx col x_col Define x values V Coly col Define y values Data
40. a column title for the column argument enclose the column title in quotes block uses the column in the worksheet whose title matches the string Example Thecommand block 5 1 block 1 1 3 24 reverses the sign for the values in the range from cell 1 1 to cell 3 24 and places them in a block beginning in cell 5 1 Related Functions blockheight blockwidth subblock blockheight blockwidth Summary Theblockheight and blockwidth functions return the number of rows or columns respectively of a defined block of cells from the worksheet Syntax blockheight block blockwidth block T he block argument can be a variable defined as a block or a block function statement Example For the statement x block 2 1 12 10 32 Transform Function Descriptions I ee Related Functions cell summary syntax Example 1 Example 2 Related Functions Figure 5 1 Transform Function Reference T he operation cell 1 1 blockheight x places the number 10 in column 1 row 1 of the worksheet T he operation cell 1 2 blockwidth x places the number 11 in column 1 row 2 of the worksheet block subblock T hecell function returns the contents of a cell in the worksheet and can specify a cell destination for transform results cell column row Both column and row arguments must be scalar not ranges To use a column title for the column argument enclose the column title in quotes cell uses the column in the workshe
41. abs x_max x_min density x data x_min X_max dx yl interpolate X1 Y1 x y2 interpolate X2 Y2 x 126 Graphing Transform Examples ke Example Transforms a interpolate x x x for i 1 to size a cell result_x 3 i 2 a i eeLit resu lt x 3 i 1 Cell result_x 3 i cell result onr cell result_y 3 1i 1 y2 1i cell result_y 3 1i end for Smooth Color Transition Transform T his transform example creates a smooth color transition corresponding to the changes across a range of values T he transform places color cells in a worksheet column that change from a specified start color to a specified end color each color cell incrementing an equivalent shade for each data value in the range T his transform example shows how the color transform can be set to display a cool blue color that corresponds to small residuals and a hot red color that corresponds to large residuals resulting from a nonlinear regression Since residuals vary positively and negatively about zero the absolute values for the residuals are used in the transform y It is unnecessary to sort the data before executing the smooth color transition transform To calculate and graph the smooth color transition of a set of data you can either use the provided sample data and graph or begin a new notebook enter your own data and create your own graph using the data 1 To usethe sample worksheet and graph open the S
42. argument is returned If the condition argument contains a range the result is anew range For Transform Function Descriptions 43 Transform Function Reference each true entry in the condition range the corresponding entry in the true value argument is returned For a false entry in the condition range the corresponding entry in false value is returned If the false value is omitted and the condition entry is false the corresponding entry in the true value range is omitted T his can be used to conditionally extract data from a range Example 1 Theoperation col 2 if col 1 lt 75 FAIL PASS reads in the values from column 1 and places the word FAIL in column 2 if the column 1 value is less than 75 and the word PASS if the value is 75 or greater Example 2 For the operation y if x lt 2 or x gt 4 99 x an x value less than 2 or greater than 4 returns a y value of 99 and all other x values return a y value equal to the corresponding x value If you set x 1 2 3 4 5 then y is returned as 99 2 3 4 99 T he condition was true for the first and last x range entries so 99 was returned T he condition was false for x 2 3 and 4 so the x value was returned for the second third and fourth x values if then else summary Theif then else function proceeds along one of two possible series of calculations based on a specified condition Syntax if condition then tatenent atment else t
43. be used to calculate averages of worksheet data across rows rather than within columns aVvg X1 X Qe SAL V2 AZT Z20S T hex yz and z are corresponding numbers within ranges Any missing value or text string contained within a range returns the string or missing value as the result Transform Function Descriptions 31 Transform Function Reference Example Theoperation avo 1 2 3 3 4 5 returns 2 3 4 1 from the first range is averaged with 3 from the second range 2 is averaged with 4 and 3 is averaged with 5 The result is returned as a range Related Functions mean block summary Theblock function returns a block of cells from the worksheet using a range specified by the upper left and lower right cell row and column coordinates Syntax block column 1 row 1 column 2 row 2 Thecolumn 1 and row 1 arguments are the coordinates for the upper left cell of the block the column 2 and row 2 arguments are the coordinates for the lower right cell of the block All values within this range are returned O perations performed on a block always return a block If column 2 and row 2 areomitted then the last row and or column is assumed to be the last row and column of the data in the worksheet If you are equating a block to another block then the last row and or column is assumed to be the last row and column of the equated block see the following example All column and row arguments must be scalar not ranges To use
44. by clicking the Column 1 17 968 0e 12 BT Sa column in the 18 7 090e 12 0 24 PO on worksheet OO J Oo O71 Be Co Po 6 Createtwo more line plots of rows 13 23 and 24 34 T he results plots should appear as three separate curves Figure 11 31 F Multiple Function Graph Multiple Function Worksheet A SigmaPlot Graph of the Predicted Results of the Multiple Function Equation 236 Example 6 Multiple Function Nonlinear Regression Advanced Regression Examples Example 7 Advanced Nonlinear Regression Overparameterized Equations Consider the function dxX b cx f 1 e X a W hen fitted to the data in columns 1 and 2 in the Advanced Techniques worksheet this equation presents several problems gt Parameter identifiability gt Very large x values gt Very large y error value range T hese problems are outlined and solved below If you want to view the regression functions for this equation open the Advanced Techniques worksheet and graph in the Advanced Techniques section of the NONLIN JNB notebook Double click the Advanced Techniques Equation to open the Regression W izard If you want to run the equation use the graph of the transformed data T he equation has four parameters a b c and d The numerator in the exponential dx b cx can have identical values for an infinite number of possible parameter combinations For example the parameter values b c landd
45. can specify these columns after you open the U SER AXIS XFM file Press F10 to open the User D efined Transform dialog box then open the USERAXIS XFM transform If necessary change the y_col tick_col and res variables to the correct column numbers Click Run T he results are placed in columns 4 and 5 or the columns specified by the res variable If you opened the U ser D efined Axis Scale graph view the page T he graph is already set up to plot the data and grid lines To plot the transformed Y data using SigmaPlot plot column 1 as the X values versus column 4 as the Y values To plot the Y axis tick marks open the Ticks panel under the Axes tab of the Graph Properties dialog box Select Column 5 from the M ajor Tick Intervals drop down list To draw the tick labels usethe Y tick interval data as the tick label source by selecting Column 3 from the Tick Label Type drop down list in the Tick Labels panel under the Axes tab of the Graph Properties dialog box For more information on creating graphs and modifying tick marks and tick labels see the SigmaPlot U s s M anual 132 Graphing Transform Examples Figure 6 20 User Defined Axis Scale Graph User Defined Axis Scale Transform USERAXIS XFM Example Transforms PLATELET DEPOSITION 5 u TEFLON 5 0 2 10 0 2 20 0 30 0 90 0 95 0 96 0 97 0 98 0 DEPOSITION MAXIMUM 99 0 99 5
46. col res 9 w2_y omega 2 y coordinates 140 Graphing Transform Examples Introduction To The Regression Wizard T his chapter describes gt An overview of regression gt TheRegression W izard see page 142 gt Opening FIT files see page 143 gt TheM arquardt Levenberg curve fitting algorithm see page 145 Regression Overview What is Regression Regression is most often used by scientists and engineers to visualize and plot the curve that best describes the shape and behavior of their data Regression procedures find an association between independent and dependent variables that when graphed on a Cartesian coordinate system produces a straight line plane or curve T his is also commonly known as curve fitting T he independent variables are the known or predictor variables T hese are most often your X axis values W hen the independent variables are varied they result in corresponding values for the dependent or response variables most often assigned to the Y axis Regression finds the equation that most closely describes or fits the actual data using the values of one or more independent variables to predict the value of a dependent variable T he resulting equation can then be plotted over the original data to produce a curve that fits the data Regression Overview 141 Introduction To The Regression Wizard The Regression Wizard Figure 7 1 Selecting an Equation from the Regression
47. column 2 30 Transform Function Descriptions ee Related Functions area Summary Syntax Example Related Functions avg Summary Syntax Transform Function Reference cos sin tan arccos arcsin T he area function returns the area of a simple polygon T he outline of the polygon is formed by the xy pairs specified in an x range and a y range T helist of points does not need to be closed If the las xy pair does not equal the first xy pair the polygon is closed from the last xy pair to the first T he area function only works with simple non overlapping polygons If line segments in the polygon cross the overlapping portion is considered a negative area and results are unpredictable area x range y range T he x range argument contains the x coordinates and the y range argument contains the x coordinates Corresponding values in these ranges form xy pairs If the ranges are uneven in size excess x or y points are ignored For the ranges x 0 1 1 0 and y 0 0 1 1 the operation area x y returns a value of 1 TheX and Y coordinates provided describe a square of 1 unit dist T he avg function averages the numbers across corresponding ranges instead of within ranges T he resulting range is the row wise average of the range arguments Unlike the mean function avg returns a range not a scalar T he avg function calculates the arithmetic mean defined as n x y x i 1 T he avg function can
48. column titles collection object To use the DataTable Object The D ataT able objects is returned from N ativeWorksheetltem Excelltem and Graphitem objects using the D ataT able method and in turn accesses data using the G amp D ata and PutD ata methods and the Cell property NamedDataRanges TheNamedD ataR anges collection contains all ranges in the D ataT able object that Collection Object have been assigned aname Column and row titles are name ranges To use the NamedDataRanges Collection The N amedD ataR anges collection is mainly used to retrieve existing ranges and add new ranges to D ataT able objects within N ativeW orksheetltem and Graphitem objects NamedDataRange Represents named data range objects e g column and row titles in the worksheet Object and page data tables To use the NamedDataRange Object T he N amedD ataR ange object is returned from the N amedR anges collection using an index or the Item property T he N amedR ange object properties are mainly the range name dimensions and other similar attributes Graphltem Object TheGraphitem object represents a SigmaPlot graph page Graphitem properties can be used to return a collection of the graphs on the page using the GraphO bjects property It can also be used to create graphs using the CreateW izardG raph method To use the Graphitem Object T he Graphitem object has the standard notebook item properties and methods A Graphitem is returned from the N otebookl
49. containsthe X data column 2 contains the Y data for the signal and the noise distortion column 3 contains the X data and column 4 contains the Y data for the original signal T he top graph plots the signal plus the noise distortion the bottom graph plots the signal 2 To us your own data place your data in columns 1 through 2 If your data isin other columns specify the new columns after you open the LOW PASS XFM transform file If necessary specify a new column for the results 3 PressF10 to open the User D efined Transform dialog box then click the O pen button and open LOW PASS XFM transform file in the XFM S directory The Low Pass Filter transform appears in the edit window y To use this transform make sure Insert mode is turned off 4 Click Run T he results are placed starting in column 5 unless you specified a different column in the transform 5 If you opened the Low Pass Smoothing graph view the graph page Two graphs appear T he top graph plots the signal plus the noise distortion using a Line Plot with a Simple Straight Line style and XY Pairs data format graphing col umn 1 asthe X data column 2 asthe Y data for the signal and the noise distor tion T he bottom graph displays two plots A Scatter Plot with a Simple Scatter Style and XY Pairs data format plots column 3 as the X data and column 4 as theY data for the original signal A second Line Plot with a Simple Straight Line style using data in columns 1 a
50. date If the axis range of you graph is manual convert it back to automatic Select the axis then open the Graph Properties dialog box and change the range to Auto matic Click you curve and run your regression W hen you are finished you must con vert the original and fitted curve x variable columns back to dates Select each column then choose the Format menu Cells command and choose D ate and Time then click OK Format Date and Time Cells S ample Apr AJB Show Date Only Cancel Help W hen the columns are converted back to dates the graph should rescale and you have completed your date and time curve fit Curve Fitting Date And Time Data 179 Regression Wizard Figure 8 35 The Data and Fitted Curve X ee Variables Converted Back to E 1 5 3 4 2 01 15 00 Apr sa 3 01 30 00 Apr 01 97 4 01 45 00 April 497 R nA A Soret sa ann Apr 01 Fa Fi B Graph Paw 1 Dala 17 Off x pr 019r z Apr0197 Apr 0197 April eo Reported Cases 4 180 Curve Fitting Date And Time Data Regression Wizard Regression Results Messages Completion status Messages W hen the initial results of a regression are displayed a message about the completion Status appears Explanations of the different messages are found below C onverged tolerance satisfied T his message appears when the convergence criterion which compares the relative change in the norm to the specified tolerance
51. different filename The last transform you entered opened or imported always appears in the edit window when you open the User D efined Transform dialog box To permanently save a transform you must use the Save or Save As options Transform Syntax and Structure Transform Syntax Entering Transforms Figure 2 2 Typing Equations into the Edit Window Use standard syntax and equations when defining user defined transforms in SigmaP lot or SigmaStat T his section discusses the basics and the details for entering transform equations Transforms are entered as equations with the results placed to the left of the equal sign and the calculation placed to the right of the equal sign Results can be defined as either variables which can be used in other equations or asthe worksheet column or cells where results are to be placed To type an equation in the transform edit box click in the edit box and begin typing W hen you complete a line press Enter to move the cursor to the first position on the next line i User Defined Transform untitled Edit Transform x 1 2 5 4 5 6 7 6 9 10 Run y x 1 3 5 Close z col 3 1 3 5 _ Lose New Open Save Save a Trigonometric Units i Degrees Radians Grads 4 Transform Syntax and Structure 2 Commenting on Equations Sequence of Expression Using Transforms You can leave spaces between equation elements x a b is the same as
52. edit box T his defines the constraint y gt 0 which forces the y intercept to be positive Parameter Constraints oo K K yO gt Of Cancel Help Figure 10 6 Adding a Parameter Constraint Option to the Regression Options Regression Options Initial Parameters Valles dialog box Automatic Parameters asdutomatic Constants Options Iterations fioo Step Size fioo Tal Jo 000700 Fit With Weight none k D 3 Click OK then click N ext to refit the data with a straight line this time subject to the constraint yp gt 0 W hen the initial results are displayed the value for y is now about 9 3 x 10 very close to zero and the slope has slightly decreased to a value of approximately 0 98 it Se Regression Wizard of the Second Fit Converged tolerance satisfied Reqr 0 926546 746 Hom 1 074836147 Value ShdE tr CY Dependencies yO 9252e9 6 508e 1 7 U34e 9 0 8181818 a 9 836e 1 1 962e 1 1 995e 1 0 81581818 xl Hep _ Cancel Back Next Finish 4 Select Constraints the C onstraints dialog box appears with the constraint y0 gt 0 flagged with the label active indicating that it was used in the nonlinear regression 208 Lesson 1 Linear Curve Fit ee Regression Lessons Pa tae The Constraints dialog box yO gt O active N ote that nonlinear regressions may find parameters that satisfy the constraints without having to activate som
53. edit window Click Run T he results are placed in column 3 of the worksheet or in the col umn specified by the ouput variable Graphing Transform Examples 119 Example Transforms 5 If you opened the Lowess Smoothing graph view the graph page T he smoothed curve is plotted on the second graph and both the orginal and smoothed data are plotted on the third If you want to plot your own results create a line plot of column 1 versus col umn 3 For more information of creating graphs see the SigmaPlot U r s M anual LOWESS XFM Lowess Smoothing Example x col CL y col 2 C O eZ EEKKRAERR GOST East eK KS Col 3 oueouL PA OR ROD OC elie Ae output lowess x y f Normalized Histogram T his simple transform creates a histogram normalized to unit area T he resulting data can be graphed as a bar chart H istogram bar locations are shifted to be placed over the histogram box locations T he resulting bar chart is an approximation to a probability density function see Figure 6 16 on page 123 To calculate and graph a normalized histogram sample you can either use the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 To usethe provided sample data and graph open the N ormalized H istogram worksheet and graph in the N ormalized H istogram and Graph section of the Transform Examples notebook T he worksheet appears with data in co
54. else if iend 3 then dx12 cell1 cx 3 cell cx 2 cell cr5 1 dx11 dx12 dx11 2 dx12 dx12 cell ere 1 dx12 dxI2 dx1t i dxITyydx1z dx2n cell1l cx nm1 cell cx nm2 cell cr4 nm2 dx2n dx2n dxln dxin dx2n cell cr5 nm2 dxln dx2n dx1ln 2 dx2n dx2n end if end if solve the tridiagonal system rarest reduce for j 2 to nm2 do Bia eal Cell tera 4 ce ll er4 J 7 ce Liters mL cell cr5 j cell cr5 j3 cell cr4 j cell cr6 jm1 Cell er7 Geller n cela ter4 7 cell er em end for next back substitute cell cr7 nml cell er7 nm2 cell ers nm2 for k nm2 1 to 1 step 1 do cell cr7 k 1 cell cr7 k cell cr6 k 90 Graphing Transform Examples OT ee Example Transforms cell cr7 k 2 cell cr5 k end for specify the end conditions if iend 1 then linear ends cell cr7 1 0 0 cell cr7 7 n 0 0 else if iend 2 then quadratic ends cell cr7 1 cell cr7 2 cell cr7 n cell cr7 nml1 else if iend 3 then cubic ends cell cr7 1 dx11 qdx12 cell cr7 2 daki receler 43I 7d cell cr7 n dx2n dx1in cell cr7 nm1 dxin cell cr7 nm2 dx2n end if end if end if compute coefficients of cubic polynomial for m 1 to nmi do mpl m 1 h cell cx mp1 cell cx m eel er4 m c elltery mol cell crT m oth Sata cell cr5 m cell cr7 m 2 b i cell cr6 m cell gy mpl cell cym h 24n cell er7 m ta cel ery mp 76 FECL
55. example of the possible effects of different tolerance values see Curve Fitting Pitfalls on page 219 D ecreasing the value of the tolerance makes the requirement for finding an acceptable solution more strict increasing the tolerance relaxes this requirement T he default tolerance setting is 0 0001 To change the tolerance value type the desired value in the Tolerance edit box or select a previously defined value from the drop down list For more details on the use of changing tolerance see Tolerance on page 201 Equation Options 161 Regression Wizard saving Regression Equation Changes W hen an equation is edited using the O ptions or Regression dialogs or when you add an equation all changes are updated to the equation in the library or notebook H owever just like other notebook items these changes are not saved to the file until the notebook is saved Changes made to regression libraries are automatically saved when the Regression W izard is closed You can also save changes to regression libraries using the Save or Save As buttons in the Regression W izard T his saves the current regression library notebook to disk Save As allows you to save the regression library to a new file If you have a regression library open as a notebook you can also save changes by saving the notebook using the File menu Save or Save As command Watching The Fit Progress Figure 8 19 The Regression Fit Progress Dialog Bo
56. fall in the first histogram interval values from gt first bucket to lt second bucket fall in the second interval etc T he buckets range must be strictly increasing in value An additional interval is defined to catch any value which does not fall into the defined ranges The number of values occurring in this extra interval including 0 or no values outside the range becomes the last entry of the range produced by histogram function For col 1 1 20 30 35 40 50 60 the operation col 2 histogram col 1 3 places the range 2 3 2 in column 2 T he bucket intervals are automatically set to 20 40 and 60 so that two of the values in column 1 fall under 20 three fall under 40 and two fall under 60 For buckets 25 50 75 the operation col 3 histogram col 1 buckets places 2 4 1 0 in col 3 Two of the values in column 1 fall under 25 four fall under 50 one under 75 and no values fall outside the range The if function either selects one of two values based on a specified condition or proceeds along a series of calculations bases on a specified condition if condition true value false value T he true value and false value arguments can be any scalar or range For atrue condition the true value is returned for a false condition the false value is returned If the false value argument is omitted a false condition returns a missing value If the condition argument is scalar then the entire true value or false value
57. function 42 Graphs transform results 14 H H anning window 94 HISTOGRAM function 42 111 120 H istogram transforms HISTOGRAM function 42 111 120 histogram with Gaussian distribution 111 113 normalized histogram transform 120 122 H omoscedasticity gee also constant variance test 172 IF function 43 71 logical operators 20 IF THEN ELSE function 44 IMAGINARY function 45 IMG function 45 Independent variables entering 190 198 s also variables Influence diagnostics regression results 173 Influential point tests 173 INT function 45 Integrating under curve transform 73 74 see also trapezoidal rule transform INTERPOLATE function 46 Interpreting results regression 163 166 214 Introduction Automation 2 transforms and regression 1 2 INV function 46 INVCPX function 47 INVFFT function 47 Iterations 145 entering 159 160 201 exceed maximum numbers 181 more iterations 181 K K aplan M eier survival curve transform 129 131 Kernel smoothing Fast Fourier transform 97 L Least squares regression 225 Leverage test regression results 173 Line plot curve shading pattern transform 122 124 Linear regression comparing with linear regression results 211 comparing with nonlinear regression results 211 Linear regression dialog 205 211 parameter values transform 83 84 Standard deviation 83 84 with confidence and prediction intervals transform 113 116 LN function 48 Local maximum sum of squares 22
58. function strips the real values from a complex block of numbers Syntax real range T he range argument consists of complex numbers Example If x complex 1 2 3 9 10 0 0 0 the operation real x returns 1 2 3 4 5 6 7 8 9 10 leaving the imaginary values out Related Functions fft invfft imaginary complex mulcpx invcpx rgbcolor Summary Thetransform function rgbcolor takes arguments r g and b between 0 and 255 and returns the corresponding color to cells in the worksheet T his function can be used to apply custom colors to any element of a graph or plot that can use colors chosen from a worksheet column Syntax rgbcolor r g b T her g b arguments define the red green and blue intensity portions of the color T hese values must be scalars between 0 and 255 Numbers for the arguments less than 0 or greater than 255 are truncated to these values Examples Theoperation rgbcolor 255 0 0 returns red T he operation rgbcolor 0 255 0 returns green T he operation rgbcolor 0 0 255 returns blue T he following statements place the secondary colors yellow magenta and cyan into rows 1 2 and 3 into column 1 cell 1 1 rgbcolor 255 255 0 cell 1 2 rgbcolor 255 0 255 cell 1 3 rgbcolor 0 255 255 Shades of gray are generated using equal arguments To place black gray and white in the first three rows of column 1 cell 1 1 rgbcolor 0 0 0 cell 1 2 rgbcolor 127 127 127 cell 1 3 rgbcolor 255 25
59. in the Symbols Fill Color drop down list in the Plots panel of the Graph Properties dialog box The Smooth Color Transition transform applies gradually changing colors to each of the data points T he smaller residual values are colored blue which gradually changes to red for the larger residuals H Smooth Color Transition Graph Smooth Color Transition 6 To create your own graph using SigmaPlot make a Scatter Plot graph with a Scatter Plot with Simple Scatter style Plot the data as Single Y data format Use the color cells produced by the transform by selecting the corresponding work sheet column from the Symbol Fill Color drop down list For more information on how to create graphs in SigmaPlot see the SigmaPlot U s s M anual Smooth Color Transition Transform RGBCOLOR XFM Smooth Color Shade Transition from a Data Column This transform creates a column of colors which change smoothly from a user defined initial intensity to a final intensity as the data changes from its minimum value to its maximum value 128 Graphing Transform Examples OT ee Example Transforms w Tap te Cie ak 2 cdata input colu nmn co 3 Colom COuLpUc Column sr 0 initial red intensity sg 50 initial green intensity Sb 255 initial blue intensity DE ZOO final red intensity fg 50 final green intensity fb 0 final blue intensity Program ad max col ci min col c2i range i
60. into a block of 9 columns Starting at ico umn er Colmmm Cr MUST be specified identically in both transforms Columns cr to cr 3 contain the x mesh the spline and the first two derivatives Columns cr 4 to crt7 contain the a b c and d spline coefficients Column cr 8 is for working variables cr 3 Ist column of results block KAKAKKKKKKKKKK PROGRAM KKKKKKKKKKKEK cr4 cr 4 column for a spline coefficients Cro Cr o column for b spline coefficients Cro er 6 column for c spline coefficients ETICE column for d spline coefficients cr8 crt 8 working column n size col cx cell cr8 1 cx cell cr8 2 cy cell cr8 3 cr cell cr8 4 xbegin Graphing Transform Examples 89 Example Transforms cell cr8 5 xend cell cr8 6 xstep compute S for n 2 rows nml n 1 nm2 n 2 cell cr8 7 cell cx 2 cell cx 1 ie bail cell cr8 8 cell cy 2 cell cy 1 cell cr8 7 6 dyl for i l to nm2 do dx2 cell cx i 2 cell cx i 1 dx2 dy2 cell cy i 2 cell cy i 1 dx2 6 dy2 Gall cr4 i cell cr8 7 dx1 cell cr5 i 2 cell cr8 7 dx2 2 dx1 dx2 cell cr6 i dx2 dx2 cell cr7 1 dy2 cell cr8 8 dy2 dy1 cell cr8 7 dx2 dxl dx2 cell cr8 8 dy2 dyl dy2 end for adjust first and last rows for end condition dx1 11 cell cx 2 cell cx 1 dxln cell cx n cell cx nml1 if iend 2 then cell cr5 1 cell cr5 1 dx11 cell cr5 nm2 cell cr5 nm2 dx1n
61. may not be valid Array ill conditioned on final iteration D uring the regression iteration process the inverse of an array the product of the transpose of the Jacobian matrix with itself is required Sometimes this array is nearly singular has a nearly zero determinant for which very poor parameter estimates would be obtained SigmaPlot uses an estimate of the condition of the array ill conditioned means nearly singular to generate this message see D ongarra J J Bunch J R M oler C B and Stewart G W Linpack U se s Guide SIAM Philadelphia 1979 for the computation of condition numbers Usually this message should be taken seriously as something is usually very wrong For example if an exponential underflow has occurred for all x values part of the equation is essentially eliminated SigmaPlot still tries to estimate the parameters associated with this phantom part of the equation which can result in invalid parameter estimates Regression Results Messages 181 Regression Wizard Error Status Messages A minority of the time the correct though poorly conditioned parameters are obtained T his situation may occur for example when fitting polynomial or other linear equations Parameters may not be valid Array numerically singular on final iteration T hisisa variant of the above condition Instead of using the condition number the inverted array is multiplied by the original array and the resulting
62. new equation 12 Starting a Transform Transform Tutorial 8 Press Enter then type y t T his variable declaration uses the function f and variable t declared in the previous equations 9 Add afew spaces then type put y into col 3 T his places the results of the preceding equation which defines y in column 3 of the worksheet N ote that you can also collapse the last two lines into one equation col 3 f t Click Run If you have entered all the transform equations correctly the data will appear as shown in Figure 3 2 Figure 3 2 The Data Generated by the Transform Tutorial ss osso ooo o zoj gO 550 9900 OO 0 O71 Be Oo Pa a a E r i oo a 14 aa o eo SiS 15 Woo 80 16 oo ee ee z P Starting a Transform 13 Transform Tutorial saving and Executing Transforms After entering the transform equations save the transform to afile then run the transform 1 Click Save and specify a file name and destination for the file T he default extension for transform filesis XFM Saved transforms can be opened with the Transform dialog box O pen button 2 Click Run If you have entered all the transform equations correctly you should generate the data shown in Figure 3 2 Graphing the Transform Results O nce the transform is executed and the results are placed in the worksheet you then treat the results like any other worksheet data 1
63. objects have a number of line and text objects that are returned with Axis object properties T heAxisT itle property is used to return the collection of axis title Text objects for the specified Axis Use the following index values to return the different titles N ote the specific title returned depends on the current axis dimension direction selected oO Bottom Left axis title a Right Top axis title 2o Sub axis title not currently shown B Sub axis title not currently shown Returns or sets the value of a cell with the specified column and row coordinates for the current D ataTable object U sed by all page objects that contain different sub objects to return the collection of those objects TheChildO bjects property returns different type of objects depending on the object type Object Returns ChildObjects Group including Autolegends all group objects Gets or sets the color for all drawn page objects Use the different color constants for the standard VGA color set For more information refer to SigmaPlot Automation from the SigmaPlot H elp menu SigmaPlot Properties 267 SigmaPlot Automation Reference Comments Property Syntax N otebook N otebookltems object C omments A standard property of notebook files and all N otebookltems objects Returns or sets the D escription field in the Summary Information for all notebook items or the Comments section under the Summary tab of the W indows 95 98 file Properti
64. of the dependent variable and the values predicted by the regression model D F Degrees of Freedom D egrees of freedom represent the number of observations and variables in the regression equation Interpreting Regression Reports 169 Regression Wizard gt Theregression degrees of freedom is a measure of the number of independent variables gt Theresidual degrees of freedom is a measure of the number of observations less the number of parameters in the equation M S Mean Square T he mean square provides two estimates of the population variances Comparing these variance estimates is the basis of analysis of variance T he mean square regression is a measure of the variation of the regression from the mean of the dependent variable or sum of squares due to regression _ SS reg MS regression degrees of freedom DF i reg T he residual mean square is a measure of the variation of the residuals about the regression plane or _ residual sum of squares _ SSe _ yc residual degrees of freedom D Fre i l 2 The residual mean square is also equal to Sy ix F statistic TheF test statistic gauges the contribution of the independent variables in predicting the dependent variable It is the ratio regression variation from the dependent variable mean _ M rey _ residual variation about the regression MS res If F isalargenumber you can conclude that the independent variables contribute to the prediction of the dep
65. or range of values consisting of the base 10 logarithm of each number in the specified range log numbers T henumbers argument can be a scalar or range of numbers Any missing value or text string contained within a range is ignored and returned as the string or missing value For log x X lt 0 returns an error message X 0 returns co T he largest value allowed is approximately x lt 104933 T he operation log 100 returns a value of 2 48 Transform Function Descriptions lookup summary syntax Transform Function Reference The lookup function compares values with a specified table of boundaries and returns either a corresponding index from a one dimensional table or a corresponding value from a two dimensional table lookup numbersx table y table T henumbers argument is the range of values looked up in the specified x table T hex table argument consists of the upper bounds inclusive of the x intervals within the table and must be ascending in value T he lower bounds are the values of the previous numbers In the table ce for the first interval You must specify numbers and an x table If only the numbers and x table arguments are specified the lookup function returns an index number corresponding to the x table interval the interval from lt o to the first boundary corresponds to an index of 1 the second to 2 etc If anumber value is larger than the last entry in x table lookup will return a mis
66. regression equation 190 Entering Regression Equation Settings Figure 9 6 Entering the Variable Definitions Automatic Initial Parameter Estimation Functions Entering Initial Parameters Editing Code Regression untitled Options Iterations fioo Step Size fioo Tolerance fo oo01 Oo Initial Parameters Constraints Trigonometric Units Degrees i Radians Grads Example To define x and y as the variables for the equation code f n xto fit f to y you could enter the code x col 1 y col 2 which defines an x variable as column 1 and ay variable as column 2 using these columns whenever the regression is run directly from the code Any user defined functions you plan on using to compute initial parameter estimates must be entered into the Variables section For more information on how to code initial parameter estimate function see Automatic Determination of Initial Parameters on page 202 Parameters are the equation coefficients and offset constants that you are trying to estimate in your equation model T he definitions or functions entered into the Parameters sections determine which variables are used as parameters in your equation model and also their initial values for the curve fitter T he curve fitter checks the parameter equations for errors and for consistency with the regression equations To enter initial parameter values 1 Click in the Initial Parameters s
67. specific sets of your data Using the Transform Dialog Box To begin atransform choose the Transforms menu User D efined Transform command or press F10 T he User D efined Transform dialog box appears Figure 2 1 ae re Tha Us r Delined User Defined Transform untitled Transform Dialog Box Edit Transform Trigonometric Units i Degrees Radians Grads Creating a Transform T hefirst step to transform worksheet data is to enter the desired equations in the edit box If no previously entered transform equations exist the edit box is empty otherwise the last transform entered appears Select the edit box to begin entering transform instructions As you enter text into the transform edit box the box scrolls down to accommodate additional lines Up to 100 lines of equations can be entered Equations can be entered on separate lines or on the same line Using the Transform Dialog Box 3 Using Transforms Transform Files Once you have completed the transform you can run it by clicking Run Transforms can be saved as independent transform files T he default extension is XFM Transform files are plain text files that can also be edited with any word processing program Use the N ew O pen Save and Save As options in the U ser D efined Transform dialog box to begin new transforms open existing transforms save the contents of the current edit box to a transform file and save an existing transform file to a
68. to the correct column number Click Run T he results are placed in columns 11 through 20 or the columns specified by the res variable If you opened the Z Plane graph view the page T he circle frequency trajectory and damping trajectory data is automatically plotted with the design data To plot the circle data using SigmaPlot create M ultiple Line Plots with Simple Spline Curves For the first plot use column 11 asthe X values versus column 12 as the Y values To plot the frequency trajectory data zeta plot column 13 ver sus column 14 and column 15 versus column 16 as the XY pairs To plot the damping trajectory data omega plot column 17 versus column 18 and column 19 versus column 20 as the XY pairs For more information on creating graphs in SigmaPlot see the SigmaPlot U s s M anual Root Locus for Compensated Antenna Design 138 Graphing Transform Examples ee Z Plane Transform ZPLANE XFM Example Transforms mxx A Transform Lor Z Plane Design Curves 7 This transform generates the data for a unit circle and curves of constant damping ratio and natural frequency See Digital Control of Dynamic Systems GeF BPrankiin Ds Powell Doe 32y 104 Root locus zero and pole data is loaded from an external source res 11 TAERE EREA CACCULATE DATA FOR UNLI CMR icky AIKA ee ae pi 3 1415926 n 50 theta data 0 2 pix 1 1 n pi n circ_x cos theta circle x coordinates cir
69. transform for shading pattern under line plot curves 122 124 z plane design curve transform 137 140 D D ata format options Regression Wizard 154 DATA function 11 37 84 D ata manipulation functions 22 D ata menu user defined 15 16 D ebug Window 253 Defining variables 11 D egrees of freedom regression results 169 D ependencies exponential equation 229 parameter 164 208 214 229 231 D ependent variables entering 190 198 s als variables D erivatives 302 computation 87 93 D escriptions of transform functions 22 66 DFFITS test regression results 174 Diagnostics influence 173 regression results 172 Dialog Box Editor 251 DIFF function 38 73 Differential equation solving 76 80 DIST function 38 Distance functions 25 DSN IP function 38 D urbin W atson test regression results 171 E Editing equations 153 macro code 250 macros 245 250 Editing Code 185 203 Entering constraints parameter 156 158 199 200 208 209 equations regression 189 190 iterations 159 160 201 options 200 202 parameters 198 199 regression comments 188 regression equation settings 188 192 regression statements 189 190 205 209 step size 160 201 tolerance 161 201 transforms 3 4 11 13 variables 190 198 Equation solving 232 233 Equations editing 153 overparameterized 237 saving 192 Equations regression entering 189 190 entering settings 188 192 examples 285 300 executing
70. using poorly chosen initial parameter values 224 Curve Fitting Pitfalls Advanced Regression Examples Example 2 Weighted Regression T he data obtained from the lung washout of intravenously injected dissolved Xenon 133 is graphed in the Weighted Graph in the Weighted Regression section of the NONLIN JN B notebook 1 Open the Weighted worksheet and graph by double clicking the graph page icon in the Weighted section of the NONLIN JNB notebook The data in the graph displays the compartmental behavior of Xenon in the body T hree behaviors are seen the wash in from the blood rapid rise the washout from the lung rapid decrease and the recirculation of Xenon shunted past the lung slow decrease Figure 11 12 The Weighted Graph Weighted Graph Weighted Worksheet Mil E Time sec o T he sum of three exponentials a triple exponential is used as a compartmental model l t W a e 2t 4 qe ts CountRate aje Least squares curve fitting assumes that the standard deviations of all data points are equal H owever the standard deviation for radioactive decay data increases with the count rate Radioactive decay data is characterized by a Poisson random process for which the mean and the variance are equal Weighting must be used to account for the non uniform variability in the data T hese weights are the reciprocal of the variance of the data For a Poisson process the variance equals the mean Y
71. variables constraints and other options used To edit the code for an equation you need to either open and edit an existing equation or create a new equation All built in equations provided in STAN DARD JFL have protected portions of code which can be viewed and copied but not edited H owever you may use Add As to create a duplicate entry that can be edited and you can also copy a built in equation from the library to another notebook or section and edit it For information on opening and editing SigmaPlot 3 0 and earlier FIT files see O pening FIT Files on page 143 About Regression Equations 185 Editing Code Opening an Existing You can open an equation by Equation Figure 9 1 Opening an Equation from a Notebook Creating a New Equation gt doubleclicking an equation icon in a notebook window or selecting the equation then clicking O pen gt starting the Regression W izard then selecting the equation by category and name Nonlin jnb OR x AT Regression Examples t C Tutorial 1 t C Tutorial 2 z S i Curve Fiting Pitfalls Summan E Pitfalls Worksheet m ili Pitfalls Graph se SUM of Squares Help Pee Sed Lorentzian Summary Info d nkhar i Weighted Regression Equation Category Select the equation to fit vour data Save g 3 Curve Fiting Pitfalls Equation Mame save 4s Mew Edit Code el i g iy Regression Wizard i
72. worksheet on which you ran the regression Check the Add Equa tion to N otebook option to save a copy of your equation Click N ext to proceed Lesson 1 Linear Curve Fit 209 Regression Lessons Graphing Results 8 To plot the regression function on the existing graph make sure the Add curve to Graph 1 option is checked Figure 10 10 The Graph Results Regression Wizard D tt Panel Add the fitted curve to the current graph ea Create new graph Extend fit to axes 9 Click Finish display your report and graphed results Figure 10 11 z Regression Results for a Times New Roman fo Linear Soe Es Ee Regression R 09459 Reqr 0 493 Adj Regr 0 8597 otandard Error of Estimate 0 4206 Coefficient Sid Error t P yi 0 0000 0 6508 0 0000 1 0000 a 0 9836 0 1962 50123 0 0133 Analysis of Variance DF zE Ms F F Regression 1 eals geals 22 3044 0 0150 Residual 4 1 1333 0 383 Total 4 10 9768 2 442 PRESS 3 6136 Durbin Vatson Statistic 1 1777 Normality Test Passed P 0 728 Constant Variance Test Passed P 0 05 210 Lesson 1 Linear Curve Fit Comparing Regression Wizard Results with Linear Regression Results Figure 10 12 Selecting a Linear Regression Figure 10 13 Comparing the Fitted Curve with a First Order Regression Regression Lessons T he original data for this graph could have been fitted automatically in SigmaPlot with a linear regression using the Stati
73. x values in range T he function takes one of two forms T he first form has two arguments both of which are ranges Values in the first range are the independent variable values T he second range represents the coefficients of the polynomial with the constant coefficient listed first and the highest order coefficient listed last T he second form accepts two or more arguments T he first argument is a range consisting of the independent variable values All successive arguments are scalar and reoresent the coefficients of a polynomial with the constant coefficient listed first and the highest order coefficient listed last Transform Function Descriptions 55 Transform Function Reference Syntax polynomial range coefficents or polynomial rangea0 al an T he range argument must be a single range indicated with the brackets or a worksheet column Text strings contained within a range are returned as a missing value T he coefficients argument is a range consisting of the polynomial coefficient values from lowest to highest Alternately the coefficients can be listed individually as scalars Example To solvethepolynomialy x2 x 1 for x values of 0 1 and 2 type the equation polynomial 0 1 2 1 1 1 Alternately you could set x 1 1 1 then enter polynomial 0 1 2 x Both operations return a range of 1 3 7 prec Summary Theprec function rounds a number or range of numbers to the specified number of signific
74. 1 and declares the tolerance condition is satisfied The very low slope in the sum of squares at this large x value causes the regression to stop Figure 1 1 3 Regression Wizard The Results Using a Step Size of 0 00001 Converged tolerance satisfied a Fsg 0 Norm 0 868156234 Vien Constraint Parameter Value StdErr Cwi Dependencies xO 9 645e 2 3 05de 3 102e 6 0 0000000 xl Help Cancel Back Next Finish 5 False convergence caused by a large step size and tolerance Click Back then click the O ptions button O pen the Step Size list and select 100 this is the default step size value Figure 11 4 Regression Options Selecting a Step Size of 100 eae Parmele CONSTANS ox Initial Parameters Values i O00 Cancel Parameters Constants Iterations fi 00 0 000001 O10 Tolerance Bf h Fit With Weight none 6 Click OK then click N ext The curve fitter takes a large step reaches negative Xo values and finds a value x 546 for which the tolerance is satisfied ite Sea Regression Wizard Using a Step Size of 100 Converged tolerance satisfied me Reg 0 Norm 0 691525 2 View Constraints Parameter Value StdErr Cv re Dependencies 0 p 455e 2 3 05de 5 599e 6 0 0000000 E Help Cancel Back E T Finish Curve Fitting Pitfalls 221 Advanced Regression Examples T he sum of squares function asymptotically app
75. 1 area and distance 25 AVG 31 BLOCK 32 94 BLOCKHEIGHT 32 BLOCKWIDTH 32 CELL 33 CHOOSE 34 COL 21 34 COMPLEX 35 COS 35 COSH 36 COUNT 36 71 curve fitting 25 DATA 37 84 data manipulation 22 defining 12 descriptions 22 DIFF 38 73 DIST 38 distance 25 DSINP 38 error 108 110 EXP 39 FACTORIAL 39 Fast Fourier 27 FFT 40 FOR 40 FWHM 41 GAUSSIAN 42 108 110 111 HISTOGRAM 42 111 120 IF 20 43 71 IF THEN ELSE 44 IMAGINARY IMG 45 INT 45 INTERPOLATE 46 INV 46 INVCPX 47 INVFFT 47 LN 48 303 Index LOG 48 logistic 232 233 LOOKUP 49 84 LOWESS 51 LOWPASS 51 MAX 52 113 MEAN 52 71 74 MIN 53 113 miscellaneous 27 MISSING 53 MOD 54 MULCPX 54 NTH 54 numeric 23 PARTDIST 55 Poisson distribution 40 POLYNOMIAL 55 PREC 56 precision 24 PUT INTO 56 RANDOM 57 random number 24 range 23 REAL 58 regression 234 237 RGBCOLOR 58 ROUND 59 RUNAVG 59 SIN 60 SINH 61 SINP 61 SIZE 61 111 SORT 62 special constructs 27 SQRT 63 statistical 25 STDDEV 63 74 STDERR 64 SUBBLOCK 64 SUM 65 TAN 65 TANH 66 TOTAL 66 71 74 trigonometric 23 user defined 6 69 70 worksheet 22 X25 66 X50 67 X75 68 XATYMAX 68 XWTR 69 ge also transforms and transform functions FWHM function 41 304 G GAUSSIAN function 42 108 110 111 Gaussian transform cumulative distribution histogram 111 113 GAUSSIAN function 108 110 111 Gaussian transforms GAUSSIAN
76. 2 and the values b c 2andd 1 result in identical numerator terms T he curve fitter cannot find a unique set of parameters T he parameters are not uniquely identifiable as indicated by the large values for variance inflation factor VIF and dependency values near 1 0 T he solution to this problem is to multiply the d parameter with the other terms to create the equation x db dcx X a f l e then treat the db and dc terms as single parameters T his reduces the number of parameters to three Example 7 Advanced Nonlinear Regression 237 Advanced Regression Examples Scaling Large The data used for the fit has enormous x values around a value of 1 x 104 see Variable Values column 1 in the worksheet above T hese x values appear in the argument of an exponential which is limited to about 700 which is much smaller than 10 H owever when the curve fitter tries to find the parameter values which are multiplied with x it does not try to keep the argument value within 700 Instead when the curve fitter varies the parameters it overflows and underflows the argument range and does not change the parameter values T he solution to this problem is to scale the x variable and redefine some of the parameters M ultiply and divide each x value by 1 x 102 to get 0 ap 4 ote 107 10 24 24 10 x a le al If you let X x 10 2 then the equation becomes Ec o Xelo a f 1 If you let CD 1024dc
77. 214 fit statements 220 iterations 159 160 201 logistic 232 parameters 198 199 regression statements 182 189 190 results 163 166 214 results messages 181 183 running again 164 Saving results 165 166 solving 232 233 step size 160 201 tolerance 161 201 variables 190 198 weight variables 194 Equations transform creating 3 entering 3 4 syntax and structure 4 5 variables 19 20 Error function Gaussian cumulative distribution 108 110 Error status messages regression results 182 183 Examples regression 219 240 regression equations 285 300 transforms 71 140 s also transform examples and regression examples Executing transforms 14 Exiting regression dialog 165 EXP function 39 Exponential equations dependency example 229 F F statistic regression results 170 FACTORIAL function 39 Fast Fourier functions 27 Fast Fourier transform 93 105 BLOCK function 94 gain filter smoothing 102 H anning window 94 kernal smoothing 97 low pass smoothing filter 99 power spectral density 94 FFT function 40 Files XFM 1 transform 4 Filtering Fast Fourier transforms 93 105 gain filter transform 102 low pass 99 Filters smoothing 116 118 Index Fit f to y with weight w 194 Fit statements modifying 220 Fit with weight 158 FOR function 40 Fractional defective control chart transform 84 86 Frequency plot 105 108 Functions ABS 28 accumulation 24 APE 28 ARCCOS 29 ARCSIN 30 ARCTAN 30 AREA 3
78. 296 3 Parameter Symmetric 296 4 Parameter Symmetric 296 M odified 2 Parameter 297 M odified 2 Parameter I1 297 M odified Pareto 297 Pareto Function 296 Rational 297 1 Parameter Rational 297 1 Parameter Rational I 297 10 Parameter Rational 299 11 Parameter Rational 299 2 Parameter Rational 297 2 Parameter Rational 297 3 Parameter Rational 298 3 Parameter Rational 298 3 Parameter Rational 298 3 Parameter Rational IV 298 4 Parameter Rational 298 5 Parameter Rational 298 6 Parameter Rational 298 7 Parameter Rational 299 8 Parameter Rational 299 9 Parameter Rational 299 Index Sigmoidal 288 3 Parameter Chapman M odel 289 3 Parameter Gompertz Growth M odd 289 3 Parameter H ill Function 289 3 Parameter Logistic 288 3 Parameter Sigmoid 288 4 Parameter Chapman M odel 289 4 Parameter Gompertz Growth M oda 289 4 Parameter H ill Function 289 4 Parameter Logistic 288 4 Parameter Sigmoidal 288 4 Parameter W abul 288 5 Parameter Sigmoidal 288 5 Parameter W eibul 288 Waveform 295 3 Parameter Sine 295 3 Parameter Sine Squared 295 4 Parameter D amped Sine 295 4 Parameter Sine 295 4 Parameter Sine Squared 295 5 Parameter D amped Sine 295 M odified D amped Sine 296 M odified Sine 295 M odified Sine Squared 296 Regression examples advanced techniques 237 240 constructor notation 196 dependencies 229 231 Lorentzian distribution 219 224 multiple function 234 237 piecewise continuous model
79. 3 Local minimum finding 222 LOG function 48 Logical operators transforms 20 Logistic function 4 parameter 212 217 5 parameter 217 four parameter 232 233 LOOKUP function 49 84 Lorentzian distribution regression example 219 224 Low pass filter 116 118 Low pass smoothing filter 99 LO WESS function 51 LOWPASS function 51 M M acro Recorder introduction 2 M acro W indow color coded display 248 O bject and Procedure lists 248 setting options 248 M acros Add Procedure D ialog Box 253 adding comments to code 250 D ebug Window 253 Dialog Box Editor 251 editing 245 250 editing code 250 Index modifying 245 250 O bject Browser 252 programming language 249 recording 241 242 running 244 245 user defined functions 251 viewing 245 250 M arquardt Levenberg algorithm 145 160 201 M ath menu transform 3 M AX function 52 113 MEAN function 52 71 74 M ean squares regression results 170 M essages completion status 181 182 error status 182 183 regression results 181 183 regression status 163 M ethods 275 Activate method 276 Add method 276 AddV ariableE xpression method 277 AddW izardAxis method 277 AddW izardPlot method 278 ApplyPagel enplate method 277 Clear method 278 Close method 278 Copy method 279 CreateG raphF romT emplate method 279 CreateW izardG raph method 279 Cut method 279 D elete method 279 D eleteC ells method 279 Execute method 280 Export method 280 GetAttribute method 280 GetD ata
80. 3 5 and 6 8 T he graph plots the raw data and the two curve fits 80 Data Transform Examples ee Example Transforms Figure 6 2 Use of the F Test Comparing Two Curve Fits 0 20 0 18 ae e Log Drug vs Bound bia a a Log Drug vs y fit 1 i Log Drug vs y fit 2 0 14 4 0 12 4 O Cc 3 0104 faa 0 08 0 06 0 04 0 02 0 00 12 11 10 9 8 7 6 5 4 Log Competitor 2 To use your own data enter the XY data to be curve fit in columns 1 and 2 respectively Select the first curve fit equation and use it to fit the data place the parameters fit results and residuals in the first empty columns 3 5 Run the second curve fit and place the results in columns 6 8 the default If desired create graphs of these results using the wizard 3 PressF10 to open the User D efined Transform dialog box then open the F TEST XFM transform file Specify n1 and n2 the number of parameters in the lower and higher order functions In the example provided these are 3 and 5 respectively If necessary specify csl and cs2 the column locations for the residuals of each curve fit and cres the first column for the two column output 4 Click Run TheF test value and corresponding P value are placed into the work Sheet If P lt 0 05 you can predict that the higher order equation provides a sta tistically better fit F test Transform Compare Two Nonlinear Curve Fit
81. 44 gt 0 0037 0 0029 0 0592 0 0618 0 0613 6 0 0045 0 0260 0 5379 0 5389 0 55358 Traditionally you can conclude that the independent variable can be used to predict the dependent variable when P lt 0 05 PRESS the Predicted Residual Error Sum of Squares is a gauge of how well a regression model predicts new data T he smaller the PRESS statistic the better the predictive ability of the model The PRESS statistic is computed by summing the squares of the prediction errors the differences between predicted and observed values for each observation with that point deleted from the computation of the regression equation T he D urbin Watson statistic is a measure of correlation between the residuals If the residuals are not correlated the D urbin Watson statistic will be 2 the more this value differs from 2 the greater the likelihood that the residuals are correlated Regression assumes that the residuals are independent of each other the D urbin Watson test is used to check this assumption If the D urbin Watson value deviates from 2 by more than 0 50 a warning appears in the report i e if the D urbin Watson statistic is below 1 50 or above 2 50 T he normality test results display whether the data passed or failed the test of the assumption that the source population is normally distributed around the regression and the P value calculated by the test All regressions assume a source population to be normally dist
82. 5 255 58 Transform Function Descriptions round summary syntax Examples Related Functions runavg summary syntax Transform Function Reference The round function rounds a number or range of numbers to the specified decimal places of accuracy Values are rounded up or down to the nearest integer values of exactly 0 5 are rounded up round numbers places T he numbers argument can be a scalar or range of numbers Any missing value or text string contained within a range is ignored and returned as the string or missing value If the places argument is negative rounding occurs to the left of the decimal point To round to the nearest whole number use a places argument of 0 T he operation round 92 1541 2 returns a value of 92 15 T he operation round 0 19112 1 returns a value of 0 2 T he operation round 92 1541 2 returns a value of 100 0 int prec T herunavg function produces a range of running averages using a window of a specified size as the size of the range to be averaged T he resulting range is the same length as the argument range runavg range window T he range argument must be a single range indicated with the brackets or a worksheet column Any missing value or text string contained within a range is replaced with 0 If the window argument is even the next highest odd number is used T he tails of the running average are computed by appending window i additional initial an
83. 6 0 0043 0 0307 0 0216 0 10453 0 0954 7 0 0033 0 0200 0 0193 0 1049 0 0942 8 0 0064 0 0293 0 0171 0 1054 0 0931 g 0 0070 0 0290 0 0150 0 1059 0 0919 10 0 0078 0 0287 0 0130 0 1065 0 0909 z T he expected leverage of a data point is E where there are p parameters and n data points Because leverage is calculated using only the dependent variable high leverage points tend to be at the extremes of the independent variables large and small values where small changes in the independent variables can have large effects on the predicted values of the dependent variable DFFITS TheDFFITS statistic isa measure of the influence of a data point on regression prediction It isthe number of estimated standard errors the predicted value for a data point changes when the observed value is removed from the data set before computing the regression coefficients Predicted values that change by more than 2 0 standard errors when the data point is removed are potentially influential If the confidence Interval does not include zero you can conclude that the coefficient is not zero with the level of confidence specified T his can also be described as P lt a aloha where is the acceptable probability of incorrectly concluding that the coefficient is different than zero and the confidence interval is 100 1 q T he confidence level for both intervals is fixed at 95 a 0 05 Row Thisisthe row number of the observation
84. A Notebooks collection is returned using the Application object N otebooks property Use the Add method to add anew notebook to the collection You can return a specific N otedook object using ether the Item property or the collection index Represents a SigmaPlot notebook file including template and equation library files N otebook properties and methods are used to set individual notebook file attributes and specify individual notebook items e g worksheets graph pages reports etc Also used to return acollection of notebook items as objects To use the Notebook Object N otebook objects are returned using the N otebooks or ActiveD ocument Application object properties Access individual notebook items using the N otebookl tems property which returns the N otebookltems collection T his collection represents all the items in a notebook and is used to create new items and open existing items Also used to specify and return the different notebook items as objects Worksheets pages equations reports macros and section and notebook folders are all notebook items and can be returned as objects To use the Notebookitems Collection T he N otebookltems collection is returned using the N otebookl tems property of a N otebook object You can return individual notebook item objects using either the Item method or collection index and add new notebook item objects such as worksheets and graph pages using the Add method T his object re
85. AI CA CUMULATIVE SURVIVAG REKER IS IS mv 0 0 missing value i data l size sur integers N size sur number of cases n N 1 pi N it l cen N i 1 cs 10 sum log pi cumulative survival Calculate standard error of survival se cs sqrt sum cen N i N it1 TATA Re PLACE RESULTS IN WORKSHEET 7 ms A res col res 0 sur col rest 1 1l cs cumulative survival probability col res 2 0 se standard error of survival User Defined Axis Scale TheUSERAXIS XFM transform is a specific example how to transform data to fit the user defined axis scale i 2 Graphing Transform Examples 131 Example Transforms T his transform gt transforms the data using the new axis scale gt creates Y interval data for the new scale 100 To usethis transform to graph data along a log 10g ey Y axis you can either use the provided sample data and graph or begin a new notebook enter your own data and create your own graph using the data I To use the sample worksheet and graph double click the graph page icon in the U ser D efined Axis Scale section of the Transforms Examples notebook T he U ser D efined Axis Scale worksheet appears with data in columns 1 through 3 The graph page appears with an empty graph with gridlines To use your own data place your original X data in column 1 Y data in column 2 and the Y axis tick interval values in column 3 If your data has been placed in other columns you
86. C Simplified Lorentzian Hep Cancel Back Next Finish You can also double click and equation in a notebook while the Regression W izard is open to switch to that equation O ncean equation is opened you can edit it by clicking the Edit C ode button If you require an equation that does not appear in the standard equation library you can create a new equation N ew equations can be created by gt Clicking the N ew button in the Regression W izard gt Choosing File menu N ew command and selecting Regression Equation gt Right clicking in the notebook window and choosing N ew Regression Equation from the shortcut menu A new equation document has no default settings for the equations parameters variables constraints or other options To create a new equation from within the Regression Wizard 1 Open the Regression W izard by pressing F5 or by choosing the Statistics menu Regression W izard command 186 About Regression Equations Figure 9 2 Selecting Regression Equation from the New dialog box Figure 9 3 Creating a New Equation from the Notebook 2 Editing Code Click N ew to create a new equation document T he Regression dialog box appears New Hew OK Regression Equation Cancel Type Regression Equation Help di Description Create a new regression equation and add it to your current section To use the File Menu New Comma
87. Changing the Regression Equation or Variables More Iterations Checking Use of Constraints Figure 8 21 The Constraints Dialog Box CV The parameter coefficients of variation expressed as a percentage are displayed in column four T his is the normalized version of the standard errors CV standard error x 100 parameter value T he coefficient of variation values and standard errors see above can be used asa gauge of the accuracy of the fitted curve Dependency T he last column shows the parameter dependencies T he dependence of a parameter is defined to be depenie She variance of the parameter other parameters constant variance of the parameter other parameters changing Parameters with dependencies near 1 are strongly dependent on one another T his may indicate that the equation s used are too complicated and over parameterized too many parameters are being used and using a model with fewer parameters may be better To go back to any of the previous panels just click Back T his is especially useful if you need to change the model equation used or if you need to modify any of the equation options and try the curve fit again If the maximum number of iterations was reached before convergence or if you canceled the regression the M ore Iterations button is available Click M ore Iterations to continue for as many iterations as specified by the Iterations equation option or until completion of t
88. ChildO bjects property Lines are creating using the Page object Add method with an object value of 6 or GPT LINE Plot lines are returned using the Line property Collections of Lines can also be returned using the D ropLines property To return the collection of axis lines use the Axis object LineAttributes property T hese include the axis lines tick marks grid lines and axis break lines The collection of function lines is returned using the Plot object Functions property Functions include linear regression and reference lines M any Line attributes and attribute values can only be returned or set using the G eAttribute and SetAttribute methods Use the Line Attribute constants to specify these attributes T he symbol object controls the symbols used in a plot Symbols have an O bjectT ype value of amp or GPT SYMBOL To use the Symbols Object T he Symbols object is returned from a Plot object using the Symbols property T he Symbols properties and methods are used to return or modify the individual symbols within the parent plot SigmaPlot Objects and Collections 261 SigmaPlot Automation Reference Solid Object Tuple GraphObjects Collection Tuple Object Function GraphObjects Collection M any Symbol attributes and attribute values can only be returned or set using the G eAttribute and SetAttribute methods Use the Symbol Attribute constants to specify these attributes A solid object can represent many diffe
89. Example Transforms Figure 6 19 Survival Curve Example with Censored Data The Survival Graph 3 tied uncensored values 3 untied censored values wea atn 0 8 2 tied uncensored amp 0 6 lt 2 tied censored values Survival 0 4 i incorrectly placed tied censored data should follow 0 2 uncensored data 0 0 Time months the sort order option as Ascending 6 Check for any ties between true response and censored data If any exist make sure that within the tied data the censored data follows the true response data 7 From the worksheet press F10 to open the U ser D efined Transform dialog box then click the O pen button and open the SU RVIVAL XFM transform in the XFM S directory 8 Click Run to run the file T he sorted time cumulative survival probability and the standard error are placed in columns res res 1 and res 2 respectively For graphical purposes a zero one and zero have been placed in the first rows of the sorted time cumulative survival curve probability and standard error columns 9 If you opened the sample Survival graph view the page T he Simple H orizontal Step Plot graphs the survival curve data from columns res as the X data versus column res l asthe Y data and a Scatter Plot graphs the data from the same col umns T he first data point of the Scatter Plot at 0 1 is not displayed by select ing rows 2 to end in the Portions of Columns Plotted area of t
90. K Column numbers for the vector output These two columns will contain the data that displays the body of each vector body_x xc 4 body_y xc 5 Columns containing the coordinates of the left hand branch of the arrow head left branch x xct 6 left_branch_y xct Columns containing the coordinates of the right hand branch of the arrow head erone pranci ero rignt branch y sets T KAKAKKKKKKKKKK Program KKKKKKKKKKKK x col xc x positions of the vector field Ve Cou Cr y positions of the vector field theta col xct 2 angles of the vectors m abs col xc 3 lengths of the vectors cos theta start_y y m 2 sin theta end _x x m 2 cos theta end_y y t m 2 sin theta Calculate the coordinates of the bodies of the vectors sx data l size end_x 3 col body_x if mod sx 3 1 start_x int sx 3 1 if mod sx 3 2 end_x int sx 3 1 0 0 col body_y if mod sx 3 1 start_y int sx 3 41 if mood sx 3 27 end y ant sx7 3 11 07 03 Calculate the coordinates of the arrow heads for Start x x m 2 the vectors vec_col_size size col body_x for i 1 to vec_col_size step 3 do temp ati c ell body x gt 4 cel body x itl pus 2 136 Graphing Transform Examples Example Transforms arctan t c ll body yyitl cell body yy 7 cell body x 141 cell bodyx 1 Theta at cell body 1 celLl body
91. M 85 86 creating 3 curly brackets 5 dialog 3 4 DIFFEQN XFM 76 77 80 entering 3 4 11 13 examples 11 14 71 140 executing 14 files 4 FREQPLOT XFM 105 108 F TEST XFM 80 81 82 function descriptions 22 66 GAINFILT XFM 102 105 GAUSDIST XFM 109 110 HISTGAUS XFM 111 113 introduction 1 2 LINREGR XFM 113 116 LOWPASS XFM 99 102 LOWPFILT XFM 116 maximum size 3 missing values 7 NORMHIST XFM 120 121 operators 17 20 order of precedence 17 18 overview 1 parentheses 6 plotting results 14 POWSPEC XFM 94 96 97 R2 XFM 82 83 ranges amp scalars 18 20 RGBCOLOR XFM 127 129 saving 4 14 SHADE_1 XFM 122 124 SHADE 2 XFM 122 126 127 SMOOTH XFM 97 99 square brackets 9 STDV_REG XFM 83 84 strings 7 SURVIVAL XFM 130 131 syntax and structure 4 5 tutorial 11 14 user defined 15 16 108 110 131 133 user defined functions 6 using 3 9 312 variables 19 20 VECTOR XFM 134 137 ZPLANE XFM 137 140 s also transform functions and examples 21 T rapezoidal rule transform 73 74 Trigonometric functions 23 T utorial user defined transforms 15 16 T utorials regression 205 217 transform 11 14 U U ser defined differential equations 76 80 F tet 80 82 U ser defined functions 6 69 70 axis scale 131 133 error functions 108 110 saving 70 U ser defined transforms for loops 40 function descriptions 22 tutorial 15 16 vector plots 134 135 V Val
92. N otebookltems Add method T he Fittltem object has an ItemType property and N otebookltems Add method value of 6 The complete list of Fitltem properties and methods also can be found in Fitltem and FitResults Properties and M ethods 264 SigmaPlot Objects and Collections FitResults Object Transformltem Object Reportltem Object Macroltem Object SigmaPlot Automation Reference T he FitR esults object is used to return the different values computed by the nonlinear regression T hese statistics and other results are specifically useful for computing additional statistics that can be derived from these results T he complete list of FitResult properties can also be found In Fitltem and FitResults Properties and M ethods Represents either an open transform or opened transform file as an object You can load transforms specify the transform code and replace variables before executing a transform To use the Transformltem Object The Transformltem object has the standard notebook item properties and methods however transforms cannot be currently saved as notebook objects only created and opened If you want to save a transform to a xfm file use the N ame property to specify a filename and path before using the Save method W hen using a Transfomitem object you must first declare a variable as an object and then define it as a newly added transform item Create a new Transformitem collection using the N otebookl tems Add m
93. NT and JFL Saves a N otebook object to disk using the current FullN ame or a notebook item to the notebook without saving the notebook file to disk If no FullN ame exists for a notebook an error occurs To save a notebook that has not yet been saved you must use the SaveAs method N ote Transform text can be saved to an xfm file by naming the transform first with the full filename extension and path Selects all of the items within the specified selection region In addition if Top equals Bottom and Right equals Left the resulting selection includes the object that the specified point lies within If AddToSelection is False then the previous selection list is replaced by the new list If True then the newly selected items are added to the existing selection list Selects the entire contents of the item Clears the current Graphitem selection list and selects the specified graph object so that it can be altered using the SetSelectedO bjectsAttribute method Line and Solid objects can only be selected if they are top level drawing objects not child objects of other objects T he SetAttribute method is used by all graph page objects to change current attribute settings Attributes are numeric values that also have constants assigned to them For a list of all these attributes and constants see SigmaPlot C onstants M essage Forwarding If you use the SetAttribute method to change an at
94. RROR TOTAL col anova 1 SUM OF SQUARES SSR SSE SSM DEG FREEDOM edof rdof tdof MEAN SQUARE SSR edof SSE rdof col anovat4 F F col anova 7 POINTS R SQUARED R STD ERR col anovati n R2 sqre RZ se col anovat2 Col anovats Area Beneath a Curve Using Trapezoidal Rule T his transform computes the area beneath a curve from X and Y data columns using the trapezoidal rule for unequally spaced X values T he algorithm applies equally well to equally soaced X values T his transform uses an example of the diff function To use the Area Under Curve transform 1 Place your X datain column 1 and your Y data in column 2 If your data has been placed in other columns you can specify these columns after you open the AREA XFM file You can use an existing or new worksheet 2 PressF10 to open the User D efined Transform dialog box then click the O pen button and open the AREA XFM transform file in the XFM S directory The Area transform appears in the edit window 3 Click Run T he area is placed in column 3 or in the column specified with the res variable Area Under TIransform for Calculating Area Beneath a Curve Curve Transform This transform integrates under curves using the AREA XFM trapezoidal rule This can be used for equal or unequally spaced x values The algorithm is sigma i from 0 to n l or Ye ea a E SCD Cae eal SSP ye See ee T P
95. Regression Options x Initial Parameters Parameter Constraints Values b0 automatic d gt O Cancel Parameters Help a tuutomatic Constants Options bs utomatic cs utomatic d 4utomatic Iterations 700 Step Size Jo Tolerance fi e 10 Fit with weight Weight variables must be defined by editing the regression code For information on how to define your own weighting options see Weight Variables on page 197 For a demonstration of weighting variable use see Example 2 Weighted Regression on page 225 T helterations option sets the maximum number of repeated fit attempts before failure Each iteration of the curve fitter is an attempt to find the parameters that best fit the model With each iteration the curve fitter varies the parameter values incrementally and tests the fit of that model to your data W hen the improvement in the fit from one iteration to the next is smaller than the setting determined by the Tolerance option the curve fitter stops and displays the results Regression Options Initial Parameters Parameter Constraints Values f O00 Cancel Parameters Help Constants Options Iterations E i Step Size 100 b Tolerance 0 00m B Fit With Weight none k Changing the number of iterations can be used to speed up or improve the regression process especially if more than the default of 100 iterations are required for a comple
96. Related Functions stddev subblock Summary Thesubblock function returns a block of cells from within another previously defined block of cells from the worksheet T he subblock is defined using the upper left and lower right cells of the subblock relative to the range defined by the source block Syntax subblock block column 1 row 1 column 2 row 2 T he block argument can be a variable defined as a block or a block function statement Thecolumn 1 and row 1 arguments are the relative coordinates for the upper left cell of the subblock with respect to the source block The column 2 and row 2 arguments are the relative coordinates for the lower right cell of the subblock All values within this range are returned O perations performed on a block always return a block If column 2 and row 2 are omitted then the last row and or column is assumed to be the last row and column of the source block All column and row arguments must be scalar not ranges Example For x block 3 1 20 42 the operation subblock x 1 1 1 1 returns cell 3 1 and the operation subblock x 5 5 returns the block from cell 7 5 to cell 20 42 Related Functions block blockheight blockwidth 64 Transform Function Descriptions sum tan Summary Syntax Example Related Functions Summary Syntax Example Related Functions Transform Function Reference T he function sum returns a range of numbers representing the accumulated
97. Select a scatter graph from the graph toolbar and select a simple scatter graph You can also choose the Graph menu Create Graph command select Scatter Plot then click N ext and select Simple Scatter 2 Select XY Pair as the D ata Format then click N ext Select column 1 as your X column and column 3 as your Y column then click Finish A Scatter Plot graph appears T he data in column 1 is plotted along the X axis and the data in column 3 is plotted along the Y axis Figure 3 3 E Graph Page 1 Data 17 Iof x A Graph of Plotting the 20 Graph 1 Transform Tutorial Data as a Scatter Plot 14 Saving and Executing Transforms Transform Tutorial Recoding Example T his example illustrates a simple recoding transform 1 Choose the D ata menu User D efined Transforms command to open the U ser D efined Transform dialog box If desired click Save to save the existing trans form to a file Click N ew to begin a new transform Figure 3 4 i User Defined T form untitled Entering the Recoding ser Detined Transform untitled Transform Example Edit Transform into the User Defined xpi K round random 15 2 0 7 2 Transform Edit Window col 1 x col 2 1 Recoded col 2 2 Variable col 3 iff lt 2 small if x gt 2 and x lt 5 medium large J Trigonometric Units i Degrees Radians Grads 2 Click the upper left corner of the edit window and type x random 15 2 0 7 T his creat
98. SigmaPlot 8 0 Programming Guide For more information about SPSS Science software products please visit our WWW site at http www spss com or contact SPSS Science Marketing Department SPSS Inc 233 South Wacker Drive 11 Floor Chicago IL 60606 6307 Tel 312 651 3000 Fax 312 651 3668 SPSS and SigmaPlot are registered trademarks and the other product names are the trademarks of SPSS Inc for its proprietary computer software No material describing such software may be produced or distributed without the written permission of the owners of the trademark and license rights in the software and the copyrights in the published materials The SOFTWARE and documentation are provided with RESTRICTED RIGHTS Use duplication or disclosure by the Government is subject to restrictions as set forth in subdivision c 1 i1 of The Rights in Technical Data and Computer Software clause at 52 227 7013 Contractor manufacturer is SPSS Inc 233 South Wacker Drive 11 Floor Chicago IL 60606 6307 General notice Other product names mentioned herein are used for identification purposes only and may be trademarks of their respective companies Windows is a registered trademark of Microsoft Corporation ImageStream Graphics amp Presentation Filters copyright 1991 1997 by INSO Corporation All Rights Reserved ImageStream Graphics Filters is a registered trademark and ImageStream is a trademark of INSO Corporation SigmaPlot
99. Stack Tab lists the program lines that called the current Statement This isa macro command audit and is helpful to determine the order of Statements in you program gt gt 254 Using the Debug Window T he first line is the current statement T he second line is the one that called the first and so on Clicking a line brings that macro into a sheet and highlights the line in the edit window sigmaPlot Automation Reference OLE Automation isa technology that lets other applications development tools and macro languages use a program SigmaPlot Automation allows you to integrate SigmaPlot with the applications you have developed It also provides an effective tool to customize or automate frequent tasks you want to perform Automation uses objects to manipulate a program O bjects are the fundamental building block of macros nearly all macro programs involve modifying objects Every item in SigmaPlot graphs worksheets axes tick marks reports notebooks etc can be represented by an object SigmaPlot uses a VBAA like macro language to access automation internally For more information on recording and editing SigmaPlot macros see About M acros T his chapter contains the following topics gt Opening SigmaPlot from M icrosoft Word or Excel on page 255 SigmaPlot O bjects and Collections on page 256 SigmaPlot Properties on page 266 SigmaPlot M ethods on page 275 VV Y Opening SigmaPlot fro
100. The Shade 2 Graph Example Transforms To use your own data to create a graph make a Line Plot with M ultiple Straight Lines plotting the column 1 data against column 2 data for the first curve and column 3 data against column 4 data as the second curve Press F10 to open the User D efined Transform dialog box then click the O pen button and open the SH ADE_2 XFM transform in the XFM S directory If nec essary change the source column numbers to the correct column numbers Set the fill density to use For a solid color between the curves use a large den sity about 500 For a nicely spaced vertical fill try a density of 50 Click Run T he data for the shade lines is placed in columns 5 and 6 or what ever columns were selected If you opened the Shade 2 graph view the graph page T he graph automatically appears with the new plot filling the space between the curves in the original plot If you created your own graph see step 3 and you want to use SigmaPlot to plot the shade between the curves add anew Line and Scatter Plot with M ulti ple Straight Lines to the graph using columns 5 and 6 for the X and Y data and if necessary turn symbols off T he new plot appears as shade between the curves of the original plot For more information on creating graphs in SigmaPlot see the SigmaPlot U s s M anual Y Axis Shading Between Lines Wie
101. Transform Examples 83 Example Transforms ME Ns mee CALCULATE PARAMETER VALUES FAAEA none em n size col x_col n must be gt 2 mx mean x my mean y sumxx total x x sumyy total y y sumxy total x y al sumxy n mx my Sumxx n mx mx slope aQ my al mx intercept WEARS CALCULATE PARAMETER STANDARD DEVIATIONS 2 sregxy if n gt 2 sqrt sumyy n a0 my al sumxy n 2 x0 s0 sregxy sqrt sumxx n Sumxx n mx mx SD a0 sl sregxy sqrt sumxx n mx mx SD al e kk keke KK PLACE RESULTS IN WORKSHEET xx col res n INTERCEPT SLOPE STD DEV INT STD DEV SLOPE col res 1 if n gt 2 n a0 al s0 s1 n lt 2 Graphing Transform Examples T he graph transform examples are provided to show you how transform equations can manipulate and calculate data to create complex graphs Each of the following descriptions provide instructions on how to use SigmaPlot to create graphs M ost of these graphs however are already set up as sample graphs If you use the provided worksheet and graphs with the corresponding transform files SigmaPlot will automatically create the graphs after you run the transform Control Chart for Fractional Defectives with Unequal Sample Sizes T his example computes the fraction of defectives p for a set of unequally sized samples using their corresponding numbers of defects the control limits for p and data for the upper and lower control lines T h
102. Values less than 2 5 or larger than 2 5 may indicate outlying cases 172 Interpreting Regression Reports Figure 8 27 Regression Report Influence Diagnostics Regression Wizard Studentized Residuals T he Studentized residual is a standardized residual that also takes into account the greater confidence of the predicted values of the dependent variable in the middle of the dataset By weighting the values of the residuals of the extreme data points those with the lowest and highest independent variable values the Studentized residual is more sensitive than the standardized residual in detecting outliers T his residual is also Known as the internally Studentized residual because the Standard error of the estimate is computed using all data Studentized D eleted Residuals T he Studentized deleted residual or externally Studentized residual is a Studentized residual which uses the standard error of the estimate Sy x _j computed after deleting the data point associated with the residual T his reflects the greater effect of outlying points by deleting the data point from the variance computation T he Studentized deleted residual is more sensitive than the Studentized residual in detecting outliers snce the Studentized deleted residual results in much larger values for outliers than the Studentized residual Report 2 Jof x Times New Roman fia E z U lel B E Eo e R gag cee Influence Diagnostics E Row C
103. WSPEC XFM 0 cotumn co If a nonzero sampling frequency fs is specified 2 then a frequency axis is placed in column co z with the psd in the next adjacent column 3 If han 1 then a Hanning window is applied to the padded data Set Trigonometric Units to Radians Input ci 1 input column number CO 2 first output column number fs 10 sampling frequency produces frequency axis Saas SO han 1 Hanning window l use 0 don t use Program pi 3 1415926 x1l col ci if han 1 then use Hanning window n size x1 nlog2 log n log 2 pad data if necessary powup int nlog2 96 Graphing Transform Examples TT aaa Example Transforms intupl if nlog2 powup lt le 14 2 powup 2 powupt1 risif mod n 2 gt 0 Aantupl ntipy 2 snbup lan e2 72 Cu Od iy 7 Step kar Lauper i xa Pe Oy ae Care i ae Oy tdata tOr Ue shy l Gater 0 O5eunie las Uys hy eae a Oy OGM yg Se Leys PALO leu SO xL datar Oy O ca cop rukte ALLF w 5 1 cos 2 p1 data 0 intupl 1 iantupl 1 xf w x multiply padded data by window else xf x1 end if tx fft xf tft of data nf size tx 4 half the zero padded data length spec real tx 2 img tx 2 power spectral density spechalf spec data 1 nft l half the symmetric psd data f fs data 0 nft 2 nf frequency axis Output col co if fs gt 0 f spechalf col co 1 1f fs gt 0 spechalf Kernel Smoothing T he example tran
104. Wizard SigmaP lot uses the Regression W izard to perform regression and curve fitting T he Regression W izard provides a step by step guide through the procedures that let you fit the curve of a known function to your data and then automatically plot the curve and produce statistical results T he Regression W izard greatly simplifies curve fitting T here is no need to be familiar with programming or higher mathematics T he large library of built in equations are graphically presented and organized by different categories making selection of your models very straight forward Built in shortcuts let you bypass all but the simplest procedures fitting a curve to your data can be as simple as picking the equation to use then clicking a button T he Regression W izard can be used to gt Select the function describing the shape of your data SigmaPlot provides over 100 built in equations You can also create your own custom regression equations gt Select the variables to fit to the function You can select your variables from either a graph or a worksheet gt Evaluate and save your results Resulting curves can be plotted automatically on a graph and statistical results saved to the worksheet and text reports T hese procedures are described in further detail in the next chapter Regression Wizard Equation Category Select the equation to fit your data Save Sigmoidal r y Equation Name save As Sigmoaid
105. X column against the cr 1 column asthe Y column For more information on creating graphs in SigmaPlot see the SigmaPlot U ser s M anual nue Cubic Spline Interpolation First and Second Derivatives Cubic Spline Graph p P 100 50 x data v y data or interp x v 1st deriv 80 interpxvinterpy f f Jo aa interp x v 2nd deriv 30 60 20 20 88 Graphing Transform Examples Example Transforms Cubic Spline Cubic Spline Interpolation and Computation 1 Transform n xxx x of Derivatives CBESPLN1 XFM l This transform takes an x y data set with increasing ordered x values and computes a cubic spline interpolation The first and second derivatives of the spline are also computed Two transform files are run in sequence This transform computes the spline coefficients The CBESPLN2 XFM transform computes the spline and two derivatives KKAKKKKKKKK Input Variables kkxk xkxkxk kxkxx kxx xx k cx 1 x data column number cy 2 y data column number xbegin 5 first x value for interpolation xend 5 last x value for interpolation xstep 025 x interval for interpolation There are 3 spline end conditions allowed jend 1 linear end conditions tend 2 quadratic end conditions aiend 3 cubic end conditions 1end 1 end condition 1 2 or 3 KKKKKKKEKKKEKHK RESULTS KKKKKKKKKKKHK The results are placed
106. You can return the label for reference lines using the N ameO bject property but only if the label is turned on first N ote that Function lines are turned on or off with Plot object attributes The D ropLines object is a special collection of lines that represent the drop lines for a plot The DropLines object is returned using the Plot object D ropLines property T here are three different sets of drop lines that can be retrieved from the D ropLines collection DropLine property indexes 1 xyplane SLA FLAG DROPZ 3D graphs only 2 Y axis x direction or yz plane SLA_ FLAG DROPX 3 X axis y direction or zx plane SLA FLAG DROPY SigmaPlot Objects and Collections 263 SigmaPlot Automation Reference Group Object AutoLegend Object GraphObject Object Fitltem Object N ote that drop lines are turned on and off using the Plot object SetAttribute method using theSLA PLOTOPTIONS property coupled with theSLA FLAG DROPX SLA FLAG DROPY orSLA FLAG DROPZ value and using the FLAG SET BIT to turn on drop lines or theFLAG CLEAR BIT to turn off drop lines O ther drop line properties are set using Line object attributes A group is any grouped collection of objects generally created with the Format menu Group command Grouped objects can be treated as a single object AutoL egends are a special class of Group object Groups have an O bjectT ype value of 12 or GPT BAG M any Group attributes and attribute values can only be return
107. a and graph or begin anew notebook enter your own data and create your own graph using the data L To use the sample worksheet and graph open the G aussian worksheet and graph by double clicking the graph page icon in the Gaussian section of the Transform Examples notebook D ata appears in column 1 of the worksheet and two empty graphs appear on the graph page To use your own data placethe X datain column 1 If your data has been placed in another column you can specify the column after you open the GAUSDIST XFM transform file Press F10 to open the User D efined Transform dialog box then click the O pen button and open the GAU SDIST XFM transform filein the XFM S directory T he Gaussian Cumulative transform appears in the edit window Click Run T he results are placed in column 2 or in the column specified by the res variable If you opened the sample G aussian graph view the graph page A Line Plot appears with a spline curve in the first graph with column 1 asthe X data versus column 2 as the distribution Y data see Figure 6 10 on page 110 To create your own graph using SigmaPlot make a Line Plot graph with a Sim ple Spline Curve T he spline curve plots column 1 astheX data versus column 2 as the distribution Y data see Figure 6 10 on page 110 For more information on how to create graphs in SigmaPlot see the SigmaPlot U s s M anual Gaussian Cumulative T he probability scale isthe inverse of the Gaussian cu
108. a shade under a curve you can either use the provided Curve with Color sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 To usethe provided sample data and graph open the Shade 1 worksheet and graph by double clicking the graph page icon in the Shade 1 section of the Transform Examples notebook T he worksheet appears with data in columns 1 and 2 The graph page appears with a line graph plotting column 1 against col umn 2 2 To useyour own data enter the XY data for your curve in columns 1 and 2 respectively If your data has been placed in other columns you can specify these columns after you open the SH ADE_1 XFM transform file Enter data into an existing or anew worksheet 3 Create a line graph with two curves using your own data by creating a Line Plot with a Simple Straight Line curve plotting the column 1 data against the column 2 data 122 Graphing Transform Examples Figure 6 16 The Shade 1 Graph Shade Beneath Curve Transform SHADE_1 XFM Example Transforms Press F10 to open the User D efined Transform dialog box then open the SH ADE_1 XFM transform file The Shade 1 transform appears in the edit win dow If necessary change the source column numbers x_data and y_ data to the correct column numbers Click Run T he data for the bar chart is placed in columns 3 and 4 or whatever columns were specified If you opened the sample Shade 1 graph v
109. adians f Grads N ote that the Equations Parameters and Variables are non editable for built in 2 SigmaPlot equations H owever you can edit and save our built in equations as new equations Simply click Add As add the equation to the desired section and then edit the Equations Variables and Parameters as desired You can also copy and paste equations from notebook to notebook like any other notebook item Pasted built in equations also become completely editable Entering the code for new equations is described in detail in Editing C ode on page 185 Viewing and Editing Code 153 Regression Wizard Variable Options Data Format Options Figure 8 9 Variable Data Format Options Multiple Independent Variables 154 Variable Options If you use data columns from the worksheet you can specify the data format to use in the variables panel By default the data format when assigning columns from the worksheet is XY Pair Regression Wizard Variable Columns Select your independent variable 0 p Save Variables save Os Options Edit Code Data Format xv Pair Help Cancel Back lee H From Code T he data format options are gt XY pair Select an x and ay variable gt Y only Select only a y variable column gt XY column means pick onex column then multiple y columns the y columns will be graphed as means gt Y column means only pick multiple y columns
110. al fft invfft complex mulcpx invcpx Theint function returns a number or range of numbers equal to the largest integer less than or equal to each corresponding number in the specified range All numbers are rounded down to the nearest integer int numbers T he numbers argument can be a scalar or range of numbers Any missing value or text string contained within a range is ignored and returned as the string or missing value Transform Function Descriptions 45 Transform Function Reference Example Theoperation int 9 1 2 2 2 3 8 returns a range of 0 0 1 0 2 0 4 0 Related Functions prec round interpolate Summary Theinterpolate function performs linear interpolation on a set of X Y pairs defined by an x range and ay range T he function returns a range of Interpolated y values from a range of values between the minimum and maximum of the x range Syntax _ interpolate x rangey range range Values in the x range argument must be strictly increasing or strictly decreasing T he range argument must be a single range indicated with the brackets or a worksheet column M Issing values and text strings are not allowed in the x range and y range Text strings in range are replaced by missing values Extrapolation is not possible missing value symbols are returned for range argument values less than the lowest x range value or greater than the highest x range value Examples For x 0 1 2 y 0 1 4 and range da
111. al parameter values must be provided All built in equations have the curve equation and initial parameters predefined T he curve fitter accepts up to 25 equation parameters and ten independent equation variables You can also specify up to 25 parameter constraints which limit the search area of the curve fitter when checking for parameter values T he regression curve fitter can also use weighted least squares for greater accuracy 144 About the Curve Fitter Introduction To The Regression Wizard Curve fitting The SigmaPlot curve fitter uses the M arquardt Levenberg algorithm to find the Algorithm coefficients parameters of the independent variable s that give the best fit between the equation and the data T his algorithm seeks the values of the parameters that minimize the sum of the squared differences between the values of the observed and predicted values of the dependent variable wherey is the observed and y isthe predicted value of the n ee SS Yi wiy i 1 dependent variable T his process is iterative the curve fitter begins with a guess at the parameters checks to see how well the equation fits then continues to make better guesses until the differences between the residual sum of squares no longer decreases significantly T his condition is known as convergence For informative references about curve fitting algorithms see below References for the Marquardt Levenberg Algorithm Pres
112. an gt or GE Greater than or equal to lt or LT Less than lt or LE Less than or equal to gt or NE N ot equal to Arithmetic Operators 19 Transform Operators T he alphabetic characters can be entered in upper or lower case Figure 4 3 User Defined Transform untitled Relational and Logical lof Operator Examples Edit Transform Run x cal 1 y cal 2 lf v gt 0 75 and x 1 z 1 Oj col 3 z Close Open Save Save Ag FLEE PETE Help Trigonometric Units Degrees Radians Grads Watch D Single Step Logical Operators Logical operators are used to set the conditions for if function statements and amp Intersection or Union not N egation 20 Logical Operators Transform Function Reference SigmaPlot provides many predefined functions including arithmetic statistical trigonometric and number generating functions In addition you can define functions of your own Function Arguments Function arguments are placed in parentheses following the function name separated by commas Arguments must be typed in the sequence shown for each function You must provide the required arguments for each function first followed by any optional arguments desired Any omitted optional arguments are set to the default value O ptional arguments are always omitted from right to left If only one argument is omitted it will be the last argument I
113. and A 10 4a the resulting scaled equation is simplified to peeo Paiet X A T he exponent argument now does not cause underflows and overflows 238 Example 7 Advanced Nonlinear Regression Advanced Regression Examples T he graph of the transformed x data is displayed below the original data eas a H Advanced Techniques Graph Advanced Techniques Worksheet for the Advanced Original Data Techniques Example Transt mre d Data ie Small Independent They values for the data range from very small values to very large values H owever Variable Values for this problem we know that the y values do not have the same errors smaller y Weighting for Non Values have smaller errors Uniform Errors T he curve fitter fits the data by minimizing the sum of the squares of the residuals Because the squares of the residuals extend over an even larger range than the data small residual squared numbers are essentially ignored T he solution to this non uniform error problem is to use weighting so that all residual squared terms are approximately the same size Example 7 Advanced Nonlinear Regression 239 Advanced Regression Examples Fitting with a weighting variable of 1 y the inverse of y squared which is proportional to the inverse of the variance of the y data produces a better fit for low y value data Figure 11 33 R ion Wizard The Results of the a ADVANCED FIT Converged tolerance satisfied Tran a with W
114. ant digits or places of significance Values are rounded to the nearest integer values of exactly 0 5 are rounded up Syntax prec numbers digits T henumbers argument can be a scalar or range of numbers Any missing value or text string contained within a range is ignored and returned as the string or missing value If the digits argument is a scalar all numbers in the range have the same number of places of significance If the digits argument is a range the number of places of significance vary according to the corresponding range values If the size of the digits range is smaller than the numbers range the function returns missing values for all numbers with no corresponding digits Example For x 13570 3 141 0155 999 1 92 the operation prec x 2 returns 14000 3 100 0160 1000 1 90 For y 123 5 123 5 123 5 123 5 the operation prec y 1 2 3 4 returns 100 0 120 0 124 0 123 5 Related Functions int round put into Summary Theput into function places calculation results in a designated column on the worksheet It operates faster than the equivalent equality relationship 56 Transform Function Descriptions syntax Example Related Functions random summary syntax Example Related Functions Transform Function Reference put results into col column T hereults argument can be either the result of an equation function or variable The column argument is either the column number of the destina
115. array elements are tested the off diagonal elements are compared to 0 0 and the diagonal elements compared to 1 0 If the absolute value of any off diagonal element or difference of the diagonal element from 1 0 is greater than a specified tolerance then the original array is considered to be singular Parameters may not be valid O verflow in partial derivatives T he partial derivatives of the function to be fit with respect to the parameters are computed numerically using first order differences M ath errors from various sources can cause errors in this computation For example if your model contains exponentials and the parameters and independent variable values cause exponential underflows then the numerical computation of the partial derivative will be independent of the parameter s SigmaPlot checks for this independence Check the parameter values in the results screen the range of the independent variable s and your equation to determine the problem Bad constraint T he regression cannot proceed because a constraint you defined either was not linear or contained syntax errors Invalid or missing fit to statement T he regression lacks a fit to statement or the fit to statement contains one or more syntax errors No observations to fit T he regression cannot proceed unless at least one x y data pair observation is included Check to be sure that the data columns referenced in the regression specifications contai
116. ary then copy the equation and paste it into the desired section of the library notebook You can also create your own library by simply combining all your old FIT filesinto a single notebook then setting this notebook to be your default equation library see Using a Different Library for the Regression W izard on page 176 Opening FIT Files 143 Introduction To The Regression Wizard Remember sections appear as categories in the library so create a new section to create a new equation category Figure 7 2 Opening a FIT file as a notebook using the File menu Look in E Nonlin E Open command Open dimen fit Hyperbal fit 3 Statfit2 fit a Advanced it a Logistic fit a Tut_1 tit a Automat fit I Multfune fit A Tut_2 fit a Dependen it a Piecewis fit i Weighted fit a Expdeay fit Pitfalls fit a Expdeay2 fit a Poly tit a Exprise fit a Solvegn fit Files of type SigmaPlot Curve Fit Cancel Jandel Notebook Template Notebook Regression Library SigmaPlot 1 0 2 0 GiamaPlot Curve Fit SigmaPlot Macintosh SigmaStat 1 0 SigmaPlot DOS SigmaStat DOS MS Excel FIT files as well as new equations do not have graphic previews of the equation About the Curve Fitter T he curve fitter works by varying the parameters coefficients of an equation and finds the parameters which cause the equation to most closely fit your data Both the equation and initi
117. atement exists and corresponds to the variable defined in the Variables edit window and that the function listed in the regression statement exists and corresponds to the function you defined in the Equations edit window U nreferenced variable T he regression specifications define a parameter that is not referenced in any other statements Either delete the parameter definition or reference it in another statement Regression Results Messages 183 TS Regression Wizard 184 Regression Results Messages Editing Code You can edit a regression equation by clicking the Edit Code button from the Regression W izard Regression equations can be selected from within the wizard or opened from anotebook directly You can also create new regression equations Creating a new equation requires entry of all the code necessary to perform a regression T his chapter covers Selecting an equation for editing see page 186 Entering equation code see page 188 D efining constants see page 190 Entering variables code see page 194 Entering parameters code see page 198 Entering code for parameter constraints and other options see page 199 VVVVVY About Regression Equations Protected Code for Built in Equations Using FIT Files Equations contain not only the regression model function but other information needed by SigmaPlot to run aregression All regression equations contain code defining the equations parameter settings
118. atenent gatenent end if To use the if then else construct follow the if condition then statement by one or more transform equation statements then specify the else statement s When an if then else statement is encountered all functions within the statement are evaluated separately from the rest of the transform y You must separate if then and all condition statement operators variables and values with spaces Inside if then else constructs you can gt type morethan one equation on a line 44 Transform Function Descriptions Example imaginary img int Summary Syntax Example Related Functions Summary Syntax Transform Function Reference gt indent equations gt nest additional if constructs N ote that these conditions are allowed only within if else statements You cannot redefine variable names within an if then else construct T he operations i cell 1 1 j cell 1 2 Ifi lt landj gt 1 then x col 3 else x col 4 end if sets x equal to column 3 if i islessthan 1 and j is greater than 1 otherwise x is equal to column 4 The imaginary function strips the imaginary values out of a range of complex numbers img block T he range is made up of complex numbers If x 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 the operation img x returns 0 0 0 0 0 0 0 0 0 0 If x 1 0 0 75 3 1 1 2 2 1 1 1 the operation img x returns 1 2 2 1 LII re
119. be treated as a data point x range and y range must have the same size and the number of valid data points must be greater than or equal to 3 Transform Function Descriptions 41 Transform Function Reference T he optional f argument defines the amount of Lowess smoothing and corresponds to the fraction of data points used for each regression f must be greater than or equal to 0 and less than or equal to 1 0 lt f lt 1 If fis omitted no smoothing is used Example For x 0 1 2 y 0 1 4 the operation col 1 fwhm x y places the x width at half maxima 1 00 into column 1 Related Functions xatymax gaussian Summary This function generates a specified number of normally Gaussian or bell shaped distributed numbers from a seed number using a supplied mean and standard deviation Syntax gaussian number seed mean tddev T he number argument specifies how many random numbers to generate T he seed argument isthe random number generation seed to be used by the function If you want to generate a different random number sequence each time the function is used enter 0 0 for the seed Enter the same number to generate an identical random number sequence If the seed argument is omitted a randomly selected seed is used The mean and dde arguments are the mean and standard deviation of the normal distribution curve respectively If mean and stddev are omitted they default to 0 and 1 N ote that function argume
120. bject in the hierarchy To change a property setting type the object reference followed with a period then type the property name an equal sign and the property value For more information refer to SigmaPlot Automation H elp from the SigmaPlot H elp menu Used without an object qualifier this property returns an Application object that reoresents the SigmaPlot application Used with an object qualifier this property returns an Application object that represents the creator of the specified object you can use this property with an Automation object to return that object s application Use the CreateO bject and G etO bject functions give you access to an Automation object Author Property Autolegend Property Axis Property Axistitles Property Cell Property ChildObjects Property Color Property SigmaPlot Automation Reference A standard property of notebook files and all N otebookl tems objects Returns or sets the Author field in the Summary Information for all notebook items or the Author field under the Summary tab of the W indows 95 98 file Properties dialog box Returns the Autolegend Group object for the specified Graph object Autolegends have all standard group properties T he first ChildO bject of a legends is always a solid the successive objects are text objects with legend symbols T he Axes property is used to return the collection of Axis objects for the specified graph object Individual axis
121. c_y sin theta circle y coordinates xx x x CALCULATE CONSTANT DAMPING TRAJECTORIES lt th data 0 pi 1 1 n pi n Data for zeta 1 zl 3 zeta 1 constant ri exp th z1 sqrt 1l 21 2 ZN _x r1 cos th r1l cos th zeta 1 x coord ZS ie Se ly 6p ae ae Cee asta ak y Cord Data for zeta 2 z2 7 zeta 2 constant r2 6xp t 22 SGre a2 7 z2_x r2 cos th r2 cos th zeta 2 x coord Ro v r2 rS ie hy ae ee nea isa A y Coord NR CALCULATE CONSTANT FREQUENCY TRAJECTORIES 2 Data for omega 1 wnT1 0 1 pi omega 1 constant Zeya Us eos v0 geo os thl wnT1 sqrt 1 z 2 r3 exp thl z sqrt 1 z 2 wl_x r3 cos th1l r3 cos th1 omega 1 x WL SYSTE Sone a ae oe Suna omega 1 y Data for omega 2 Whi2 5 p1 omega 1 constant th2 wnT2 sqrt 1 z 2 P4 exp Hch2 27 Sare 1S2 rry w2_x r4 cos th2 r4 cos th2 omega 2 x W227 sIn CCN Sey Ha wean Ch omega 2 y gt PLACE CIRCLE AND TRAJECTORY DATA IN WORKSHEET col res circ_x circle x coordinates col res 1l circ_y circle y coordinates col rest 2 zl_x zeta 1 x coordinates col res 3 zl_y zeta 1 y coordinates col res 4 zeta 2 x coordinates col res 5 z zeta 2 y coordinates col res 6 wl omega 1 x coordinates Graphing Transform Examples 139 SS Example Transforms col rest 7 wl_y omega L y coordinates col res 8 w2_x omega 2 x coordinates
122. column 2 cos sin tan arcsin arctan Transform Function Descriptions 29 Transform Function Reference arcsin Summary This function returns the inverse of the corresponding trigonometric function Syntax arcsin numbers T he numbers argument can be a scalar or range You can also use the abbreviated function name asin T he values for the numbers argument must be within 1 and 1 inclusive Results are returned in degrees radians or grads depending on the Trigonometric U nits selected in the User D efined Transform dialog box Any missing value or text string contained within a range is ignored and returned as the string or missing value T he function domain in radians is arcsin 2to fh 2 2 Example The operation col 2 asin col 1 places the arcsine of all column 1 data points in column 2 Related Functions cos sin tan arccos arctan arctan Summary This function returns the inverse of the corresponding trigonometric function Syntax arctan numbers T he numbers argument can be a scalar or range You can also use the abbreviated function name atan T he numbers argument can be any value Results are returned in degrees radians or grads depending on the Trigonometric U nits selected in the U ser D efined Transform dialog box T he function domain in radians is TU TU arctan to 2 2 Example Theoperation col 2 atan col 1 places the arctangent of all column 1 data points in
123. cs Colunn Tor Control limit line data MAE RED RE RAR CALCULATE ERACTION DEFECTIVE a ee ae n col n_col sample sizes def col def_col defectives col p_col def n fraction defective pbhar total def total n NKKKKKKKKKKHK CALCULATE CONTROL LIMITS KKKKKKKKKKKHK stddev sqrt pbar 1 pbar n ucl pbar 3 stddev upper control limit lcl pbar 3 stddev lower control limit lcolt if lcl gt 0 lcl 0 truncated lower control limit SIRE DATA FOR CONTROL LIMIT LINE STEP CHART col cl uc1 col cl 1 lclt 86 Graphing Transform Examples Example Transforms Cubic Spline Interpolation and Computation of First and Second Derivatives T his example takes data with irregularly soaced X values and generates a cubic spline interpolant The CBESPLN 1 XFM transform takes X data which may be irregularly spaced and generates the coefficients for a cubic spline interpolant The CBESPLN 2 XFM transform takes the coefficients and generates the spline interpolant and its two derivatives T he values for the interpolant start at a specified minimum X which may be less than equal to or greater than the X value of the original first data point The interpolant has equally spaced X values that end at a specified maximum which may be less than equal to or greater than the largest X value of the original data N ote that this is not the same algorithm that SigmaPlot uses this algorithm does not handle multiple value
124. curve point with the closest points more heavily weighted T he lowpass function returns smoothed y values from ranges of x and y variables using an optional user defined smoothing factor that uses FFT and IFFT T his function returns an estimate of the phase in radians of sinusoidal functions This function returns the x value for the y value 25 of the distance from the minimum to the maximum of smoothed data for sigmoidal shaped functions T his function returns the x value for the y value 50 of the distance from the minimum to the maximum of smoothed data for sigmoidal shaped functions T his function returns the x value for the y value 75 of the distance from the minimum to the maximum of smoothed data for sigmoidal shaped functions T his function returns the x value for the maximum y in the range of y coordinates for peak shaped functions T his function returns x75 x25 for sigmoidal shaped func 26 Transform Function Descriptions Transform Function Reference Miscellaneous These functions are specialized functions which perform a variety of operations Functions choose T he choose function is the mathematical n choose r func tion histogram The histogram function generates a histogram from a range or column of data interpolate T he interpolate function performs linear interpolation between X Y coordinates polynomial The polynomial function returns results for specified inde pendent variables for a
125. d by the sum of two sine waves plus G aussian random noise 94 Graphing Transform Examples Example Transforms T he data is represented by f t sin 2 pi f1 t 0 3 sin 2 pi f2 t 9 t where f1 10 cycles sec cps f2 100cps and the Gaussian random noise has mean 0 and standard deviation of 0 2 The lower graph is empty To use your own data place your data in column 1 If your data isin a different column specify the new column after you open the POW SPEC XFM transform file Press F10 to open the User D efined Transform dialog box then click the O pen button and open POW SPEC XFM transform file in the XFM S directory The Power Spectral D ensity transform appears in the edit window X To use this transform the Trigonometric U nits must be set to Radians 4 Click Run Since the frequency sampling value fs isnonzero a frequency axisis generated in column 2 and the power spectral density data in column 3 If you opened the Power Spectral D ensity graph view the graph page Two graphs appear on the page T hetop graph plots the data generated by the sum of two sine waves plus G aussian random noise using a Line Plot with Simple Straight Line style graphing column 1 versus row numbers T he lower graph plots the power spectral density using aLine Plot with a Simple Straight Line style graphing column 2 asthe X data frequency and column 3 asthe Y data To plot your own data using SigmaPlot choose the Graph menu Create
126. d final values to their respective ends of range Transform Function Descriptions 59 Transform Function Reference Example Theoperation runavo 1 2 3 4 5 3 returns 1 33 2 3 4 4 67 Related Functions sin summary syntax Example Related Functions T he value of the window argument is 3 so the first result value is calculated as CGE 2 3 T he second value is calculated as ALC 14 2 3 3 avg mean This function returns ranges consisting of the sine of each value in the argument given This and other trigonometric functions can take values in radians degrees or grads This is determined by the Trigonometric U nits selected in the U ser D efined Transform dialog box sin numbers T he numbers argument can be a scalar or range If you regularly use values outside of the usual 27 to 27 or equivalent range use the mod function to prevent loss of precision Any missing value or text string contained within a range is ignored and returned as the string or missing value If you choose D egrees as your Trigonometric Units in the transform dialog box the operation sin 0 30 90 180 270 returns values of 0 0 5 1 0 1 acos asin atan cos tan 60 Transform Function Descriptions sinh summary syntax Example Related Functions sinp size Summary Syntax Summary Syntax Transform Function Reference This function returns the hyperbolic sine of the specified ar
127. d for the sake of simplicity O mit the observed dependent variable name from the regression model T he observed dependent variable typically your y variable is used in the fit tate ment Press the Enter key when finished with the regression equation model then type the fit statement T he simplest form of the fit statement is fit f to y W here f is the predicted dependent variable from the regression model and y is the variable that will be defined as the observed dependent variable typically the variable plotted as y in the worksheet You can also define whether or not weighting is used For more information on how to perform weighted regressions see Weight Variables on page 197 Regression untitled Vanables Cancel Bur Help Initial Parameters Constraints Options Iterations fo Add s Step Size fioo Tolerance fo oo01 O0 Trigonometric Units f Degrees i Radians f Grads Entering Regression Equation Settings 189 Editing Code Defining Constants Entering Variables Example The code f n xto fit f to y can be used as the model for the function f x mx b and also defines y as the observed dependent variable In this example x is the independent variable and m and b the equation parameters Constants that appear in the equations can also be defined under the equations heading If you decide that an equation parameter should be a constant rather than a paramet
128. d functions on page 251 U sing the D ialog Box Editor on page 251 U sing the O bject Browser on page 252 U sing the Add Procedure D ialog Box on page 253 U sing the D ebug W indow on page 253 VVVVVVYVYV Creating Macros Record a macro any time that you find yourself regularly typing the same keystrokes choosing the same commands or going through the same sequence of operations Before you Record Before you record the macro 1 Analyze the task you want to automate If the macro has more than a few steps write down an outline of the steps 2 Rehearse the sequence to make sure you have included every single action 3 Decide what to call the macro where to assign it and where to save it Creating Macros 241 Automating Routine Tasks Recording a Macro To learn how to place macros on the menu see Creating M acros as M enu Commands on page 243 Figure 12 1 The Status Bar Figure 12 2 Macros Options Dialog Box 242 Creating Macros To record a macro L On the Tools menu click M acro and then click Record N ew M acro TheREC appears in the status area of SigmaPlot s main window indicating that the macro is recording your menu selections and keystrokes OVA REC o fo Complete the activity you want to include in this macro N ote that the M acro Recorder does not record cursor movements W hen you are finished recording the macro on the Tools menu click M acro
129. d functions whereas SigmaPlot does To use the transform to generate and graph a cubic spline interpolant you can either use the provided sample data and graph or begin a new notebook enter your own data and create your own graph using the data 1 To usethe provided sample data and graph open the Cubic Spline worksheet and graph by double clicking the graph page icon in the Cubic Spline section of the Transform Examples notebook T he worksheet appears with data in columns 1 and 2 and the graph page appears with two graphs T he first graph plots the original XY data as a scatter plot The second graph appears empty 2 To use your own data enter the irregularly soaced XY data into the worksheet TheX values must be sorted in strictly increasing values T he default X and Y data columns used by the transform are columns 1 and 2 respectively 3 PressF10 to open the User D efined Transform dialog box then click the O pen button and open the CBESPLN1 XFM transform file in the XFM S directory The first Cubic Spline transform appears in the edit window 4 Moveto the nput Variables heading Set the X data column variable cx the Y data column cy the beginning interpolated X value xbegin the ending interpo lated X value xend and the X increments for the interpolated points xstep A larger X step results in a smoother curve but takes longer to compute 5 Enter the end condition setting tend for the interpolation 6 You can use first
130. d regression attempts is useful if you do not want to regression to proceed beyond a certain number of iterations or if the regression exceeds the default number of iterations T he default iteration value is 100 To change the number of iterations simply enter the maximum number of iterations in the Iterations edit box Iterations must be non negative H owever the setting Iterations to 0 causes no iterations occur instead the regression evaluates the function at all values of the independent variables using the parameter values entered under the Initial Parameters section and returns the results If you are trying to evaluate the effectiveness of automatic parameter estimation function setting Iterations to 0 allows you to view what initial parameter values were computed by your algorithms U sing zero iterations can be very useful for evaluating the effect of changes in parameter values For example once you have determined the parameters using the regression you can enter these values plus or minus a percentage run the regression with zero iterations then graph the function results to view the effect of the parameter changes T he initial step size used by the M arquardt Levenberg algorithm is controlled by the Step Size option T he value of the Step Size option is only indirectly related to changes in the parameters so only relative changes to the step size value are important T he default step size value is 100 To change t
131. e T he sargument specifies whether or not a constant is used s 0 specifies no constant term Yo in the numerator s 1 specifies a constant term yg in the numerator smust be either 0 or 1 If n 0 s cannot be 0 there must be a constant The number of valid data points must be greater than or equal to n m s T he optional f argument defines the amount of Lowess smoothing and corresponds to the fraction of data points used for each regression f must be greater than or equal to 0 and less than or equal to 1 0 lt f lt 1 If f is omitted no smoothing is used For x 0 1 2 y 0 1 4 the operation col 1 ape x y 1 1 1 0 5 places the 3 parameter estimates for the equation a bx 1 cx as the values 5 32907052e 15 0 66666667 0 33333333 in column 1 f x T his function returns the inverse of the corresponding trigonometric function arccos numbers T he numbers argument can be a scalar or range You can also use the abbreviated function name acos T he values for the numbers argument must be within 1 and 1 inclusive Results are returned in degrees radians or grads depending on the Trigonometric U nits selected in the U ser D efined Transform dialog box Any missing value or text string contained within a range is ignored and returned as the string or missing value T he function domain in radians is arccos Otot T he operation col 2 acos col 1 places the arccosine of all column 1 data points in
132. e 2 7 040e 0 62661 Sb Help Cancel Back New 216 Lesson 2 Sigmoidal Function Fit Figure 10 21 Results of the Five Parameter Logistic Equation Fit More Iterations Figure 10 22 The SigmaPlot Graph with both Four and Five Parameter Logistic Equation Fit Results 4 Regression Lessons T he regression continues to completion converging after four more iterations Regression Wizard Converged tolerance satisfied Fisqr 0 999999266 Nom 0 152113538 View Constraints Parameter Value StdErr Cv rs Dependencies 1i40e 4626 2 4057e2 0 7031467 9 106e 0 3284e 2 3 606e 1 0 965636 3095e 0 7 3rle z 2 36 1e 0 0 9985315 o 160e 1 2 664e 7 3 510e 1 0 9999516 4133e 1 242te 2 5703e 2 O 6226955 Help Cancel Back Next Examine the results T he norm value standard deviations and CV values are smaller than for the four parameter fit indicating that this may be a better fit H owever two of the dependencies are close to 1 0 suggesting that the fifth parameter may not have been needed Click Finish to save the results of this regression Another report more data and the curve for this regression equation are all added to your notebook To distinguish between the two regression lines double click one of them and change the line color to blue then use the Plot drop down list to change the other regression curve to red Compare the curve fits visually As expected the five parameter function ap
133. e Add Equation to N otebook option in the results panel and a copy of the equation used is added to the same section as reports and other results T he Equation section of the Regression dialog box defines the model used to perform the regression as well as the names of the variables and parameters used T he regression equation code is defined using the transform language operators and functions T he equation must contain all of the variables you wish to use T hese include all independent variables the predicted dependent variable and observed dependent variable All parameters and constants used are also defined here T he Equation code consists of two required components gt Theequation modd describing the function s to be fit to the data gt Thefit tatenent which defines the predicted dependent variable and optionally the name of a weighting variable The independent variable and parameters are defined within the equation function Also any constants that are used must also be defined under the Equations section T he equation model sets the predicted variable called f in all built in functions to be a function of one or more independent variables called x in the built in two dimensional Cartesian functions and various unknown coefficients called parameters The model may be described by more than one function For example the following three equations define a dependent variable f which isa constant for x lt 1 anda
134. e Automatic setting from within the Regression O ptions dialog box N ote that these values may not at all reflect the final values but they are approximate enough to prevent the curve fitter from finding false or invalid results Automatic Determination of Initial Parameters 203 N otes Regression Lessons Lesson 1 Linear Curve Fit Figure 10 1 The NONLIN JNB Notebook T his tutorial lesson is designed to familiarize you with regression fundamentals T he Sample graph and worksheet files for the tutorials are located in the NON LIN JN B Regression Examples notebook provided with SigmaPlot Wonlin_jnb be o Regression Examples H i Tutorial 1 m Tutorial 2 Peas d i Curve Fiting Pitfalls __ Summary h C Weighted Regression H C Piecewise Continuous C Dependencies a ie Solving Nonlinear Equation HB ie Multiple Function Delete H C Advanced Techniques SPSS Inc Created 09 76 95 09 57 20 Modified 01703797 11 44 37 Description Regression Examples In this lesson you will fit a straight line to existing data points 1 Open the Tutorial 1 Graph in the NONLIN JNB notebook and examine the Lesson 1 Linear Curve Fit 205 SSS Regression Lessons graph T he points appear to nearly follow a straight line Figure 10 2 B Tutorial 1 Graph Tutorial 1 Worksheet The Graph with Unfitted Data Points 2 Choose the Statistics menu Regression W izard command or press F5 The Regre
135. e information about interpreting reports see Interpreting Regression Reports on page 16 7 To add the current regression equation to the current notebook check the Add Equation to N otebook check box If this option is selected a copy of the equation is added to the current section of your notebook Graphing Regression Equations SigmaPlot can graph the results of a regression as a fitted curve A curve or graph is created by default If you want to disable graphed results you can change the options in the Regression W izard graph panel N ote that these settings are retained from session to session From the graph panel you can choose to plot the results either by gt adding aplot to an existing graph T his option is only available if the fitted variables were assigned by selecting them from a graph gt creating anew graph of the original data and fitted curve To add a plot to an existing graph click the Add Curve to check box option then select the graph to which you want to add a plot from the drop down list T he drop down list includes all the graphs on the current page If there is no existing graph this option is dimmed If you want to specify the columns used to plot the fitted curve click N ext O therwise the data is placed in the first available columns 166 Graphing Regression Equations ee Figure 8 23 A Fitted Curve Added to a Graph Data Plotted for Regression Curves Figure 8 24 The Regre
136. e macro script Editing Macros W hen you record a macro SigmaPlot generates a series of program statements that are equivalent to the actions that you perform T hese statements are in a form of SigmaPlot language that has custom extensions specifically for SigmaPlot automation and appear in the M acro Window You can edit these statements to modify the actions of the macro You can also add comments to describe code Editing Macros 245 Automating Routine Tasks To edit a macro 1 OntheTools menu click M acro and then click M acros The M acros dialog box appears 2 Select a macro from the M acro list 3 Click Edit 4 TheM acro Window appears Object Browser Programming Editor Figure 12 7 The Macro Window Survival Curve Macro OR x Z of al ml oh lael alesse Object General Proc declarations X The Macro Toolbar Option Explicit Sub Main Dim Current Worksheet Current Worksheet Survival Worksheet ActiveDocument NotebookItems CurrentWorksheet Open Opens alect defa Determine the data range and define the first empty colunn Dim WorksheetTable As Ohject net WorksheetTable ActiveDocument NotebookItems CurrentWorksheet Dati Dim LastColumn As Long Color coded Text Dim LastRow As Long LastColumn O LastRow oO Worksheet Table GetHaxUsedSiczce LastColumn LastRoam Using the Macro TheM acro Window toolbar appears at the top of the M acro Window It contains Window T
137. e main menu that you specify For example your new macro could appear on the main menu under the macro command M y M acros To create a new menu command On the Tools menu click M acro and then click M acros The M acros dialog box appears Macro Mame Record laste bo PowerPoint Slide By Group Data Split Cancel Color Transition values Frequency Plot F test Comparison of Curves un Label Symbols Edit Paste to PowerPoint Slide Edt Plotting Polar and Parametric Equations att Power Spectral Density pes a Quick Re Plot Rank and Percentile Delete Survival Curve vector Plot Help Source All Active Notebooks Browse 1 Description This macra formats and pastes selected SigmaPlot graphs to the current PowerPoint slide ly Select a macro from the M acro N ame scroll down list Creating Macros 243 Automating Routine Tasks 3 Click Options TheM acro O ptions dialog box appears Figure 12 5 Macro Options Macros Options Dialog Box ae OK laste bo PowerPoint Slide Description This macro Formats and pastes selected SigmaPlot graphs to Fhe current PowerPoint slide Help E 4551gn to M Command Mame aPaste to PowerPoint Slide Menu Name Toolbots Sawedin C Program Files SigmaPlothsPw7SigmaPlat I 4 Select Command Name 5 Enter the name of the macro in the Command N ame field If the Command N ame is cleared the macro doe
138. e or all of the constraints C onstraints that are not used are not flagged as active 5 Click OK to return to the N onlinear Regression Results dialog box then click N ext to proceed Saving Results 6 You can select the results to save for a regression T hese results are destroyed by default each time you run another regression equation You can save some of your results to a worksheet and other results to a text reoort To save worksheet results make sure the results you want saved are checked in the results list You have the option to save parameter values pre dicted dependent y variable values for the original independent x variable and the residuals about the regression for each original dependent variable Figure 10 9 Regression Wizard Saving the Nonlinear Select the columns for your resulte Save 4 First Empty Regression Results Columns Using the Keep Regression Results dialog box Results save As I Parameters First Empty Iw Predicted First Empty Residuals First Empty a Bani Help Cancel Back Ea Enin 7 To saveatext report make sure the Report option is checked T he report for a nonlinear regression lists all the settings entered into the nonlinear regression dialog box a table of the values and statistics for the regression parameters and some regression diagnostics You can also save a copy of the regression equation you used to the same section as the page or
139. e transform statements describing how gain filter snoothing works are P 4000 osd threshold x col 1 data tx fft x compute fft of data md real tx 2 1img tx 2 compute sd kc if md gt P 1 0 remove frequencies with psd lt P sd mulcpx complex kc tx remove frequency components from x td real invfft sd convert back to time domain col 2 td place results in worksheet To calculate and graph the smoothing of a set of data using again filter you can either use the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 To usethe sample worksheet and graph open the Gain Filter Smoothing work sheet and graph by double clicking the graph page icon in the Gain Filter Smoothing section of the Transform Examples notebook D ata appears in col umns 1 through 3 of the worksheet and two graphs showing plots and one 102 Graphing Transform Examples OT ee Example Transforms blank graph appear on the graph page Column 1 contains the Y data for the sig nal plus noise column 2 contains the X data and column 3 contains the Y data for the power spectral density graph The top graph plots the signal plus the noise distortion the middle graph plots the power spectral density 2 To use your own data place your data in column 1 If your data isin a different column specify the new column after you open the GAIN FILT XFM transform
140. ect or collection index and created using the N otebookltems Add method T he M acroltem object has an ItemT ype property and N otebookltems Add method value of 0 Represents the notebook item in the notebook window You can use this object to rename the notebook item T he notebook item can always be reference with N otebookl tems 0 To use the Notebookltem Object T he N otebookltem object has most of the standard notebook item properties and methods and created using the N otebookltems Add method T he N otebookltem object has an ItemType property and N otebookltems Add method value of 7 Represents the section folders within a SigmaPlot notebook To use the Sectionltem Object T he Sectionitem object most of the standard notebook item properties and methods A Sectionitem is returned from the N otebookl tems collection using the Item property or collection index and created using the N otebookl tems Add method T he Section tem object has an ItemType property and N otebookltems Add method value of 3 SigmaPlot Properties Application Property pa 266 SigmaPlot Properties A property is a setting or other attribute of an objectothink of a property as an adjective For example properties of a graph include the size location type and style of plot and the data that is plotted To change the settings of an object you change the properties settings Properties are also used to access the objects that are below the current o
141. ection and type the name of the first parameter as it appears in your equation model followed by an equals sign 2 Enter the initial parameter value used by the curve fitter Ideally this should be as close to the real value as possible T his value can be numeric or a function Entering Regression Equation Settings 191 Editing Code Constraints Options that computes a good guess for the parameter U sing a function for the initial parameter value is called automatic parameter estimation For more information on parameter estimation see Automatic D etermination of Initial Parameters on page 202 Example If your data for the equation code f n xto fit f to y appear to rise to the right and run through the origin you could define your initial parameter as m 0 5 b 0 T hese are good initial guesses since the m coefficient is the slope and the b constant is the y intercept of a straight line Parameter C onstraints are completely optional and should only be entered if you suspect they will improve the performance of the curve fitter See Constraints on page 199 for when and how to enter constraints T helterations Step Size and Tolerance options sometimes can be used to improve or limit your curve fit T he default settings work for the large majority of cases so you do not need to change these setting unless truly required For conditions that may call for the use of these options see Curve F
142. ection or YZ plane SLA FLAG DROPX 3 X axis Y direction or ZX plane SLA FLAG DROPY Some drop line properties are controlled from the Plot object for example use the SetAttribute SLA PLOTOPTIONS SLA FLAG DROPX OrFLAG SET BIT plot object method to turn on y axis drop lines O ther drop line properties are set using Line object attributes Expanded Property A property of notebook window notebooks and sections which opens or closes the tree for that notebook section or returns a true or false value for the current view 268 SigmaPlot Properties Fill Property FullName Property Functions Property Graphs Property GraphPages Property SigmaPlot Automation Reference T he Fill property is used to return the Solid object for the specified Plot object Solid objects for plots include bars and boxes Returns the filename and path for either the application or the current notebook object If the notebook object has not yet been saved to a file an empty string is returned T he Functions property is used to return the collection of Function objects for the specified Plot object Plot functions include regression and confidence lines and all reference Q C lines T he individual function lines are specified using an index Ane et 2 SAFINE con upecao a Sane cone ior fe Sane eb Uipe renin s ianen ioone fe SAFUNe oci iereencetnetupe Sion 2nd Reference Line U pper Control Line fe SAFuNe ocs SeRdeecetneMen
143. ed Functions x50 summary syntax Example Related Functions Transform Function Reference x25 x range y range f T hex range argument specifies the x variable and the y range argument specifies the y variable Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must have the same size and the number of valid data points must be greater than or equal to 3 T he optional f argument defines the amount of Lowess smoothing and corresponds to the fraction of data points used for each regression f must be greater than or equal to 0 and less than or equal to 1 0 lt f lt 1 If fis omitted no smoothing is used For x 0 1 2 y 0 1 4 the operation col 1 x25 x y places the x atYmin 22 as 1 00 into column 1 x50 x75 xatymax xwtr The x50 function returns value of the x at min ange in the ranges of coordinates provided with optional Lowess smoothing T his is typically used to return the x value for the y value at 50 of the distance from the minimum to the maximum of smoothed data for sigmoidal shaped functions x50 x range y range f T hex range argument specifies the x variable and the y range argument specifies the y variable Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must have the same size and the number of valid data po
144. ed or set using the G eAttribute and SetAttribute methods Use the Group Bag Attribute constants to specify these attributes T he AutoL egend object is really a specific Group object consisting of a solid object and text objects T he AutoLegend object is returned from a graph using the AutoLegend property To use the AutoLegend Object M anipulate the AutoLegend object as you would a Group object Use the ChildO bjects property to return the members of the AutoLegend ChildO bjects 0 always returns the Solid rectangle object used as the AutoL egend border background and indexes gt 0 to return the individual Text objects used for the legend keys Legends can also be manipulated with many Text attributes using the G etAttribute and SetAttribute methods The GraphO bject object corresponds to non SigmaPlot objects residing on a graph page such as pasted bitmaps or metafiles or embedded or linked OLE objects The Fitlltem object corresponds to the a SigmaPlot equation and all the equation code parameters and settings Fitltems are used not only for regressions but for other nonlinear curve fitting applications and function plotting and solving T he results of a Fitltem are accessed from a FitR esults object To use the Fitltem Object The Fitltem object has the standard notebook item properties and methods A Fitltem is returned from the N otebookl tems collection using the Item property or collection index and created using the
145. eet Transforms can be saved as independent XFM files for later opening or modification Because transforms are saved as plain text ASCII files they can be created and edited using any word processor that can edit and save text files T he transform chapters describe the use and structure of transforms followed by a brief tutorial reference sections on transform operators and functions and finally a list and description of the sample transform files and graphs included with SigmaP lot T he SigmaPlot Regression Wizard replaces the older curve fitter with anew interface and over one hundred new equations T he major new features of this interface include gt agraphical interface rather than text code gt alibrary of over 100 built in equations in twelve different categories gt graphical examples of the curves and equations for built in equations Transforms 1 Introduction The Curve Fitter Automation 2 Automation gt automatic initial parameter determination no coding is required in most cases gt selection of variables directly from either worksheet columns or graph curves gt full statistical report generation gt automatic curve plotting to existing or new graphs gt new regression equation documents for the notebook gt new text report documents for the notebook T he Regression W izard chapters describe how to use these features T he Regression W izard uses the curve fitter to fit user defined li
146. egression or nonlinear regression T he original Y values the Y data from the fitted curve and the parameters are used to generate the table T he transform assumes you have placed the original Y data in column 2 the fitted Y data in column 3 and the regression coefficients or function parameters in column 4 You can either place this data in these columns or change the column numbers used by the transform TheOne Way AN OVA transform contains examples of the following transform functions gt count gt if gt total gt mean gt constructor notation Data Transform Examples 71 Example Transforms To use the One Way ANOVA transform 1 Make sure your original Y data isin column 2 Perform the desired regression using the Regression W izard and save your Predicted values fitted Y data in column 3 and Parameters the regression coefficients in column 4 For more information on using the Regression W izard see Chapter 8 R egres sion W izard 2 PressF10 to open the User D efined Transform dialog box then click the O pen button and open the AN OVA XFM transform file in the XFM S directory The AN OVA transform appears in the edit window 3 Click Run TheAN OVA results are placed in columns 5 through 9 or begin ning at the column specified with the anova variable One Way xxx Analysis of Variance ANOVA Table x ANOVA Transform This transform takes regression or curve fit ANOVA XFM
147. eighting Eee feelers Rag 0 999 734243 Horn 0 47 7408957 View Constramts CY Value StdErr Dependencies 1 054e 1 4765e 2 3 506e 1 0 9813525 CD B 003e 3 F 565e2 12b0e 3 04573765 db 1d42e 1 64 le2 3 333e 0 952193 zl Help Cancel Back H il Finish To see the results of the regression without weighting open the O ptions dialog box and change the weighting to none before finishing Figure 11 34 m f B Advanced Techniques Graph Advanced Techniques Worksheet The Graph Showing the ts e a Results of Weighted and Unweighted Nonlinear Regressions Transformed Data fxe 4 The dotted line indicates the unweighted fit 240 Example 7 Advanced Nonlinear Regression Automating Routine Tasks SigmaPlot uses a VBA like macro language to access automation internally H owever whether you have never programmed or are an expert programmer you can take advantage of this technology by using the M acro Recorder T his chapter describes how to use SigmaPlot s M acro Recorder and integrated development environment ID E It also contains descriptions of related features accessible in the M acro window including the Sax Basic programming language debugging tool dialog box editor and user defined functions T his chapter contains the following topics y Creating M acros on page 241 Running Your M acro on page 244 Editing M acros on page 245 About user define
148. eleteCells Method SigmaPlot Automation Reference Copies the currently selected item within the specified notebook item If no item is selected then an error is returned Creates a graph for a Graphitem from the Graph Style Gallery Creates a graph in the specified Graphlitem object using the Graph W izard options T hese options are expressed using the following parameters Removes the current selection from the specified object placing the contents on the clipboard T his method is equivalent to using the Copy method followed by the Clear method H owever whereas C opy places O LE link formats on the clipboard for Graphitem objects Cut does not D eletes a notebook item from a N otebookl tems collection as specified using an index number or name If the item does not exist an error is returned D eletes the specified cells from the worksheet T he remaining cells can be moved in two different directions to fill in the deleted region 1 Shift CellsUp 2 Shift Cells Left SigmaPlot Methods 279 a SigmaPlot Automation Reference To delete an entire column or row simply set the column bottom or row right value to the system maximum Rows 32 000 000 Columns 32 000 Execute Method Used to execute the specified Transformitem Export Method SigmaPlot Automation supports export of N ativeW orksheetltem objects Graphitem objects and N otebookltem objects of type CT NOTEBOOK gt If applied to aN ativeWorksheetl
149. end for CUBICSHINE Z errs Spline Generation feast eres Transform Rut this transform after you run CBESPLENL XFM CBESPLN2 XFM Make sure to enter the same results column number value cr as in CBESPLN1 XFM KKKKKKKKKK Input Variables KKKKKKKKKK cr 3 lst column of results block contains spline x mesh This must be the same value as in CBESPLNI1 XFM KKKKKKKKKKKK PROGRAM KKKKKKKKKKKK crl cr l column for spline values cr2 cr 2 column for 1st derivative of spline cr3 cr 3 column for 2nd derivative of spline cr4 cr 4 column for a spline coefficients crs cer o column tor bY spline coecrricrents ertb cert column tor Te spline cocrricrents cr8 cr 8 working column xbegin cell cr8 4 Graphing Transform Examples 91 Example Transforms xend cell cr8 5 xstep cell cr8 6 cx cell cr8 1 cy cell cr8 2 n size col cx xlend int xend xbegin xstep 1 cell cr8 9 1 index of x value x col cx f a b c Y dXX y dxx c dxx b dxx a f1 a b c dxx c dxx 2 b dxx 3 a f2 a b dxx 2 b 60 a dxx for ul 1 to xlend do u xbegint ul 1 xstep cell cr ul u pu U value In CoL er xj cell cr8 9 if u lt x n then if u lt x xjt l then test u lt x itl dx u x x J dx cellers vil jHECoeli era xq roeL Cr 507 gt CELI Gy 34 Weel ey ye rdx cell cr2 ul1 f 1 cell cr4 xj cell ers x gt ceLl cre6 x dx
150. endent variable i e at least one of the coefficients Is different from zero and the unexplained variability is smaller than what is expected from random sampling variability of the dependent variable about its mean If the F ratio is around 1 you can conclude that there is no association between the variables i e the data is consistent with the null hypothesis that all the samples are just randomly distributed P value TheP value is the probability of being wrong in concluding that there is an association between the dependent and independent variables i e the probability of falsely rejecting the null hypothesis or committing a Type error based on F The smaller the P value the greater the probability that there is an association 170 Interpreting Regression Reports Figure 8 26 Regression Report PRESS Statistic Durbin Watson Statistic Normality Test Regression Wizard Report 2 Iof x Times New Roman fio B z U lel B SERRE BEERS Ee EEE eee eee eee PRESS 0 1758 E Durbin Watson Statistic 2 4780 Normality Test Passed F 0 4760 Constant Variance Test Passed P 0 53315 Power of performed test with alpha 0 0500 1 0000 Regression Diagnostics Row Predicted Residual oid Res stud Res stud Del Res 1 0 0004 0 10320 2 1326 2 2823 2 3046 2 0 0012 0 0173 0 33587 0 3812 0 3786 3 0 0021 0 0403 0 8358 0 8824 0 8808 4 0 0029 0 029 0 6168 0 6474 0 64
151. er Plot with a Simple Regression plotting column 1 against column 2 as the symbols and using col umn 3 plotted against column 4 as the regression Add confidence and predic tion intervals using column 3 asthe X column and columns 7 and 8 as the Y columns For more information on creating graphs in SigmaPlot see the SigmaPlot U s s M anual Figure 6 12 Linear Regression Graph 95 Confidence and Prediction Intervals 1500 Confidence Prediction 1000 500 114 Graphing Transform Examples I a Linear Regression Transform LINREGR XFM Example Transforms xxx Transform to Compute a Linear Regression See wath Contadence Prediction Intervals Place your x data im Gol and y data in y GoL 0r change the column numbers to suit your data Results are placed in columns res through res 5 x col 1l column number for x data y_col 2 column number for y data res 3 first results column x col x_col Define x values y col y col Define y values Define z value for 95 confidence interval F r 99 Gontrdence interval Use z 2 57176 Z 1 96 z for 95 confidence z 2 576 7 for 99 confidence CREERAR RN DEFINE REGRESSION PARAMETERS X X n size x number of data points v n 2 n must be gt 2 xbar mean x mean of x denom total x xbar 2 sum of sqs about mean alpha total x 2 n denom 1 1 coeff of X X 1 beta xbar denom 1 2 c
152. er in fact finds the exact parameter values used to generate the data producing a perfect fit with an R of 1 Figure 11 22 The Results of Fitting the Data to the Converged tolerance satisfied eee tetas Sum of Two Exponentials e Raq 1 Norm 4 897 898036e 6 View Constraints Parameter Value StdE rr CY 2 Regression Wizard Dependencies a 3 000e 1 2fode 6 3 098e 4 O92 7 753 b 1 000e 0 4209e 6 4 209e 4 0 875668 B 1 000e 1 2oa0e 6 2 630e 3 0 979850 d 2 000e 1 4 189e 6 2 084e 5 0 914044 zl Help Cancel Back Einizh Dependencies Over 5 Click Back twice and change the equation to a Triple 6 Parameter exponential an Extended Range decay equation Click N ext twice Figure 11 23 Selecting the 6 Parameter Equation Category Triple Exponential Decay Select the equation to fit your data save Equation Exponential Decay Equation Name save As Single 2 Parameter Single 3 Parameter Double 4 Parameter Double 5 Parameter ET rple 6 Parameter Triple 7 Parameter Hele _ caes pack _ wee finish T he results show that the parameter dependencies for a b c and d are 1 00 suggesting that the three exponential model is too complex and that one expo nential may be eliminated Click Cancel when finished x Regression Wizard g An y ae fer Figure 1 1 24 Regression Wizard The Results of Fitting the Data to the Converged
153. er to Digital Control of D ynamic Systens Gene F Franklin and J D avid Powell Addison Wesley pp 32 and 104 for the equations and graph To calculate the data for the design curves you can either use the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 Tousethe sample worksheet and graph double click the graph page icon in the Z Plane section of the Transform Examples notebook The Z Plane worksheet appears with data in columns 1 through 10 TheZ Plane graph page appears with the design curve data plotted over some sample root locus data T his plot uses columns 1 and 2 as the first curve and columns 3 and 4 as the second curve Graphing Transform Examples 137 Example Transforms Figure 6 22 Z Plane Graph To use your own data place your root locus zero and pole datain columns 1 through 10 If your locus data has been placed in other columns you can change the location of the results columns after you open the ZPLAN E XFM file To plot the design curves of your data create a Line Plot with M ultiple Spline Curves then plot column 1 asthe X data against column 2 as the Y data for the first curve and column 3 asthe X data against column 4 as the Y data as the sec ond curve Press F10 to open the User D efined Transform dialog box then click the O pen button and open the ZPLANE XFM transform in the XFM S directory If necessary change the res variable
154. er to be determined by the regression define the value for that constant here then make sure you dont enter this value in the parameters section Constants defined here appear under the Constants option in the Regression O ptions dialog box Independent dependent and weighting variables are defined in the Variables section O ne of the variables defined must be the observed values of the dependent variable that is the unknown variable to be solved for T he rest are the independent variables predictor or Known variables and an optional weighting variable To define your variables 1 Click in the Variables section and type the character or string you used for the first variable in your regression equation 2 Typean equal sign then enter a range for the variable Ranges can be any transform language function that produces a range but typically is simply a worksheet column N ote that the variable values used by the Regression W izard depend entirely on what are selected from the graph or worksheet the values entered here are only used if the From C ode data format is selected or if the regression is run directly from the Regression dialog box 3 Repeat these steps for each variable in your equation Up to ten independent variables can be defined but you must define at least one variable for a regres sion equation to function T he curve fitter checks the variable definitions for errors and for consistency with the
155. es Hore terations Asq 0 977619532 Norm 0 593295879 Vien Constraints Value StdE rr Cv re Dependencies 9 400e 1 3593 1 3 822e 1 0 618188 1240e 0 1083 1 8 7 3be 0 0 8181818 E Hep Cancel Back New Finish The next column is an estimate of the standard error for each parameter T he intercept has a standard error of about 0 36 not that good and the slope has a standard error of about 0 10 which isn t bad Thethird column isthe coefficient of variation CV for each parameter T his is defined as the standard error divided by the parameter value expressed as a percentage The CV for the intercept is about 38 2 which is large in com parison to the CV for the dope about 8 7 Lesson 1 Linear Curve Fit 207 Regression Lessons T he dependencies are shown in the last column If these numbers are very close to 1 0 they indicate a dependency between two or more parameters and you can probably remove one of them from your model Adding a Parameter To make y always positive when x is positive you cannot have a negative y intercept Constraint You can recalculate the regression with this condition by constraining the parameter Yq to be positive T hat way y will never be negative when x gt 0 1 From the initial results panel click Back T he variables panel is displayed 2 Click the Options button T he O ptions dialog box is displayed Enter a value of y0 gt 0 into the Constraints
156. es dialog box for notebook files Count Property A property available to all collection objects that returns the number of objects within that collection CurrentDataltem TheCurrentD ataltem property returns the worksheet window in focus as an object Property You must still use the ActiveD ocument property to specify the currently active notebook N ote that if a worksheet is not in focus an error is returned Currentltem Property This property returns whatever notebook item currently has focus as an object You must still use the ActiveD ocument property to specify the currently active notebook CurrentPageltem Returnsthe current graph page window asa Graphitem object You must still use the Property ActiveD ocument property to specify the currently active notebook If the current item in focus is not a page an error is returned DataTable Property Returns the D ataT able object for the specified worksheet object DefaultPath Property Sets or returns the default path used by the Application object to save and retrieve files Files are opened using the N otebooks collection O pen method and saved using the N otebook object Save or SaveAs methods DropLines Property Returns the DropLines line collection for a Plot object Line objects within the D ropLines collection have standard line properties Use an index to return a specific set of drop lines from the D ropLines collection 1 XYplane SLA FLAG DROPZ 3D graphs only 2 Y axis X dir
157. es uniformly random numbers distributed between 0 and 7 using 2 as a seed H owever the numbers generated have fifteen significant digits To round off the numbers to two decimal places modify this function to read X round random 15 2 0 7 2 3 Press Enter then type col 1 x to place the random numbers in column 1 4 Press Enter and type col 2 1 Recoded Recoding Example 15 Transform Tutorial Figure 3 5 Results of the Recoding Example Transform 16 Recoding Example N ote the space between the d and the quotation mark All characters including space characters within quotes are entered into cells as part of the label Press Enter then type col 2 2 Variable To create the code data press Enter then type col 3 if x lt 2 small Press Enter add a couple of spaces then type if x gt 2 and x lt medium large If you want an equation to use more than one line start each additional line with a blank space or two to distinguish it from anew equation Click Run If you have entered all the transform equations correctly the data will appear as shown in Figure 3 5 2 E 4 6600 esis e S e 4 3600 a a m4400 E a 2m0 mean CS 4 2900 medium g esoo tage o o S 10 35400 medum o o 11 3300 medum o o 14 saoo mein CS 15 3 3500 u You can save your new data with the Save command from the File menu Transform Operators
158. ession procedure are gt thefunction results saved to the worksheet gt astatistical report gt acopy of the regression equation To save the regression results using the default save setting click Finish at any point the Finish button Is active If you want to see or modify the results that are produced you can use the N ext button to advance to the results options panel Function results can be saved to the current worksheet T hese are gt equation parameter values gt predicted values of the dependent variable for each independent variable value gt residuals or the difference between the predicted and observed dependent variable values Saving Regression Results 165 Regression Wizard Figure 8 22 Generating and Saving a Report from the Regression Wizard Saving a Report Adding the Equation to the Notebook To place any of these values in a column in the worksheet simply check the results you want to keep If you want to set a specific column in which to always place these values you can click a column on a worksheet for each result Regression Wizard Columns Select the columns for your results jave First Empty Results Tave As Parameters First Empty Predicted First Empty Residuals First Empty 56 190 Az M Report Add Equation to Notebook Help Cancel Back i Finish Regression reports are saved to the current section by checking the Report option For mor
159. ession W izard command 2 Click Back to view the library panel To change the library used enter the new library path and name or click Browse 3 TheFileO pen dialog box appears Change the path and select the file to use as your regression library When you start the Regression W izard next it will con tinue to use the equation library selected in the library panel N ote that opening a regression equation directly from a notebook does not reset the equation library Curve Fitting Date And Time Data Figure 8 31 You can curve fit dates but you must convert the dates to numbers first Time only data as shown in column 1 does not require a conversion You can run the Regression wizard on data plotted versus calendar times and dates D ates within and near the twentieth century are stored internally as very large numbers H owever you can convert these dates to relatively small numbers by setting D ay Zero to the first date of your date then converting the date data to numbers After curve fitting the data you can switch the numbers back to dates 01 00 00 4 i 01 15 00 ap0azg7 20000 01 30 00 Aporer 40000 01 45 00 02 00 00 Fy Graph Page 1 Data 17 BE Ea 02 15 00 02 30 00 02 45 00 03 00 00 03 15 00 03 30 00 03 45 00 04 00 00 04 15 00 04 30 00 e ae i 1 Wi m a a a a oa a oc If you have entered clock times only then you can directly curve fit those time without hav
160. et whose title matches the string D ata placed in a cell inserts or overwrites according to the current insert mode For the worksheet shown in Figure 5 1 both the operations cell 2 3 and cell EXP2 3 return a value of 0 5 For the worksheet shown in Figure 5 1 the operation cell 3 3 64 cell 2 3 raises 64 to the power of the number in cell 2 3 and places the result in cell 3 3 col 2 D 0 00 7 Oo a a a e a L l r 4 F Transform Function Descriptions 33 Transform Function Reference choose summary syntax Examples col summary syntax Example 1 Example 2 T he choose function determines the number of ways of choosing r objects from n distinct objects without regard to order choose n r For the arguments n and r r lt n and n chooser is defined as o B Oon r rn n r To create a function for the binomial distribution enter the equation binomial p n r choose n r p r 1 p n r T he col function returns all or a portion of a worksheet column and can specify a column destination for transform results col column top bottom The column argument is the column number or title To use a column title for the column argument enclose the title in quotation marks T he top and bottom arguments specify the first and last row numbers and can be omitted T he default row numbers are 1 and the end of the column respectively if both are
161. etc can only be returned or set using the G etAttribute and SetAttribute methods Use the Axis Attribute constants to specify these attributes 260 SigmaPlot Objects and Collections Text Object Line Object Symbol Object SigmaPlot Automation Reference All characters and labels found on a SigmaPlot change correspond to atext object and can be modified using text object properties and methods Axes have an O bjectT ype value of 5 or GPT TEXT To use the Text Object The Text object for most graph objects can be returned using the N ameO bject property Text objects are also found below both AutoLegend and Axis objects Use the TickLabelAttributes property to access the tick label Text object Use the AxisT itles property to access the axis titles To access the text objects within a Page or an AutoLegend use the ChildO bjects property Use the N ame property to change the string used for the text M ost other Text attributes and attribute values can only be returned or set using the G etAttribute and SetAttribute methods Use the Text Attribute constants to specify these attributes O bjects that correspond to drawn lines T hese lines include all lines used for axes and plots regression and reference lines drop lines and manually drawn lines Lines have an O bjectType value of 6 or GPT _LIN E To use the Lines Object Lines are returned from anumber of different objects D rawn lines on a page are returned using the
162. eter Triple 6 Parameter Edit Code Triple T Parameter E C Help Cancel Back Next T he results show that the dependencies are not near 1 0 indicating that the sin gle exponential parameters a and b are not dependent on one another Figure 11 20 Regression Wizard The Results of Fitting the Data Converged tolerance satisfied eean to a Single Exponential Asqr 0 993760026 Norn 0 092999738 View Constraints Value StdErr Cwi Dependencies a 9 7 98e 1 1 546e 2 1 578e 0 3083758 b 6 11 e 1 218le2 2 687e 0 0 3083758 z O Hep Cancel Back j Finish 4 Click Back twice and change the equation to the D ouble 4 parameter exponen tial decay equation C lick N ext twice x Figure 11 21 Regression Wizard Selecting the 4 Parameter Equation Category Double Exponential Decay Select the equation to fit your data save Equation Exponential Decay Equation Mame save As Single 2 Parameter Single 3 Parameter Double 4 Parameter Hew Double 5 Parameter Edit Code i Triple amp Parameter Triple 7 Parameter ee ee er Oa E a POEN _ Help _ Cancel Back New Erin 230 Example 4 Using Dependencies Advanced Regression Examples T he results show that the parameter dependencies for the double exponential are acceptable indicating that they are unlikely to be dependent and that using a double exponential produces a better fit the curve fitt
163. eter New Logistic 3 Parameter Logistic 4 Parameter Edit Code Weibull 4 Parameter ee eee ee ee ee Help Cancel Back Next Finizh E Click N ext twice If you have correctly selected the curve the Iterations dialog box appears displaying the value for each parameter and the norm for each iter ation N ote that the iterations proceed more slowly than those for the linear fit T hisis because the equation is much more complex and there are more parameters Watch the norm value decrease this number is an index of the fit closeness and decreases as the fit improves W hen the fit condition is satisfied the initial results are displayed Examine the results T he first column displays the parameter value and the next column displays the estimated standard error The third column is the coeffi cient of variation CV for each parameter N ote that these CV values are unrealistically good the largest is about 3 9 Generally CV values for physiological measurements are greater than 5 Regression Wizard Converged tolerance satisfied Samaras Req 0 999450833 Nom 4 159974939 View Constraints Parameter Value StdErr Cy rs Dependencies a q 133e 4 1 097 e 0 9684 1 0 65587 66 b FO0l3e 0 271961 3 876e 0 0 3366703 0 B 68le 3 093e 1 4 495e 0 3420053 yi 4124 6215e 1 1 507e 0 06171334 E o Hep Cancel Back i Mert i Finish True nonlinear regression problems
164. eter f was chosen to be 1 Visualizing Data William S Cleveland 118 Graphing Transform Examples Figure 6 14 U S Wheat data and the lowess smoothed curve f 0 2 Notice the definite decreased production during World War Il Example Transforms 0 2 since this produced a good tradeoff between noisy undersmoothing and oversmoothing which misses some of the peak and valley details in the data Production bushels x 10 Lowess Smoothed U S Wheat Production 1400 1200 1200 1000 1000 800 600 e Sou 2e 400 T T T T T 200 T T T T T 1860 1880 1900 1920 1940 1960 1980 1860 1880 1900 1920 1940 1960 1980 1400 1200 1000 800 5 600 400 5 200 T T T T T 1860 1880 1900 1920 1940 1960 1980 To use the provided sample data and graph open the Lowess Smoothing work sheet and graph in the Lowess Smoothing section of the Transform Examples notebook T he worksheet appears with data in columns 1 2 and 3 To use your own data enter the XY data for your curvein columns 1 and 2 respectively If your data has been placed in other columns you can specify these columns after you open the LOWESS XFM transform file Enter data into an existing or anew worksheet Press F10 to open the User D efined Transform dialog box then click the O pen button and open the LOW ESS XFM transform filein the XFM S directory The Lowess transform appears in the
165. ethod using a value of 9 After defining the transform object open it using the O pen method Specify the transform code using the Text property To change the value of a transform variable use the AddVariableE xpression method Run transforms using the Execute method N ote After executing a transform it is a good idea to close it as you are limited to four concurrent transforms that can be open simultaneously A Reportltem represents the RTF Rich Text Format documents used for text and regression reports in SigmaPlot You can use the Reportl tem properties to add and remove block of text from a report To use the Reportitem Object The Reportiten object has the standard notebook item properties and methods A Reportitem is returned from the N otebookltems collection using the Item property or collection index and created using the N otebookltems Add method SigmaPlot reports have an ItemT ype property and N otebookltems Add method value of value of 5 and SigmaStat reports have a value of 4 Represents a SigmaPlot macro You can use this command to edit and run macros from within macros or to run macros from outside applications To use the Macroltem Object TheM acroltem object has the standard notebook item properties and methods A M acroltem is returned from the N otebookl tems collection using the Item property SigmaPlot Objects and Collections 265 SigmaPlot Automation Reference Notebookltem Object sectionltem Obj
166. f d 0 1 d es olci Mmi Col Ci Arange ig fr sr t sr g Fg 5g CS9 b IDS p CFO OUCPUT COL CO robcolor r 9g b place colors Into worksheet Survival Kaplan Meier Curves with Censored Data T his transform creates K aplan M eier survival curves with or without censored data T he survival curve may be graphed alone or with the data To usethe transform you can either use the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 Tousethe sample worksheet and graph double click the graph page icon in the Survival section of the Transforms Examples notebook T he Survival worksheet appears with data in columns 1 and 2 T he graph page appears with an empty graph If you open the sample worksheet and graph skip to step 7 2 To use your own data enter survival times in column 1 of the worksheet Ties identical survival times are allowed You can enter data into an existing or a new worksheet 3 Enter the censoring identifier in column 2 T his identifier should be 1 if the cor responding data point in column 1 isa true response and 0 if the data is cen sored 4 If desired save the unsorted data by copying the data to two other columns 5 Select columns 1 and 2 then choose the Transforms menu Sort Selection com mand Specify the key column in the Sort Selection dialog box as column 1 and Graphing Transform Examples 129
167. f Degrees i Radians f Grads variable that is the unknown variable to be solved for T he rest are the independent variables predictor or Known variables and any optional weighting variables U p to ten independent variables can be defined To define your variables select the Variables edit window then type the variable definitions You generally need to define at least two variables one for the dependent variable data and at least one for the independent variable data Variable definitions use the form variable range You can use any valid variable name but short single letter names are recommended for the sake of simplicity for example x and y T he range can either be the column number for the data associated with each variable or a manually entered range M ost typically the range is data read from a worksheet T he curve fitter uses SigmaPlot s transform language so the notation for a column number is col column top bottom The column argument determines the column number or title To use a column title for the column argument enclose the column title in quotation marks T he top and bottom arguments specify the first and last row numbers and can be omitted The default row numbers are 1 and the end of the column respectively If both are omitted the entire column is used For example to define the variable x to be column 1 enter x col 1 D ata may also be entered directly in the variables
168. f methods as verbs For example the WorksheetEditltem object has Copy and Clear methods M ethods can have parameters that specify the action adverbs For more information refer to SigmaPlot Automation H elp from the SigmaPlot H elp menu SigmaPlot Methods 275 SigmaPlot Automation Reference Activate Method Makesthe specified notebook the object specified by the ActiveD ocument property Add Method TheAdd method is used in collections to add a new item to the collection The parameters depend on the collection type a a Proteins e roe Ooo p oome ene erates Ce ee Oooo p ooe fe ooe Oooo p osoa a E enorme errno TS errrenee orn ore sso ferrous ferrin ie formeo a orme errr N amedR anges Name string Left long Top long Width long H eight long N amedR ange 276 SigmaPlot Methods AddVariable Expression Method ApplyPageTemplate Method AddWizardAxis Method SigmaPlot Automation Reference The GraphO bjects collection uses the CreateG ranhFromTemplate and CreateW izardG raph methods to create new GraphO bject objects Allows the substitution of any transform variable with a value O verwrites the current G raphl tem using anew page template specified by the template name O ptionally you can specify the notebook file to use as the source of the template page If no template file is specified the default template notebook is used as returned by the Template property Adds an additiona
169. f two are omitted the last two arguments are set to the default value You can use a missing value i e 0 0 as a placeholder to omit an argument Example T he col function has three arguments column top and bottom T herefore the syntax for the col function is col column top bottom Thecolumn number argument is required but the first top and last bottom rows are optional defaulting to row 1 asthe first row and the last row with data for the last row col 2 returns the entirety of column 2 col 2 5 returns column 2 from row 5 to the end of the column col 2 5 100 returns column 2 from row 5 to row 100 col 2 0 0 50 returns column 2 from row 1 to the 50th row in the column Function Arguments 21 Transform Function Reference Transform Function Descriptions Worksheet Functions Data Manipulation Functions T he following list groups transforms by function type It is followed by an alphabetical reference containing complete descriptions of all transform functions and their syntax with examples T hese worksheet functions are used to specify cells and columns from the worksheet either to read data from the worksheet for transformation or to specify a destination for transform results bok sha blocCTuncHon alimica a o eao block function returns a specified block of cells from the worksheet blockheight block T he blockheight and blockwidth functions return a speci width fied block of cells or bl
170. f2e t0 1 720e 2 8 290e 1 0 2497 759 T a0 le 1 715e1 5 716e 1 0 405022 x Help Cancel Back a Einish A message displaying the condition under which the regression completed is displayed in the upper left corner of the Regression W izard If the regression completed with convergence the message Converged tolerance satisfied is disolayed O therwise another status or error message is displayed For a description of these messages see Regression Results M essages on page 181 R is the coefficient of determination the most common measure of how well a regression model describes the data T he closer R is to one the better the independent variables predict the dependent variable R2 equals 0 when the values of the independent variable does not allow any prediction of the dependent variables and equals 1 when you can perfectly predict the dependent variables from the independent variables T he initial results are displayed in the results window in five columns Parameter T he parameter names are shown in the first column T hese parameters are derived from the original equation Value T he calculated parameter values are shown in the second column StdErr The asymptotic standard errors of the parameters are displayed in column three T he standard errors and coefficients of variation see next can be used asa gauge of the fitted curve s accuracy Interpreting Initial Results 163 Regression Wizard
171. file If necessary specify a new column for the results 3 PressF10 to open the User D efined Transform dialog box then click the O pen button and open GAIN FILT XFM transform file in the XFM S directory The Gain Filter transform appears in the edit window X To use this transform make sure Insert mode is turned off 4 Click Run T he results are placed in column 5 unless you specified a different column in the transform 5 If you opened the Gain Filter Smoothing graph view the graph page T hree graphs appear T he top graph plots the signal plus the noise distortion using a Line Plot with a Simple Straight line style and Single Y data format plotting col umn 1 asthe Y data for the signal plus noise T he middle graph plots the power spectral density using a Line Plot with a Simple Straight Line style and XY Pairs data format plotting column 2 asthe X data and column 3 asthe Y data for the power spectral density graph T he lower graph isa plot of the gain filtered signal using a Line Plot with a Simple Straight Line style and single Y data format from column 5 6 To plot your own data using SigmaPlot choose the G raph menu Create Graph command or select the G raph W izard from the toolbar C reate two graphs Plot the signal plus the noise distortion using a Line Plot with a Simple Straight line style and Single Y data format plotting column 1 asthe Y data for the signal plus noise Plot the gain filtered signal using a Line P
172. form is a smoothing filter which produces a data sequence with reduced high frequency components T he resulting data can be graphed using the original X data To calculate and graph a data sequence with reduced high frequency components you can either use the provided sample data and graph or begin a new notebook enter your own data and create your own graph using the data 1 To usethe provided sample data and graph double click the Low Pass Filter graph page icon in the Low Pass Filter section of the Transform Examples note book T he worksheet appears with data in columns 1 and 2 The graph page appears with two graphs T he first is a line graph plotting the raw data in col umns 1 and 2 see Figure 6 11 on page 112 T he second graph is empty 2 To useyour own data place your Y data amplitude in column 2 of the work sheet and the X data time in column 1 If your data isin other columns you can specify these columns after you open the LOW PFILT XFM file You can enter your data in an existing or new worksheet 3 PressF10 to open the User D efined Transform dialog box then click the O pen button and open the LOW PFILT XFM transform file in the XFM S directory T he Low Pass Filter transform appears in the edit window 4 Set the sampling interval dt the time interval between data points and the half power point fc values T he half power point is the frequency at which the 116 Graphing Transform Examples Figure 6 13 L
173. form normalizes a bar chart to unit area Box locations are shifted since bars are drawn about their center points Place your sample data in x_col or change the column number to suit your data Results are placed in columns res through restl x_col 1 sample data column res 2 first results column Set histogram box width and upper limit PIMES O9 upper limit of last box delta 0 5 histogram box width x col x_col Graphing Transform Examples 121 Example Transforms x x CALCULATE AND NORMALIZE HISTOGRAM DATA r data delta limit delta histogram boxes h histogram x Tr create histogram hli h data 1 size h 1 remove last box Sherk bar center locations xl r delta 2 histogram x values normalize histogram Vien total al delta histogram Y values PLACE NORMALIZED HISTOGRAM DATA IN WORKSHEET col res xl col rest 1l yl shading Beneath Line Plot Curves T hese are a pair of transforms that use two different methods to draw colors or hatches below a curve SH ADE_1 XFM uses bar chart fills or colors to fill the area below a curve T his method must be used If you want to fill with a color however you can only shade to an axis and you can only use the default W indows fill patterns SHADE _ 2 XFM uses line plots to fill below curves T his transform can also be used to draw fill lines between two curves Shading Below a To usthis transform to create
174. g a 0 7 L l Transform Function Descriptions 53 Transform Function Reference mod summary syntax Example mulcpx summary syntax Example Related Functions nth summary syntax The mod function returns the modulus the remainder from division for corresponding numbers in numerator and divisor arguments T his is the real not integral modulus so both ranges may be nonintegral values mod numerator divisor The numerator and divisor arguments can be scalars or ranges Any missing value or text string contained within arange is returned as the string or missing value For any divisor 0 the mod function returns the remainder of ease ivisor For mod x 0 that is for divisor 0 X gt 0 returns 00 X 0 returns 00 X lt 0 returns oo T he operation mod 4 5 4 5 2 2 3 3 returns the range 0 1 1 2 T hese are the remainders for 4 2 5 2 4 3 and 5 3 T he mulcpx function multiplies two blocks of complex numbers together mulcpx block block Both input blocks should be the same length T he mulcpx function returns a block that contains the complex multiplication of the two ranges If u 4 1 1 0 10 1 1 the operation mulcpx u u returns 1 0 1 0 2 0 fft invfft real imaginary complex invcpx Thenth function returns a sampling of a provided range with the frequency indicated by a scalar number T he result always begins with the first entr
175. g box Any missing value or text string contained within a range is ignored and returned as the string or missing value T he operation x cosh col 2 sets the variable x to be the hyperbolic cosine of all data in column 2 sinh tanh The count function returns the value or range of values equal to the number of non missing numeric values in arange M issing values and text strings are not counted count range T he range argument must be a single range indicated with the brackets or a worksheet column 36 Transform Function Descriptions ee Examples Related Functions Figure 5 3 data summary syntax Examples Related Functions Transform Function Reference For the worksheet in Figure 5 1 the operation count col 1 returns a value of 5 the operation count col 2 returns a value of 6 and the operation count col 3 returns a value of 0 missing size 2 3 2 3000 Sample 1 2 5 9000 0 o 3 B 2000 F000 4 7 1000 ee S S 5 asooo seo D To o B 9 5000 10 2000 i O 7 o Oooo o y a 5 0 1 L l T he data function generates a range of numbers from a starting number to an end number in specified increments data start top te All arguments must be scalar T he tart argument specifies the beginning number and the end argument sets the last number If the tep parameter is omitted it defaults to 1 T he start parameter can be more than or less than the stop pa
176. gence to a local minimum and alocal maximum 1 Findingalocal minimum Click Back then click the O ptions button Change the initial value of Xp to 10 using the drop down Parameter Values list 222 Curve Fitting Pitfalls Figure 11 8 Changing the Initial Parameter Value of xg to 10 and the Tolerance to 0 0001 Figure 11 9 The Nonlinear Regression Results Using an Initial Parameter Value of Xq 10 Advanced Regression Examples Ea Regression Options Initial Parameters Parameter Constraints Cancel Help Options Iterations 100 Shep Size 100 Tolerance n 000 Constants Fit With Weight none k Select the Tolerance option and change the tolerance back to the default value of 0 0001 then click OK Click N ext The regression converges to Xo 4 03 which corresponds to the local minimum Hore Iterations view lonstraints Regression Wizard Converged tolerance satisfied Reg Norm 0 763206307 Parameter Value StdErr Cy re Dependencies xO 4030e 0 1 871e 0 46426 1 0 0000000 Help Cancel Back Einish In this example you know that a local minimum was found by viewing the sum of squares function for the single parameter Xo H owever when there are many parameters it is usually not obvious whether an absolute minimum or a local minimum has been found Finding a local maximum Click Back then click the O ptions button C hange the i
177. ggles the breakpoint on the current line T he breakpoint stops program execution Quick View Shows the value of the expression under the cursor in the Immediate W indow O pens the M acros dialog box D ialog Box Editor O pens the D ialog Box Editor O bject Browser O pens the O bject Browser Reference O pens the R eference dialog box which contains a list of all programs that are extensions of the SigmaPlot Basic language Editing Macros 247 Automating Routine Tasks Color Coded Display T he color coding of text in the M acro W indow indicates what type of code you are viewing T he following table describes the default text colors used in the script text Blue Identifies reserved words in Visual Basic for example Sub End Sub and Dim M agenta Identifies SigmaPlot macro commands and functions Green Identifies comments in your macro code Separates program documentation from the code as you read through your macros Object and TheObject and Procedure lists show SigmaPlot objects and procedures for the Procedure Lists current macro T hese lists are useful when your macros become longer and more complex gt Theobject identified as General groups all of the procedures that are not part of any specific object gt TheProcedure list shows all of the procedures for the currently selected object Setting Macro You can set appearance options for the M acro window in the M acros tab of the Window Option
178. gument sinh numbers T he numbers argument can be a scalar or range Like the circular trig functions this function also accepts numbers in degrees radians or grads depending on the units selected in the U ser D efined Transform dialog box T he operation x sinh col 3 sets the variable x to be the hyperbolic sine of all data in column 3 cosh tanh Thesinp function automatically generates the initial parameter estimates for a sinusoidal functions using the FFT method T he three parameter estimates are returned as a vector sinp x range y range T hex range argument specifies the x variable and the y range argument specifies the y variable Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must be the same size and the number of valid data points must be greater than or equal to 3 sinp is especially used to perform smoothing on waveform functions used in determination of initial parameter estimates for nonlinear regression The size function returns a value equal to the total number of elements in the specified range including all numbers missing values and text strings Notethat size X 2 count X missing X size range T he range argument must be a single range indicated with the brackets or a worksheet column Transform Function Descriptions 61 Transform Function Reference Example Related Func
179. h 3 Click Finish to complete the regression or click N ext if you want to view initial results or change your results options Creating New Regression Equations You can create new regression equations two different ways by using the N ew button in the Regression W izard or by creating a new item for a notebook W hen you create a new equation the Regression editing dialog box appears with blank headings For information on how to fill in these headings see Editing C ode on page 185 152 Creating New Regression Equations Regression Wizard Viewing and Editing Code Viewing Code To view the code for the current equation document click the Edit Code button For more information see Editing Code on page 185 You can click the Edit Code button from the equation or variables panels T he Edit Code button opens the Regression dialog box All settings for the equation are displayed Figure 8 8 Viewing the code for a built in equation in the Regression dialog box Regression Gaussian 3 Parameter Equations fea expl 5 k xO b 2 Fit Fto y yecallZ Automatic Initial Parameter E peaksign ql it tatal g q 1 1 satyminjg rj satumasig mair Run Initial Parameters a if peaksign y gt 0 masiy miniy A b fwhmis abaly 2 2 Auta ii peaksigniy 0 ratymanis y xa Options Iterations fioo Step Size fioo Tolerance fo oo01 O0 Trigonometric Units f Degrees i R
180. he D ata section in the Plots tab of the Graph Properties dialog box As shown in Figure6 19 atied censored data point has been incorrectly placed it should follow uncensored data 10 To graph a survival curve using SigmaPlot create a Line graph with a Simple H orizontal Step Plot graphing column res as the X data versus column res l as the Y data If desired create an additional Scatter plot superimposing the sur vival data using the same columns for X data and Y data To turn off the symbol drawn at x 0 and y 1 select Plot 2 and set Only rows 2 to end by 1 in the 130 Graphing Transform Examples ee Example Transforms Plots tab and D ata sections of the Graph Properties dialog box For more information on creating graphs see the SigmaP lot U s s M anual Survival Transform Kaplan Meier Survival Curves with Censored Data SURVIVAL XFM This transform calculates cumulative survival probabilities and their standard errors Enter survival times in column sur_col anda censor index in column cen_col 0O censored 1l not or change the column numbers to suit your data Results are placed in columns res and restl Procedure 1 sort by increasing survival time 2 place censored data last if ties 3 run this transform 4 plot survival data as columns 3 vs 4 as f a stepped line shape with symbols sur_col 1 cen_col 2 res 3 sur col sur_col survival data cen col cen_col Censored data TARAKEA C
181. he progress 162 Relational operators transforms 19 20 Reports regression 167 175 Residual tests D urbin W atson statistic 171 PRESS statistic 171 Residuals effect of weighting 197 regression diagnostic results 172 Standardized 172 studentized 173 310 Studentized deleted 173 Results completion status messages 181 182 error status messages 182 183 regression 163 166 205 208 214 regression messages 163 181 183 saving regression 165 166 viewing constraints 164 RGBCOLOR function 58 ROUND function 59 RUN AVG function 59 S Sample transforms 71 140 Satisfying tolerance 181 182 Saving regression equation changes 162 regression results 165 166 209 211 transforms 4 14 user defined transforms 70 Scalars operators 18 20 Scale probability 109 Scale axis user defined axis 131 133 Settings regression equations 188 Shading between curves 124 Shading pattern transform for line plot curve 122 127 SigmaPlot Basic introduction 2 SIN function 60 SINH function 61 SIN P function 61 SIZE function 61 111 Smooth color transition transform 127 129 Smoothing Fast Fourier transforms 93 105 gain filter 102 kernal 97 low pass filter 99 116 118 Solving differential equations 76 80 SORT function 62 Special construct functions 27 SQRT function 63 Square brackets in transforms 9 Standard deviation of linear regression coefficients trans form 83 84 Standard error parameter 163 207
182. he regression If you used parameter constraints you can determine if the regression results involved any constraints by clicking the View Constraints button T his button is dimmed if no constraints were entered Constraints Linear p active T he Constraints dialog box displays all constraints and flags the ones encountered with the word active A constraint is flagged as active when the parameter values lie on the constraint boundary For example the constraint a b lt 1 164 Interpreting Initial Results Quitting the Regression Regression Wizard is active when the parameters satisfy the condition a b 1 but if a b lt 1 the constraint is inactive N ote that an equality constraint is always active unless there are constraint inconsistencies If the regression results are unsatisfactory you can click Back and change the equation or other options or you can select Cancel to close the wizard If you want to keep your results click Finish You can also click N ext to specify which results you want to keep saving Regression Results Saving the Results using Default Settings Saving Results to the Worksheet Regression reports and other data results are saved using the Regression W izard results options panel which appears after the initial results panel Settings made here are retained from session to session T he type of data results that can be saved to the current notebook for each regr
183. he slope of the regression Alpha a Alpha is the acceptable probability of incorrectly concluding that the model is correct An error is also called a Type I error a Type error is when you reject the hypothesis of no association when this hypothesis is true Smaller values of result in stricter requirements before concluding the model is correct but a greater possibility of concluding the model is incorrect when it is really correct a Type II error Larger values of make it easier to conclude that the model is correct but also increase the risk of accepting an incorrect model a Type error T he regression diagnostic results display the values for the predicted values residuals and other diagnostic results Row Thisisthe row number of the observation Predicted Values T hisis the value for the dependent variable predicted by the regression model for each observation Residuals T hese are the unweighted raw residuals the difference between the predicted and observed values for the dependent variables Standardized Residuals T he standardized residual is the raw residual divided by the standard error of the estimate Sx If the residuals are normally distributed about the regression about 66 of the standardized residuals have values between 1 and 1 and about 95 of the standardized residuals have values between 2 and 2 A larger standardized residual indicates that the point is far from the regression
184. he step size value type a new value into the edit box T he step size number equals the largest step size allowed when changing parameter values Changing the step size to a much smaller number can be used to prevent the curve fitter from taking large initial steos when searching around suspected minima For an example of the possible effects of step size see C urve Fitting Pitfalls on page 219 If you are familiar with this algorithm step size is the inverse of the M arquardt parameter T he Tolerance option controls the conditions that must be met in order to end the regression process W hen the absolute value of the difference between the norm of the residuals from one iteration to the next is less than the tolerance the regression is considered to be complete Other Options 201 Editing Code T he curve fitter uses two stopping criteria gt When the absolute value of the difference between the norm of the residuals square root of the sum of squares of the residuals from one iteration to the next is less than the tolerance value the iteration stops gt When all parameter values stop changing in all significant places the regression stops W hen the tolerance condition has been met a minimum has usually been found T he default value for tolerance is 0 0001 To change the tolerance value type the required value in the Tolerance edit box T he tolerance number sets the value that must be met to end the itera
185. he y variable Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must be the same size and the number of valid data points must be greater than or equal to 3 T he optional f argument defines whether FFT and IFFT are used f must be greater than or equal to 0 and less than or equal to 100 0 lt f lt 100 If f is omitted no Fourier transformation is used lowpass is especially designed to perform smoothing on waveform functions as a part of nonlinear regression Transform Function Descriptions 51 Transform Function Reference Example Related Functions max summary syntax Example mean summary syntax Example Related Functions For x 0 1 2 y 0 1 4 the operation col 1 Sowpass x y 88 places the newly smoothed data 0 25 1 50 2 25 into column 1 lowess T he max function returns the largest number found in the range specified max range T he range argument must be a single range indicated with the brackets or a worksheet column Any missing value or text string contained within a range is ignored For x 7 4 4 5 the operation max x returns a value of 7 and the operation min x returns a value of 4 T he mean function returns the average of the range specified Use this function to calculate column averages as opposed to using the avg function to calculate row averages T he mean f
186. ic Parameters O 4uUtomeatic a 4utomatic Fit ith Weight Constants that appear in the Constants edit window have been previously defined as a constant rather than a parameter to be determined by the regression To edit a constant value or define new constant values use the Edit C ode option of the W izard dialog box For more information on editing and defining new constant values see D efining Constants on page 190 Constants are defined when an equation is created Currently you can only define new constants by editing the regression equation code H owever you can redefine any existing constants C hange only the value of the constant Do not add new constant values constant variables must exist in the equation and not be defined already under variables or parameters so they can only be defined within the code of an equation You can select from any of the weights listed Some built in equations have some predefined values although most do not If no weighting options are available for your equation only the N one option will be available Figure 8 15 Selecting a Predefined Weight Variable Iterations Figure 8 16 Changing Iterations Regression Wizard Weighting options appear in the Fit with Weight drop down list By default the weighting applied to the fit is None To apply a different weighting setting select a weighting option from the drop down list
187. ic Unite f Degrees i Radians f Grads Examine the fit statements T he fit equation is an if statement which uses differ ent equations depending on the value of d which is the data set identifier vari able If d 0 the data is fit to f1 if d 1 the data is fit to f2 and if d 2 the data is fit to f3 T hefunctions share theT and n parameters but have individual E parameters of E E gt and E3 Click Run to execute the regression T he fit proceeds slowly but fits each data set to the separate equation Click N ext to ensure that the Predicted function results are saved to the worksheet then N ext again and make sure no graph is being cre ated Click Finish to end the fit To graph the results you need to create a plot of the predicted results View the page and select the graph then create a straight line plot of rows 1 12 of column Example 6 Multiple Function Nonlinear Regression 235 Advanced Regression Examples 1 versus rows 1 12 of the predicted results column Figure 11 30 Creating a Plot of a DECE Restricted Data nz 1 2 3 Range 326 5e 18 0 00 0 00 498 8e 12 04 000 87 85e 15 OF 000 4547615 018 0 00 46 50e 15 33 0 00 5 687e 15 50 0 00 797 6e 9 0 58 000 48 50e 12 BF 000 9 6784918948 00 069 D00 10 24 96e 9 ann 11 798 8e 18 D069 12 oro 6e 9 DoM Data forr 13 499 5e 9 cous sd 14 456 5e 12 MEME Ss Sclectthe ee 15 321 3e 15 e akani e Selected Columns 16 15 92e 12 EE aN
188. iew the graph page T he graph auto matically appears plotting the curve of the original data and the data represent ing the shade under the curve If you created your own graph see step 3 and you want to use SigmaPlot to plot the shade under the curve add the shade under the curve by creating a Sim ple Vertical Bar Chart that plots columns 3 and 4 setting the bar width to max imum and the bar fill to either no pattern and the same color fill and edge as the line or with a default W indows hatch pattern and fill and edge colors of none For more information on creating graphs in SigmaPlot see the SigmaPlot U s s M anual Y Axis Shading Below a Curve with Color Gee ODALA CO A ALIO VEFFE This transform uses vertical bars to create a fill between a curve and an axis The x data MUST be sorted in increasing or decreasing order Graphing Transform Examples 123 Example Transforms Apply this transform to your x y data column pair y KKKKKKKKKKKK Input KKKKKKKKKKKK x data col l column for x data y data col zZ column for y data density 200 The density determines how many bars are used to create the fill under the curve The larger the density the more bars are used and the longer the graph takes to draw or print For relatively flat curves try using a smaller value for the density like about 150 For sharply peaked curves it may be necessary
189. ighting multiplies the corresponding squared term in the sum of squares dividing the absolute value of the residual by its standard error T his Weight Variables 197 Editing Code causes all terms of the sum of squares to have a similar contribution resulting in an improved regression For weighted least squares the weights w are included in the sum of squares to be minimized ae SS Y wiy i 1 W hen weighting is used the norm that is computed and displayed in the Progress dialog box and initial resultsis S S and includes the effect of weighting The residuals computed are the weighted residuals w y 3 Initial Parameters Initial Param eter Values Automatic Parameter Estimation 198 nitial Parameters T hecodeunder the nitial Parameters section specify which equation coefficients and constants to vary and also set the initial parameter values for the regression To enter parameters select the Initial Parameters window then type the parameters definitions using the form paramete initial value All parameters must appear in the equation model All equation unknowns not defined as variables or constants must be defined in Initial Parameters For the initial values a best guess may speed up the regression process If your equation is relatively simple only two or three parameters the initial parameter values may not be important For more complex equations however good initial parameter
190. igmaPlot macros you can automatically create the necessary dialog box code and dialog monitor function code with the D ialog Box About user defined functions 251 Automating Routine Tasks Editor Like the other automated coding features in SigmaPlot the code may require further customization To create a custom dialog box 1 IntheM acro Window placethe insertion point where you want to put the code for the dialog box 2 OntheM acro Window toolbar click the D ialog Box Editor button A blank dialog grid appears 3 Now you can select a tool such as a button or check boxes from the Toolbox T he cursor changes to a cross when you move it over the grid 4 Toplaceatool on the dialog box click a position on the grid A default tool will be added to the dialog grid 5 Resizethe dialog box by dragging the handles on the sides and the corners 6 Right click any of the controls that you have placed on the dialog surface after Selecting the control and enter aname for the control 7 Right click the dialog form with no control selected and enter a name for the dialog monitor function in the D ialogFunc field 8 To finish click OK T he code for the dialog box with controls will be written to the M acro W indow 9 Finally and in most cases you must edit the code for dialog box monitor func tion to define the specific behavior of the elements in your dialog box For more information see the Automation on line hel
191. ination for nonlinear regressions 82 83 control chart 84 86 cubic spline 87 93 cubic spline interpolation 87 93 differential equation solving 76 80 F test to determine statistical improvement in regression 80 82 Fast Fourier transforms 93 105 fractional defective control chart 84 86 Frequency plot 105 108 Gaussian cumulative distribution 108 110 histogram with Gaussian distribution 111 113 Kaplan M eier survival curves 129 131 linear regression parameters 83 84 linear regression standard deviations 83 84 linear regressions 113 116 low pass filter 116 118 normalized histogram 120 122 polynomial approximation for error functions 108 shading pattern for line plot curves 122 127 smooth color transition 127 129 trapezoidal rule beneath a curve 73 74 user defined axis scale 131 133 vector plot 134 135 Z plane design curves 137 140 s also transforms Transform functions 21 70 arguments 21 DATA 11 defining 12 defining variables 196 descriptions 22 66 multiple regression 234 237 user defined 6 69 70 131 133 s also transforms and functions Transform operators 17 20 arithmetic 19 defining variables 196 logical 20 order of operation 17 18 311 Index ranges amp scalars 18 20 relational 19 20 Transforms ANOVA XFM 72 AREA XFM 73 74 arguments 21 BIVARIAT XFM 75 CBESPLN 1 XFM 87 89 91 CBESPLN 2 XFM 87 91 93 components 6 9 CONTROL XF
192. indow or specified notebook document window in pixels or the size of pages and page objects in 1000ths of an inch Returns the Line object for the specified Plot object Lines are available in both line plots and line and scatter plots Returns the collection of axis Line objects for the specified Axis object Usethe collection index to return a specific line object M ajor Ticks M ajor Grid N ote that many axis line attributes are set with the different Axis object attributes using the Axis object SetAttribute method rere A standard property of almost all SigmaPlot objects Returns or sets the T itle name and field in the Summary Information for all notebook items the filename for a notebook file and the object name or title for page objects To set the title used for a notebook use the N otebook object Title property or set the name for N otebookl tems 0 N ote If you attempt to set the name of a document to the existing name you will receive an error message and the macro will halt Returns the collection of N amedD ataR anges from a D ataT able object Use the N amedD ataR anges collection to return a specific N amedD ataR ange object Returns the Text object that corresponds to the name of the specified object SigmaPlot Properties 271 SigmaPlot Automation Reference NameOfRange Sets or returns the name for a N amedD ataR ange object U seful for returning lists of Property column and row titles which a
193. information for the data t statistic T het statistic tests the null hypothesis that the coefficient of the independent variable is zero that is the independent variable does not contribute to predicting the dependent variable t is the ratio of the regression coefficient to its standard error or regression coefficient standard error of regression coefficient You can conclude from large t values that the independent variable can be used to predict the dependent variable i e that the coefficient is not zero P value P istheP value calculated for t TheP value isthe probability of being wrong In concluding that the coefficient is not zero i e the probability of falsely rejecting the null hypothesis or committing a Type error based on t The smaller the P value the greater the probability that the coefficient is not zero Traditionally you can conclude that the independent variable can be used to predict the dependent variable when P lt 0 05 TheAN OVA analysis of variance table lists the AN OVA statistics for the regression and the corresponding F value for each step SS Sum of Squares The sum of squares are measures of variability of the dependent variable gt T hesum of squares due to regression measures the difference of the regression plane from the mean of the dependent variable gt Theresidual sum of squares is a measure of the size of the residuals which are the differences between the observed values
194. ing to convert these to numbers Time only entries assume the internal Curve Fitting Date And Time Data 177 Regression Wizard start date of 4713 B C the start of the Julian calendar H owever if you have entered times using a more recent calendar date you must convert these times to numbers as well To convert your dates to numbers 1 Choosethe Tools menu O ptions command then select D ate and Timefrom the Show Settings For list Figure 8 32 Options Setting Day Zero Worksheet Fage System Graph Defaults Show Settings For Date and Time Sample Apr 1 96 154213 Date MMM Time Hms E Day Zero anni iti s siSY Regional Settings Cancel Apply Help 2 Set Day Zero to bethe first date of your data or to begin very close to the start ing date of your data You must include the year as well as month and day 3 Click OK then view the worksheet and select your data column Choose the Format menu Cells command and choose N umeric 178 Curve Fitting Date And Time Data Figure 8 33 Converting Dates to Numbers Figure 8 34 Selecting the Regression Equation Library Regression Wizard Your dates are converted to numbers Septet Aotebeesk 1 Ble aw 200 cul H PJ ELLI TiN ZIJ ra Fanin n Pardi i Bai I TAF 2 LE T hese numbers should be relatively small numbers If the numbers are large you did not select aD ay Zero near your data starting
195. ingle number string or missing value Anything that can be placed in a single worksheet cell is a scalar Transform Components 7 Using Transforms Array References 8 Transform Components A range sometimes called a vector or list isa one dimensional array of one or more scalars Columns in the worksheet are considered ranges Ranges can also be defined using curly bracket notation T he range elements are listed in sequence Inside the brackets separated by commas M ost functions which accept scalars also accept ranges unless specifically restricted Typically whatever a function does with a scalar it does repeatedly for each entry in a range A single function can operate on either a cell or an entire column Example 1 T he entry 1 2 3 4 5 produces a range of five values from 1 through 5 Example 2 T he operation col 1 col 2 concatenates columns 1 and 2 into a single range N ote that elements constituting a range need not be of the same type i e numbers labels and missing values Example 3 T he entry x col 4 3 1 s1n col 3 also produces a range Individual scalars can be accessed within a range by means of the square bracket constructor notation If the bracket notation encloses a range each entry in the enclosed range is used to access a scalar resulting in anew range with the elements rearranged Example For the range X 1 4 3 7 3 3 4 8 the notation x 3 retu
196. initial parameter estimates Consider the logistic function as an example T his function has the stretched s shape that changes gradually from alow value to a high value or vice versa 202 Automatic Determination of Initial Parameters Editing Code T he three parameters for this function determine the high value a the x value at which the function is 50 of the function s amplitude x0 and the width of the transition b As expressed in the transform language the function is entered into the Equation window as f a 1 exp x x0 b fit f to y N oise in the data can lead to significant errors in the estimates of x0 and b Therefore a smoothing algorithm is used to reduce the noise in the data and three functions are then used on the smoothed data to obtain the parameter estimates To estimate the parameter athe maximum y value is used T he x value at 50 of the amplitude is used to estimate x0 and the difference between the x values at 75 and 25 of the amplitude is used to estimate b As entered into the Initial Parameters window these are a max y Auto b xwtr x y 5 4 Auto x0 x50 x y 5 Auto Both the fwhm and xwtr transform functions have been specifically designed to aid the estimation of function parameters For more details on these specialized transform functions see Curve Fitting Functions on page 25 The Auto comment that follows each parameter is used to identify that parameter value as th
197. ints must be greater than or equal to 3 T he optional f argument defines the amount of Lowess smoothing and corresponds to the fraction of data points used for each regression f must be greater than or equal to 0 and less than or equal to 1 0 lt f lt 1 If fis omitted no smoothing is used For x 0 1 2 y 0 1 4 the operation col 1 x50 x y places the x atYinin 722 as 1 00 into column 1 X25 X75 xatymax xwtr Transform Function Descriptions 67 Transform Function Reference X75 Summary Syntax Example Related Functions xatymax Summary Syntax Thex75 function returns value of the x aty tans in the ranges of coordinates provided with optional Lowess smoothing T his s typically used to return the x value for the y value at 75 of the distance from the minimum to the maximum of smoothed data for sigmoidal shaped functions x75 x range y range f T hex range argument specifies the x variable and the y range argument specifies the y variable Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must have the same size and the number of valid data points must be greater than or equal to 3 T he optional f argument defines the amount of Lowess smoothing and corresponds to the fraction of data points used for each regression f must be greater than or equal to 0 and less than or equal to 1 0 lt f lt 1
198. is y Yo ae Four Parameter Weibull A lIe E 4_ C l c Tedd x 4 S ape Mak ea b c y t ety el l yet Five Parameter Weibull A l c C lIe a m gt x lt gt lt oN a m Sa ol 7 oN _1 c a eaa 287 Regression Equation Library Sigmoidal 288 Three Parameter Sigmoid LTS Four Parameter Sigmoid S Five Parameter Sigmoid E a y yyt ae y y A _ X iil a l agaa lt Three Parameter Logistic Four Parameter Logistic a Va y Vo Xr 1 x5 Four Parameter Weibull 1 paaur b y a l e Five Parameter Weibull Nc re E b y Y a l e Regression Equation Library Three Parameter Gompertz Growth Model 7 Four Parameter Gompertz Growth Model J 2 Three Parameter Hill Function C X Four Parameter Hill Function lan ax y Yor cP x Three Parameter Chapman Model y al e Four Parameter Chapman Model F y yyta l e 289 Regression Equation Library Exponential Decay Two Parameter Single Exponential Decay Three Parameter Single Exponential Decay Four Parameter Double Exponential Decay bx y ae ce Five Parameter Double Exponential Decay y y
199. is Boolean property is set to True SigmaPlot opens up a statistics window that displays statistics about the specified N ativeW orksheetl tem Statistics include mean standard deviation standard error half widths for 95 and 99 confidence intervals sample size total minimum maximum smallest positive value and number of missing values If this property is set to False the statistics window Is closed If open T his property returns True if the statistics worksheet window is open or False if the worksheet window is not open or the specified N ativeW orksheet is not open If the specified N ativeW orksheet object is not open setting this property has no effect Returns the Column Statistics worksheet as a D ataT able object Returns an object expression representing the read only data table belonging to the N ativeW orksheetl temis statistics worksheet If the worksheet has not been opened using the ShowStatsW orksheet property this property returns nothing SigmaPlot Properties 273 SigmaPlot Automation Reference StatusBar Property Sets or returns the SigmaPlot application window status bar text N ote that when a macro is running within SigmaPlot it will also issue status messages that will overwrite messages set with the StatusBar property A macro running in VB or VBA outside SigmaPlot will not create its own status bar messages other than those set with StatusBar Returns the property scheme val
200. is transform contains examples of the following transform functions gt stddev gt sqrt To calculate and graph the fraction of defectives and control lines for given sample sizes and number of defects per sample you can either use the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 84 Graphing Transform Examples Example Transforms To use the provided sample data and graph open the Control Chart worksheet and graph in the Control Chart section of the Transform Examples notebook T he worksheet appears with data in columns 1 2 and 3 The graph page appears with an empty graph To use your own data place the sample sizesin column 1 and the corresponding number of defects data in column 2 of anew worksheet If your data isin other columns you can specify these columns after you open the CONTCHRT XFM transform file You can enter your data in an existing or anew worksheet Press F10 to open the User D efined Transform dialog box then click the O pen button and open the CON TCHRT XFM transform filein the XFM S directory The Control Chart transform appears in the edit window Click Run T he results are placed in columns 4 through 5 of the worksheet If you opened the Control Chart graph view the graph page T he graph plots the fraction of defectives using a Line and Scatter plot with a Simple Straight Line style graphing column 3 as Y data versus the row numbe
201. istance T hedistance function calculates the distance of a line whose segments are described in X Y coordinates partdist T hepartdist function calculates the distances from an initial X Y coordinate to successive X Y coordinates in a cumula tive fashion Curve Fitting T hese functions are designed to be used in conjunction with SigmaPlot s nonlinear Functions curvefitter to allow automatic determination of initial equation parameter estimates from the source data Transform Function Descriptions 25 Transform Function Reference You can use these functions to develop your own parameter determination function by using the functions provided with the Standard Regression Equations library provided with SigmaPlot T his function is used for the polynomials rational polyno mials and other functions which can be expressed as linear functions of the parameters A linear least squares estima tion procedure is used to obtain the parameter estimates T his function returns an estimate of the phase in radians of damped sine functions fwhm This function returns the x width of a peak at half the peak s maximum value for peak shaped functions T he inv function generates the inverse matrix of an invert ible square matrix provided as a block T he lowess algorithm is used to smooth noisy data Low ess means locally weighted regression Each point along the smooth curve is obtained from a regression of data points close to the
202. it You can create alternate fit statements that call different weight variables T hese Statements statements appear as fit statements preceeded by two single quotes not a double quote For each weight variable you define you can create a weighting option by adding commented fit statements to the equation window For example an Equation window that reads f a exp b x c exp d x g exp h x fit f to y fit f to y with weight Reciprocal would display the option Reciprocal in the Regressions O ptions dialog box Fit With Weight list Variables Independent dependent and weighting variables are defined in the Variables edit window O ne of the variables defined must be the observed values of the dependent 194 Variables Figure 9 7 An Equations Window with Alternate Fit Statements Variable Definitions Editing Code Regression Triple 6 Parameter fea exp b s c exp d 4 g exp h s Fit F to y Ht Fto y with weight reciprocal y Lenca REF to y with weight reciprocal _ysguarg F un Automatic Initial Parameter E O ql bsig ab snear q max abs g abs qg Help Initial Parameters Options asyatsnearljy sia Auto b Inf 5 0 5 2504 4 min x Auto coyatxnearl y sa Auto d Inf 5 7 0 250 4 y min s Auto Iterations f O0 fo 1 Step Size Tolerance f e 10 g yatxnearl y e 3 Auto h lnf 5 71 S s50 s oe nincs Auto Trigonometric Units
203. itting Pitfalls on page 219 For more information on the effect of these options see O ther O ptions on page 200 Saving Equations 192 Saving Equations Once you are satisfied with the settings you have entered into the Regression dialog box you can save the equation Clicking OK automatically updates the equation entry in the current notebook or regression library If you created a new equation you are prompted to name it before it is added to your notebook If you are editing an existing equation you can click Add Asto add the code as a new equation to the current library or notebook In order to save your changes to disk you must also save the notebook or library Changes to your current regression library are automatically saved when you closethe wizard You can also save changes before you close the wizard by clicking the Save button Click Save As to save the regression library to a new file If your equation is part of a visible notebook you can save changes by saving the notebook using the Save button or the File menu Save or Save As commands Saving Equation Copies with Results Equations Defining the Equation Model Number of Parameters Editing Code N ote that when an equation is edited using the Regression O ptions dialog box all the changes are also automatically updated and saved You can save equations along with the targeted page or worksheet while saving your regression results Just check th
204. l axis to the current graph and plot on the specified Graphitem object using the AddW izardAxis options If there is only one plot for the current graph SigmaPlot will return an error Use the following parameters to specify the type of scale the dimension and the position for the new axis Dimension DIM X TheX dimension a TheY dimension DIM Z TheZ dimension if applicable Position AxisPosRightN ormal 0 AxisPosRightO ffset AxisPosT opN ormal AxisPosT opO ffset SigmaPlot Methods 277 SigmaPlot Automation Reference AddWizardPlot Method Clear Method Position AxisPosL eftN ormal KA AxisPosLeftO ffset AxisPosBottomN ormal e AxisPosB ottomO ffset Adds another plot to the current graph on the specified Graphitem object using the following parameters to define the plot Clears the selection in items that support this Close Method TheClose method is used to close notebooks and notebook items T he parameters 278 SigmaPlot Methods for each object type depend on the object Notebook Save before closing Boolean filename string Notebookltems Save before closing Boolean Specifying a Save before closing value of False closes the notebook or notebook item without saving changes made to the object N ote that for N otebookltems and Sectionltems a Close corresponds to an Expanded False Copy Method CreateGraphFrom Template Method CreateWizardGraph Method Cut Method Delete Method D
205. l distance between symbol centers user units ypos if intvl 1 w if intvl 2 w 2 0 y display POSPTETON for g e Go colti do multiple column loop Coly col cyfi 1 e buckets data ys max coly wte w h histogram coly buckets histogram of data hO if h gt 0 h histogram with zero values excluded buckets0O 1f h gt 0 buckets corresponding bucket values hsO sum h0 COolVcolLiit2 4 hookup dave Cl total ho Isum 0 buckers yYpos y values tem lookup data 1 total h0O sum h0O h0 col colfit2 j x j wx mod data 1 size tem tem tem 1 2 x values cols colit 3 5425 57 7 Er Gol tx Remy 2 emily 2507 O x values for mean lines COIS cortito ro 27 07 4 Hk milo 41 07 0 meam eoL C7 av values for mean lines end for Gaussian Cumulative Distribution from the Error Function Rational approximations can be used to compute many special functions T his transform demonstrates a polynomial approximation for the error function T he error function is then used to generate the G aussian cumulative distribution function T he absolute maximum error for the error function approximation is less than 2 5 x 10 M Abramowitz and L A Stegun H andbook of M athematical Functions p 299 108 Graphing Transform Examples Example Transforms To calculate and graph the G aussian cumulative distribution for given X values you can either use the provided sample dat
206. l value cel 3 1 0 ayan dnie ral varie cell 4 1 0 y3 initial value cell 5 1 0 y4 initial value K kK kK RESULTS KKK The output will be placed in columns 1 through neqn 1 x is placed in column 1 The yi values are placed in columns 2 through neqn 1 Other columns are used for 78 Data Transform Examples ee Example Transforms program working space RES Parameter Values Aas Enter all necessary parameter values below EOS Zaz r75 2 3 r85 8 4 r56 4 2 Col 0452 KKKKAKKKKKK PROGRAM KKKKAKKKKKK fo syle VZV 3rp yor IE mal tel Vly v2 y3774 LEMSA OAV Ly Py Wo ye sy Le M LPS UX pyle V2 yS yaa if m 4 fp4 x yl y2 y3 y4 h xl x0 nstep i gt 10 45 a h6 h 6 cell 1 1 x0 n2 neqn 2 a us n3 neqnt 3 dydx n4 neqn 4 dyt nS neqn t gt 5 dym Fixed Step Size Fourth Order Runge Kutta for k 1 to nstep do xk x0 k 1 h xh xk hh ror 41 to negn do CELL Iose cor RE pp Celi Ky cell 4 k cell 5 k i dydx cell n2 i cell i 1 k hh cell n3 i E end for for il 1 to neqn do eel L A sci Rot ey een yh woe lh tne A cell n2 3 cell n2 4 il aye cell n2 il cell il 1 k hh cell n4 il1 Vt end for for 12 1 to neqn do Gelitmo a2 to xh cell nZ yi cell nye y celt nes 3 Cell Any 4 4a dym cell n2 i2 cell i2 1 k Data Transform Examples 79 Example Transfor
207. l values or a block of complex values For complex values there are two columns of data T he first column contains the real values and the second column represents the imaginary values T his function works on data sizes of size 2 numbers If your data set is not 2 in length the fft function pads 0 at the beginning and end of the data range to make the length 2 T he fft function returns a range of complex numbers For X 1 2 3 4 5 6 7 8 9 10 the operation fft x takes the Fourier transform of the ramp function with real datafrom 1 to 10 with 3 zeros padded on the front and back and returns a 2 by 16 block of complex numbers invfft real imaginary complex mulcpx Invcpx T he for statement is a looping construct used for iterative processing for loop variable initial value to end value step increment do equation equation end for Transform equation statements are evaluated iteratively within the for loop When a for statement is encountered all functions within the loop are evaluated separately from the rest of the transform T he loop variable can be any previously undeclared variable name T he initial value for the loop is the beginning value to be used in the loop statements T he end value for the loop variable specifies the last value to be processed by the for statement After the end value is processed the loop is terminated In addition you can specify a loop 40 Transform Function Descriptions fwhm E
208. lace your x data in x_col and y data in y_col or change the column numbers to suit your data Results are placed in column res x_col 1 column number for x data y_col 2 column number for y data res 3 Column number for result Define x and y data Data Transform Examples 73 Example Transforms x col x_col y col y_col NKKKKKKKKKKKKKKKSK CALCULATE AREA KKKKKKKKKKKKKKKK Compute the range of differences between x i amp x i 1 xdifl ditt x n count x Delete first value xdif xdifl data 2Z n not a difference Compute the range of differences between yl eye ydifl difft y Delete first value ydif ydif1 dative 211 not a difference Use only y values from y 1 to y n l1 yl y data 1 n 1 Calculate trapezoidal integration Tico r lay l xd tO Ss vai sds T a total intgrl xxx x xx x x PLACE RESULTS IN WORKSHEET emer mn cee col res a Put area in column res Bivariate Statistics T his transform takes two data columns of equal length and computes their means standard deviations covariance and correlation coefficient The columns must be of equal length T he Bivariate transform uses examples of these transform functions gt mean gt stddev gt total 74 Data Transform Examples Bivariate Statistics Transform BIVARIAT XFM Example Transforms To use the Bivariate transform 1 Placeyour X datain column 1 and your Y data in co
209. lection M ost generic GraphO bject properties are not retained by tuples instead use the SetAttribute and G eAttribute methods to return or change the tuple properties Use the Tuple Attribute constants to specify these attributes The Functions collection consists of all regression confidence prediction and reference lines for a plot To use the Functions Collection T he functions collection is basically used to return individual function objects Return the Functions Collection from a Plot object using the Functions property 262 SigmaPlot Objects and Collections Function Object DropLines Collection SigmaPlot Automation Reference A Function object represents one of the various function lines of a Plot object In addition to Line object properties functions also have properties and attributes specific to regression and reference lines Functions have an O bjectT ype value of 10 orGPT FUNCTION To use the Function Object The Function object is returned from the Functions collection as follows a SA FINE EGR rse 2 BARING con urcoaren a Ae cone towed fe Sane eb verenna 5 saroe eb onenean fs seon 1Rdeetrele on fe sarees 3R eowetneen o sarune oci erRdeeestietow tat 0 SAN acs vRdeceetieow Siti M ost Function attributes and attribute values can only be returned or set using the G etAttribute and SetAttribute methods Use the Function Attribute constants to specify these attributes
210. lick the object with the mouse gt Usethe SelectO bject method Pastes the data in the clipboard into the worksheet transposing the row and column indices of the data such that rows and columns are swapped If thereis nothing in the clipboard or the data is not of the right type nothing will happen U ndoes the last performed action for the specified object If undo has been disabled in SigmaPlot for either the worksheet or page this method has no effect Regression Equation Library T his appendix lists the equations found in the Regression Equation Library Polynomial Linear Quadratic Cubic Inverse First Order y Yo aX y Y tax bx y Yo tax bx cx qd y me Nea Inverse Second Order m asl r Jo T 285 Regression Equation Library Inverse Third Order remiss Peak Three Parameter Gaussian K s Four Parameter Gaussian NI pepa Three Parameter Modified Gaussian gd ote Four Parameter Modified Gaussian cass y yg ae D Three Parameter Lorentzian 286 Regression Equation Library Four Parameter Pseudo Voigt Five Parameter Pseudo Voigt SN ee cee 0 5 8 y alc PR 1 oOe p b a C os 2 r w a 1 oe b Three Parameter Log Normal Four Parameter Log Normal
211. linear array To ensure that G amp D ata retrieves all data in a row or column specify the worksheet maximum as the right of bottom parameter GetMaxLegalSize Initializes the values of the maximum worksheet column and row values so that they Method can be returned as a variables GetMaxUsedSize Initializes the values of the maximum used worksheet column and row values so that Method they can be returned as a variables 280 SigmaPlot Methods Goto Method Help Method Import Method InsertCells Method Mesh Method Item Method ModifyWizardPlot Method SigmaPlot Automation Reference M oves worksheet cursor position to the specified cell coordinate for the current N ativeW orksheetltem or Excelltem object O pens an on line W indows help file to a specific topic context map ID number asa long or search index keyword K word You can use either the ID number or an index keyword If any of the parameters are left empty the SigmaPlot help file defaults are used Imports a data file with the specified file name into an existing N ativeW orksheetltem You can specify both the import starting location in the SigmaP lot worksheet as well as the range of data imported Inserts the specified block of cells into the worksheet T he existing cells can be moved in two different directions to accommodate the inserted region 1 Shift Cells Down 2 Shift Cells Right To insert an entire column or row simply set the column bot
212. lot with a Simple Straight Line syle and single Y data format from column 5 Graphing Transform Examples 103 Example Transforms For more information on how to create graphs in SigmaPlot see the SigmaPlot U ser s M anual Figure 6 8 5 Gain Filter Smoothing Graph 4 Signal plus noise 3 2 The top graph shows the 1 signal plus noise distortion 0 The middle graph shows the sad power spectral density of the signal plus noise distortion 2 47 The lower graph shows the 3 gain filter smoothed data 0 50 100 150 200 Time 50000 40000 Power Spectral Density 30000 20000 10000 Ge US 0 10 20 30 40 50 Frequency 5 4 Gain filtered signal na P 4000 2 1 0 4 1 2 3 0 50 100 150 200 Time Gain Filter Transform Gain Filtering GAINFILT XFM X This transform filters data by removing frequency components with power spectral density magnitude less than a specified value Input 104 Graphing Transform Examples ee Example Transforms ci all vi input data column number CO 5 output column number P 4000 psd threshold Program x col ci n size x tx fft x compute fft md real tx a img tx 2 compute psd ko an mda gt Pye find frequencies with psd lt P sd mulcpx complex kc tx remove frequency components from x td real invfft
213. ltem object 264 FitR esults object 265 Function graphobjects collection 262 Function object 263 Graph object 259 Graphlitem object 258 GraphO bject object 264 Group object 264 Line object 261 M acroltem object 265 N amedD ataR ange object 258 N amedD ataR anges collection object 258 N ativeW orksheetl tem object 257 N otebook object 257 N otebookl tem object 266 N otebookl tems collection object 257 N otebooks collection object 257 Page graph objects collection 259 Pages collection Page object 259 Plot graph objects collection 259 Plot object 260 Reportltem object 265 SectionItem object 266 Solid object 262 Symbol object 261 T ext object 261 Transformltem object 265 T uple graph objects collection 262 Tuple object 262 OLE Automation introduction 2 O ne way analysis of variance AN OVA transform 71 73 O perators see transform operators O ptions button Regression Wizard 153 O ptions regression p entering 200 202 iterations 159 160 201 regression equations 188 192 step size 160 201 tolerance 161 201 222 P value regression results 169 170 Parameters coefficient of variation 164 207 214 217 constraints 156 158 199 200 208 209 convergence message 181 default settings in Regression Wizard 156 defined but not referenced 183 dependencies 164 208 214 229 231 entering 198 199 identifiability 237 initial values 198 initial values determining 202 in
214. lumn 1 T he data is made up of exponentially distributed random numbers generated with the transform x random 200 1 1 e 10 1 col 1 In x T he graph page appears with an empty graph 2 To use your own data place your data in column 1 of the worksheet If your data has been placed in another column you can specify this column after you open theNORMHIST XFM transform file You can enter data into an existing or new worksheet 3 PressF10 to open the User D efined Transform dialog box then click the O pen button and open theNORMHIST XFM transform filein the XFM S directory T he N ormalized H istogram transform appears in the edit window 120 Graphing Transform Examples Figure 6 15 Normalized Histogram Graph Normalized Histogram Transform NORMHIST XFM Example Transforms 4 Click Run T he results are placed in columns 2 and 3 of the worksheet or in the columns specified by the res variable 5 If you opened the N ormalized H istogram graph view the graph page A histo gram appears using column 2 as X data versus column 3 asthe Y data 6 To create your own graph in SigmaPlot create a Vertical Bar chart with simple bars then set the bar widths as wide as possible For more information of creating bar charts and setting bar widths see the SigmaP lot U s s M anual Normalized Histogram of Exponential Random Numbers n 200 0 8 xx Transform to Generate Normalized Histogram This trans
215. lumn 2 If your data has been placed in other columns you can specify these columns after you open the BIVARIAT XFM transform file You can enter data into an existing worksheet or a new worksheet 2 PressF10 to open the User D efined Transform dialog box then click the O pen button and open the BIVARIAT XFM transform file in the XFM S directory T he Bivariate Statistics transform appears in the edit window 3 Click Run T he results are placed in columns 3 and 4 or beginning in the col umn specified with the res variable This transform integrates under curves using the trapezoidal rule ea Transform to Compute Bivariate Statistics This transform takes x and y data and returns the means standard deviations covariance and correlation coefficient rxy Place your x data an K Cok and y data am y COL or change the column numbers to suit your data Results are placed in columns res and res 1 x_col 1 column number for x data y_col 2 column number for y data res 3 first results column Define x and y data X COl x_col y col y_col NKKKKKKKKKKKKHK CALCULATE STATISTICS KKEKKKKKKKKKEKHK n size col x_col number of x values n must be gt 1 mx mean x mean of x data my mean y mean of y data sx stddev x standard deviation of x data sy stddev y standard deviation of y data covariance of x and y sxy if n gt 1 total x y n mx my n 1 0 correlation coefficien
216. m Microsoft Word or Excel To open SigmaPlot from M icrosoft Word or Excel you must first create a macro from within either application To create the macro 1 In Excel or Word choose Tools M acro V isual Basic Editor Visual Basic appears 2 Chooselnsert M odule 3 Type Sub SigmaPloc Opening SigmaPlot from Microsoft Word or Excel 255 SigmaPlot Automation Reference SigmaPlot Macro Dim SPApp as Object Set SPApp CreateObject SigmaPlot Application 1 SPApp Visible True SPApp Application Notebooks Add End Sub 4 Choose Run Run Sub U ser Form to run the macro SigmaPlot appears with an empty worksheet and notebook window To open SigmaPlot from Word or Excel in the future 1 Choose Tools M acro M acros to open the M acros dialog box 2 Select SigmaPlot 3 Click Run sigmaPlot Objects and Collections Application Object An object represents any type of identifiable item in SigmaPlot Graphs axes notebooks worksheets and worksheet columns are all objects A collection is an object that contains several other objects usually of the same type for example all the items in a notebook are contained in a single collection object Collections can have methods and properties that affect the all objects in the collection Properties and methods are used to modify objects and collections of objects To specify the properties and methods for an object that is part of acollection you need to return
217. method 280 GetM axLegalSize method 280 GetM axU sedSize method 280 Goto method 281 H elp method 281 Import method 281 InsertC ells method 281 Interpolate3D M esh method 281 Item method 281 M odifyW izardPlot method 281 N ormalizeT ernaryD ata method 282 Open method 282 Paste method 282 Print method 282 PrintStatsW orksheet method 282 PutD ata method 282 Quit method 282 305 Index Redo method 282 Remove method 282 Run method 283 Save method 283 SaveAs method 283 Select method 283 SelectAll method 283 SelectO bject method 283 SetAttribute method 283 SetC urrentO bjectAttribute method 283 SetO bjectC urrent method 284 SetSelectedO bjectsAttribute method 284 T ransposePaste method 284 Undo method 284 MIN function 53 113 MISSING function 53 M issing values in transforms 7 MOD function 54 M odifying recorded macros 245 250 MULCPX function 54 M ultiple independent variables 154 N N onlinear regression see regression Norm effect of weighting 197 in iterations dialog 214 N ormality test regression 171 Normalized histogram gee histogram transforms NTH function 54 N umbers functions 23 precision functions 24 random generation functions 24 Numeric functions 23 O O bject Browser 252 Objects 256 Application object 256 AutoLegend object 264 Axes graph objects collection 260 Axis object 260 Cell property 267 D ataT able object 258 D ropLines collection 263 Excelltem object 258 306 Fit
218. metric Units Degrees C Radians f Grads axl a gt 2 are inconsistent T he parameter a cannot be both less than 1 and greater than 2 If you execute a regression with inconsistent constraints a message appears in the Results dialog box warning you to check your constraint equations You can use several special options to influence regression operation T he different options can be used to speed up or improve the regression process but their use is optional T he three options are gt Iterations the maximum number of repeated regression attempts gt Step Size the limit of the initial change in parameter values used by the regression as it tries different parameter values gt Tolerance one of the conditions that must be met to end the regression process W hen the absolute value of the difference between the norm of the residuals from one iteration to the next is less than the tolerance this condition is satisfied and the regression considered to be complete O ptions are entered in the O ptions section edit boxes T he default values are displayed for new equations T hese settings will work for most cases but can be changed to overcome any problems encountered with the regression or to perform other tasks such as evaluating parameter estimation Iterations Evaluating Parameter Values Using 0 Iterations step Size Tolerance Editing Code Setting the number of Iterations or the maximum number of repeate
219. mn contains the real values and the second column represents the imaginary values T he worksheet format of a block of complex numbers is where r values are real elements and i values are imaginary elements In transform language syntax the two columns fr1 r2 nhia lo I teare written as DLOek Atay Tor dem eee iy ee a T his function works on data sizes of size 2 numbers If your data set is not 2 in length the fft function pads 0 at the beginning and end of the data range to make the length 2 A procedure for unpadding the results is given in the example Smoothing with a Low Pass Filter on page 99 Graphing Transform Examples 93 Example Transforms T hefft function returns a range of complex numbers T he Fast Fourier Transform is usually graphed with respect to frequency To produce a frequency scale use the relationship f s data 0 n 2 H L 7H where fs is the sampling frequency T he example transform POW SPEC XFM includes the automatic generation of a frequency scale see page 94 T he Fast Fourier Transform operates on data which is assumed to be periodic over the interval being analyzed If the data is not periodic then unwanted high frequency components are introduced To prevent these high frequency components from occurring windows can be applied to the data before using the fft transform T he H anning window is a cosine function that drops to zero at each end of the data The example transfo
220. mooth Color Transition worksheet and graph by double clicking the graph page icon in the Smooth Color Transition section of the Transform Examples notebook D ata appears in columns 1 and 2 of the worksheet and a scatter graph appears on the graph page 2 To useyour own data place your data in columns 1 and 2 For the residuals example column 2 is the absolute value of the residuals in column 1 To obtain absolute values of your data use the abs transform function For example to obtain the absolute values of the data set in column 1 type the following trans form in the U ser D efined Transform dialog box col 2 abs col 1 If your data is in a different column specify the new column after you open the RGBCOLOR XFM transform file Graphing Transform Examples 127 Example Transforms 3 Figure 6 18 Smooth Color Transition Transform Example Graph Press F10 to open the User D efined Transform dialog box then click the O pen button and open theRGBCOLOR XFM transform filein the XFM S directory The Smooth Color Transition transform appears in the edit window Click Run T he results are placed starting one column over from the original data or in the column you specified in the transform If you opened the sample Smooth Color Transition graph view the graph page A Scatter Plot appears plotting column 2 as a Simple Scatter plot style using Sin gle Y data format T he symbol colors are obtained by specifying column 3
221. mple 6 Multiple Function Nonlinear Regression Figure 11 28 The Multiple Function Graph with Three Curves You can use the Regression W izard to fit more than one function at atime T his process involves combining your data into additional columns then creating a third column which identifies the original data sets T his example fits three separate equations to three data sets wee eta es 1 Open theM ultiple Function worksheet and graph by double clicking the graph page icon in the M ultiple Function section of the NONLIN JNB notebook T he data points are for three dose responses fix Columns 1 and 2 hold the combined data for the three curves Column 3 is used to identify the three different data sets A 0 corresponds to the firs dataset 1 to the second and 2 to the third Log ose m 2 Doubleclick the M ultiple Functions Equation T he Regression W izard opens with the variables panel displayed Click Edit Code 234 Example 6 Multiple Function Nonlinear Regression Figure 11 29 The Multiple Function Statements Advanced Regression Examples Regression Multiple Functions Equation Equations ifid 0 A if d 1 f2 F3 A T eB 1 ni HET n F2 T HES ni HE2 n T E3 ni HES n Fit F toy concatonated di concatonated y d d cal 3 function identifier Cancel Run Options Iterations fioo Step Size fioo Tolerance 0 000 Oo Initial Parameters Trigonometr
222. ms h cell n5 i2 ee cell n5 i2 cell n5 i2 cell n4 12 dym dym dyt end for for is 1 to negn do Cellini 13 otk hy cel ln cell nay yy cell n2 3 cell n2 4 i3 ayt cell i3 1 k 1 cell i3 1 k h6 Geil i373 cell n4 i3 2 cell n5 i3 end for cell 1 k 1 cell 1 k h end for F test to Determine Statistical Improvement in Regressions T his transform compares two equations from the same family to determine if the higher order provides a statistical improvement in fit Often it is unclear whether a higher order moda fits the data better than a lower order Equations where higher orders may produce better fits include simple polynomials of different order the sums of exponentials for transient response data and the sums of hyperbolic functions for saturation ligand binding data F TEST XFM uses the residuals from two regressions to compute the sums of squares of the residuals then creates the F statistic and computes an approximate P value for the significance level You can try this transform out on the provided sample graph or run it on the residuals produced by your own regression sessions Residuals are saved to the worksheet by the Regression W izard 1 To use the provided sample data and graph open the F test worksheet and graph in the XFM S NB notebook T he worksheet contains raw data In col umns 1 and 2 and curve fit results for the two competitive binding models in columns
223. mulative distribution function Distribution ona When a Gaussian cumulative distribution function is graphed using the probability Probability Scale scale the result is a straight line l 2 If you opened the sample G aussian graph view the graph page A straight line plot appears in the second graph plotting the distribution data in column 3 along a probability scale To create your own graph using SigmaPlot create a Line Plot with a Simple Straight Line using column 1 as your X data and column 3 as your Y data and set the Y axis scale to Probability For information on how to create graphs in SigmaPlot see the SigmaPlot U s s M anual Graphing Transform Examples 109 Example Transforms Figure 6 10 Gaussian Cumulative Distribution Function Gaussian Cumulative Distribution Graphs Linear Scale Probability Scale 1 2 99 999 99 99 1 0 4 99 9 m 99 0 8 F 90 4 0 6 4 70 b B 50 0 4 F 30 F m 10 0 2 H a Palle B 0 0 4 0 1 J 0 01 7 0 2 0 001 5 4 3 2 1 0 1 2 3 4 5 5 4 3 2 1 0 1 2 3 4 5 Gaussian Distribution Gaussian Cumulative Distribution Function GAUSDIST XFM NKKKKKKKKKKIKKIKHK C D F Transform KKEKKKKKKKKKKKEKHK This transform takes x data and returns the results of a Gaussian Cumulative Distribution function Place your x data in x_col or change the column number to s
224. n Expanded True Place the contents of the W indows Clipboard into the selected notebook item document at the current position if applicable T he format specified is an available clipboard format as displayed by the Edit menu Paste Special command Prints the selected item including any items within specified N otebookltems and SectionItems Specifying the N otebook prints all items in the notebook Prints the N ativeW orksheetl temis statistics worksheet If the worksheet has not been opened using the ShowStatsW orksheet property this method fails Places the specified variant into the worksheet starting at the specified location The data can bea 2D array Ends SigmaPlot If SigmaPlot isin use then this method is ignored R edoes the last undone action for the specified object If redo has been disabled in SigmaPlot for either the worksheet or page this method has no effect D eletes the specified object The index can be a number or a name If the specified index does not exist an error is returned Run Method SaveAs Method Save Method Select Method SelectAll Method selectObject Method SetAttribute Method setCurrentObject Attribute Method SigmaPlot Automation Reference Runs a Fitltem or M acro without closing the object Save a notebook file for the first time or to anew file name and path N ote that you need to provide thefile extension Recognized SigmaPlot notebook file extensions are JNB J
225. n Fit After Five Iterations T he iterations option specifies the maximum number of iterations to perform before displaying the current results You can see if a long regression is working correctly by limiting the number of iterations to perform If the regression does not complete within the number of iterations specified you can continue by clicking the M ore Iterations option in the initial results panel Click OK Regression Options Initial Parameters Values Automatic Parameters Parameter Constraints Ok o gt Cancel Mal Help Options Constants Iterations H Step Size 100 iai Tolerance 0 000100 i Fit With Weight none Click N ext to calculate the new fit N ote that the Iteration dialog box now says Iteration n of 5 Each iteration also requires much more time to calculate and more iterations are required to produce a result After five iterations the initial results panel is displayed N ote that the M ore Iterations option is no longer dimmed Click M ore Iterations for five more itera tions Regression Wizard More Iterations View Constraints Did not converge exceeded masinum number of iterations Reqr 0 599998924 Norm 0 1841 5203 Value StdE rr CY 2 Dependencies 1 140e 2 5 5 fe 2 4 690e 2 0 701364 9 095e 0 3 945e 2 4 F35 e 0 9625315 3 059e 0 F 80le 2 2 5560e 0 0 9953396 B 146e 1 3257e 1 3 995e 0 9986340 4 199e 2 956
226. n data No parameters to fit T he regression specifications do not include any parameter definitions To add parameter definitions return to the Edit Regression dialog box and type the parameter definitions in the Parameters edit window No weight statement T he regression specifications include afit to statement with an unknown weight variable C heck the Variables edit window to see if a weight variable has been defined and that this corresponds to the variable in the regression statement N ot enough or bad number of observations In regression the x and y data sets must be of the same size T he data sets x and y columns you specified contain unequal numbers of values 182 Regression Results Messages Regression Wizard Problem loading the file Filename File too long truncated T he fit file you tried to load is too long Regression files can be up to 50 characters wide and 80 lines long Any additional characters or lines were truncated when the file was loaded into the Edit Window Section has already been submitted T his regression section has already been defined Symbol Variable or Function has not been defined T he fit to statement in the regression definition contains an observed variable which is undefined or the fit to Statement in the regression definition contains an undefined function Examine the regression specifications you have defined and be sure that the dependent variable listed in the regression st
227. nal 2 4 _ at bxt ex dx ex y 2 re re 1 fx gx hx i1x jXx Eleven Parameter Rational 2 4 5 y St b OX dx ex fx E N 5 l gox hx 1x jx kx Logarithm Two Parameter yo y Yot alnx Two Parameter II ye y aln xX Xo 299 Regression Equation Library Two Parameter III a y In a bx an Second Order y yo alnx b Inx Third Order A y yo alnx b Inx c Inx 3 Dimensional Plane Z Z ax by 2 2 Z 2Z ax by cx dy 300 ndex FIT files 143 XFM files 1 4 A ABS function 28 Absolute minimum sum of squares 223 224 Accumulation functions 24 Add Procedure D ialog Box 253 Adjusted R regression results 168 Algorithm M arquardt Levenberg 145 160 201 Alpha value power 172 ANOVA one way ANOVA transform 71 73 ANOVA table regression results 169 APE function 28 ARCCOS function 29 ARCSIN function 30 ARCTAN function 30 Area and distance functions 25 Area beneath a curve transform 73 74 AREA function 31 Arguments transform 21 s also function arguments Arithmetic operators transforms 19 Array reference example of use 111 Automation 241 254 introduction 2 methods 275 objects 256 properties 266 AVG function 31 Axis scale user defined 131 133 user defined transform 131 133 Bar chart histogram with Gaussian distribution 111 113
228. nan va D 2 0 100 200 300 400 500 600 700 800 900 Low Pass Filter Lowpass Smoothing Filter Transform o This transform computes the fft eliminates LOWPASS XFM x specified high frequencies and computes the inverse fft Input ci 2 input data column number CO 5 output lowpass filtered data column number pr 88 high frequencies to remove CO 100 Program x col ci n size x Dr bar or 0 OLEDE L00 LOO pE urap APU pI errors f int pr1 100 mp number of channels to eliminate tx Tie Cx fft of data Graphing Transform Examples 101 Example Transforms r data 1 size tx 2 number of data padded channels mp size tx 4 mid point of symmetric channels To Se Pearl Or Teme daa lt 9 eliminate high frequencies td mulcpx complex fc tx sd invfft td convert back to time domain Output ru 1 ft mod ny2 50 2 mpentl 72 AZARIA 2 remove padded channels El IT mod nira 0 4 2 AMp ru 2 mp rut col co real sd data ru ri block 6 1 tx place results in worksheet cell 8 1 mp cell 8 2 f cell 8 3 prl cell 8 4 n col 9 fc col 10 r col 11 real tx 2 img tx 2 PSD Gain Filter Smoothing TheGAINFILT XFM transform example demonstrates gain filter smoothing T his method eliminates all frequencies with power spectral density levels below a specified threshold T h
229. nction returns a range of values consisting of the number e raised to each number in the specified range T his is numerically identical to the expression e numbers but uses a faster algorithm exp numbers T henumbers argument can be a scalar or range of numbers Any missing value or text string contained within a range is ignored and returned as the string or missing value T he operation exp 1 returns a value of 2 718281828459045 In T he factorial function returns the factorial of a specified range factorial range T he range argument must be a single range indicated with the brackets or a worksheet column Any missing value or text string contained within a range is ignored and returned as the string or missing value N on integers are rounded down to the nearest integer or 1 whichever is larger For factorial x X lt 0 returns a missing value 0 lt x lt 180 returns x and X gt 180 returns 20 T he operation factorial 1 2 3 4 5 returns 1 2 6 24 120 Transform Function Descriptions 39 Transform Function Reference fft for Example 2 Summary Syntax Example Related Functions Summary Syntax To create a transform equation function for the Poisson distribution you can type Poisson m x m x exp m factorial x T hefft function finds the frequency domain representation of your data using the Fast Fourier Transform fft range T he parameter can be a range of rea
230. nd l 3 Select the notebook section where you want to add the equation If you want the equation to be created in a new section click the notebook icon Choose the File menu N ew command and select Regression Equation from the N ew drop down list Click OK to create the new equation T he Regression dialog box opens To create an Equation from the Notebook View 1 Right click the section where you want the equation to go If you want the equa tion to be created in anew section right click the notebook icon Choose N ew from the shortcut menu and choose Regression Equation T he Regression dialog box opens Notebook 0 Notebook BT Section 1 pen Data 1 Graph Page 1 Graph Page 2 Delete SUMMAN Open Help Copy rae Summary Info Paste Edit Info E SP55 Ie Clear Worksheet Excel Worksheet Graph Page Report Regression Equation Section About Regression Equations 187 Editing Code Copying Equations You can copy an existing equation from any notebook view to another and modify it as desired Adding Equations as Equations can also be edited from within the Regression Wizard and added as new New Entries equations to the current library using the Add As button in the Regression dialog box Entering Regression Equation Settings To enter the settings for new equations click the desired edit window in the Regression dialog box and enter your settings Figure 9 4
231. nd 5 plots column 1 asthe X data and column 5 as the Y data using XY Pairs data format 6 To plot your own data using SigmaPlot choose the G raph menu Create Graph command or select the Graph W izard from the toolbar Create two graphs Graph the signal plus the noise distortion using a Line Plot with a Simple Straight Line style and XY Pairs data format graphing column 1 as the X data column 2 asthe Y data for the signal and the noise distortion Create a second graph with two plots Plot the original signal using a Scatter Plot with a Simple Scatter Style and XY Pairs data format plotting column 3 asthe X data and col umn 4 astheY data for the original signal Add a second Line Plot with a Simple 100 Graphing Transform Examples I ee Example Transforms Straight Line style using data in columns 1 and 5 plotting column 1 as the X data and column 5 asthe Y data using XY Pairs data format For more information on how to create graphs in SigmaPlot see the SigmaPlot U s s M anual Figure 6 7 40 Low Fass rilter Signal plus noise Smoothing Graph 847 mere 6 4 The top graph shows the The bottom graph shows the signal and the low pass filtering set at 88 gt signal plus noise distortion 2 0 100 200 300 400 500 600 700 800 900 10 g Signal A ga 88 lowpass filtered f Y a Sei 6 i J e 49 oy f 17 ai o 0o 2 s oe By N g i A 0 A Tava y co
232. ndependent and dependent variables Standard Error of T he standard error of the estimateS y x 1Sa measure of the actual variability about the the Estimate S yix regression plane of the underlying population The underlying population generally falls within about two standard errors of the observed sample Statistical T he standard error t and P values are approximations based on the final iteration of Summary Table the regression Estimate T he value for the constant and coefficients of the independent variables for the regression model are listed 168 nterpreting Regression Reports Analysis of Variance ANOVA Table Regression Wizard Standard Error T he standard errors are estimates of the uncertainties in the estimates of the regression coefficients analogous to the standard error of the mean T he true regression coefficients of the underlying population are generally within about two standard errors of the observed sample coefficients Large standard errors may indicate multicollinearity T he default procedure for computing standard errors is based on whether or not the regression problem is weighted In an unweighted problem the standard error for each parameter includes a factor that estimates the standard deviation of the observed data In this case it is assumed that the errors for all data points have the same variance In aweighted problem this factor isignored because the weights themselves provide the error
233. near equations to data T he curve fitter modifies the parameters coefficients of your equation and finds the parameters which cause the equation to most closely fit your data You can specify up to 25 equation parameters and ten independent equation variables When you enter your equation you can specify up to 25 parameter constraints which limit the search area when the curve fitter checks for parameter values T he curve fitter can also use weighted least squares for greater accuracy User defined equations can be saved to notebooks or regression libraries and selected for later use or modification SigmaPlot OLE Automation technology provides you with a wide range of possibilities for automating frequently performed tasks using macros and user defined features SigmaPlot s M acro Recorder lets you record is a set of procedures and then run them automatically with a single command M ost of the operations that you perform in SigmaPlot can be recorded TheM acro Window provides a fully featured programming environment that uses SigmaP lot Basc as the core programming language If you are familiar with M icrosoft Visual Basic most of what you know will apply as you use SigmaPlot s macro language Using Transforms Transforms are math functions and equations that generate and are applied to worksheet data Transforms provide extremely flexible data manipulation allowing powerful mathematical calculations to be performed on
234. ng distances are placed in column 5 Saving Frequently used variable values and custom transforms can be saved to a transform User Defined file then copied and pasted into the desired transform Functions To save user defined functions to a file then apply them to a transform 1 Definethe variables and functions in the Transform window then click the Save button 2 When the Save dialog box appears name the file something like U ser D efined Functions 3 Select the function you want to use in the transform then press Ctrl C or CtriHns 4 Open thetransform file you want to copy the function to click the point in the text where you want to enter the function then press Ctri V or ShiftHns 70 User defined Functions Example Transforms M any mathematical transform examples along with appropriate graphs and worksheets are included with SigmaPlot T his chapter is describes the data transform examples and the graphing transform examples provided Each description contains the text of the transform and where applicable a graph displaying the possible results of the transform T he sample transforms and the XFM S JNB notebook can be found in the XFM S folder Data Transform Examples T he data transform examples are provided to show you how transform equations can manipulate and calculate data One Way Analysis of Variance ANOVA A One Way Analysis of Variance AN O VA table can be created from the results of a r
235. ngth heading 7 Makesure that Radians are selected as the Trigonometric Units they should be by default 8 Click Run to run the transform T he transform produces six columns of three XY pairs which describe the arrow body and the upper and lower components of the arrow head 9 If you opened the Vector graph view the page The Line Plot with M ultiple 134 Graphing Transform Examples NN ay Example Transforms Figure 6 21 The Vector Graph gt gt gt gt gt _ gt gt gt gt a gt gt gt gt gt Si oe AS te es ee Se Se Se Be Se a SE SRE eee rere Cah gee ee a See SE a Te SL PAS ee A S AO gh Ae Ce ee E aS oe ree eer ete ie Uh ae A ee AS gt gt gt ery sf ns A Aras gt Ee Se A A a eee ee oe Se YP fn fp fA A 77s gt gt a PA O A a ee S eS er ae OE GO a S pee ee a a ae ee oa ae E ee ee oS gt gt gt gt gt oC ee LA LA awh mvnh e lr gt gt gt gt gt gt gt gt gt _ gt gt gt gt gt gt gt gt gt gt gt SB a eR Se eg SE Se Ae eR Sa ee gt gt gt gt SS Bee D gt SS la gt gt gt gt Straight Line appears plotting columns 5 through 10 as XY pairs 10 To plot the vector data using SigmaPlot create a Line Plot with M ultiple Straight Line graph that plots columns 5 through 10 as three vector XY column pairs For more information on creating graphs in SigmaPlot see the SigmaP lot U s s
236. ninn sananteinagsiptontsilsoratnan tesa i auans dials cameras 252 Using the Add Procedure Dialog BOX tatisetvcueshicniisencsbyanisenseihddadeslalivin aiteadialetinsd 253 Using the Debug WINGOW cssessrsrgniecei ae a a 253 SigmaPlot Automation Reference cccscceeseeeeseeeeeeeeeeeeeeeeaeseganeneas 255 Opening SigmaPlot from Microsoft Word or Excel ccceccescescstcessseeesseessseeessaees 255 SigmMaPlot Objects and Collections c ccccssccssssecsssceessseesseeeesseeeessnesessnresseneeseegs 256 SigmaPlot Properties srna r A AA a AEA 266 SMa FOt MEMOS aasien ena a a a a amines 275 Regression Equation Library ssssssssnsnsnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 285 iTo E EEE E E E E E E EE E E E E 301 Transforms Regressions Introduction T he Programming Guide provides you with complete descriptions of SigmaPlot s powerful math data manipulation regression and curve fitting features It also describes how to use SigmaPlot s Interactive D evelopment Environment IDE and M acro Recorder to automate and customize SigmaPlot tasks Transforms are sets of equations that manipulate and calculate data M ath transforms apply math functions to existing data and also generate serial and random data To perform atransform you enter variables and standard arithmetic and logic operators into atrangorm dialog Your equations can specify that a transform access data from a worksheet as well as save equation results to a worksh
237. nitial parameter value of X to 2 5 then click OK Curve Fitting Pitfalls 223 Advanced Regression Examples 5 Click Next Because this initial parameter value happens to correspond to the maximum of the sum of squares function the regression stops immediately T he Slope is zero within the default tolerance so the curve fitter falsely determines that aminimum has been found Figure 11 10 Regression Wizard The Results Using 7 an Initial Parameter Converged tolerance satisfied meea Value of Xo 2 5 Fsg 0 Norm 1 067775619 Menco Value StdErr Cv rs Dependencies 0 2 50le 0 1 436e 0 5 75le 1 0 0000000 E Help Cancel Back i Mert i Finish 6 Finding the absolute minimum Click Back then click O ptions Change the initial value of x to 2 0 7 Click OK to close the O ptions dialog box then click N ext to execute the regres sion T heinitial parameter value is reasonably close to the optimum value so the regression converges to the correct value Xp 0 0 Figure 11 11 The Results Using Regression Wizard an Initial Param eter Converged tolerance satisfied e e Value of Xq 2 0 Risqr 1 Norm 2 292920901 e 6 Vien Constraints Parameter Value StdE rr CVE Dependencies 0 1 510e 6 2294e 6 1 520e 2 0 0000000 fe Help Cancel Back Finish Summary These last examples demonstrate how the curve fitter can find a local minimum and even a local maximum
238. nized in four tabs that allow you to type in statements observe program execution responses and iteratively modify your code using this feedback If you have never used a debugging tool and are new to Using the Add Procedure Dialog Box 253 Automating Routine Tasks programming it would be a good idea to supplement the following description with further study Immediate Tab Thelmmediate Tab lets you evaluate an expression assign a specific value to a variable or call a subroutine and evaluate the results Trace mode prints the code in the tab when the macro is running gt VV Y y Type expr and press Enter to show the value of expr Type var expr and press Enter to change the value of var Type set var expr and press Enter to change the reference of var Type subname args and press Enter to call a subroutine or built in expression subname with arguments args Type trace and press Enter to toggle trace mode Trace mode prints each statement in the Immediate Tab when a macro is running Watch Tab TheWatch Tab lists variables functions and expressions that are calculated during execution of the program gt gt gt gt Each time program execution pauses the value of each line in the window Is updated T he expression to the left of the gt may be edited Pressing Enter updates all the values immediately Pressing Ctri Y deletes the line Stack Tab T he output from the
239. nizh Click Finish or click N ext to select the graphed results If you selected your variables from a graph you can add your equation curve to that graph automatically You can also plot the equation on any other graph on that page You also always have the option of creating a new graph of the original data and fitted curve Regression Wizard Do vou want to W Add curve to Add the fitted curve to the current graph Create new graph Help Cancel Back Nest Finish After selecting the graphed results you want click Finish Click N ext only if you want to select the specific columns used to contain the data for the equation 150 Using the Regression Wizard Figure 8 6 Selecting the Graph Results Columns These settings are retained between sessions Finishing the Regression Regression Wizard 9 To select the columns to use for the plotted results click the columns in the worksheet where you want the results to always appear Remember these set tings are re used each time you perform a regression Regression Wizard Columns Select the columns for your graph E Curve Data Column x column First E mpt y column First Empty Finish W hen you click Finish all your results are displayed in the worksheet report and graph T he initial defaults are to save parameter and computed dependent variable values to the worksheet to create a statistical report and to gra
240. nly used to characterize the dynamic behavior of compartmental models In this example you mode data generated from the sum of two exponentials with one two and three exponential models and you examine the parameter dependencies in each case Dependencies Overa Thefirs fit is made to data over a restricted range which does not reveal the true Restricted Range nature of the data 1 Open the D ependencies worksheet and graph by double clicking the graph page icon in the D evendencies section of the Regression Examples notebook T he data generated from the sum of two exponentials f t 0 9e 0 1le 7 is graphed on asemi logarithmic scale over the range 0 to 3 Figure 11 18 The Dependencies Graph Showing the Data for the Sum of Two Exponentials Although the data is slightly curved the break associated with the two distinct exponentials is not obvious 2 Right click the curve and choose Fit Curve to open the Regression W izard 3 Select the Exponential D ecay category and the Single 2 Parameter exponential Example 4 Using Dependencies 229 Advanced Regression Examples decay equation then click N ext twice Figure 11 19 R ion Wizard x Selecting the 2 Parameter en IRE Es Single Exponential Decay Select the equation to fit your data Len 2 a Save Equation Exponential Decay n Equation Name Save As oe Single 2 Parameter M Single 3 Parameter Double 4 Parameter New Double 5 Param
241. ns lowpass summary syntax Transform Function Reference T he lowess function returns smoothed y values as a range from the ranges of x and y variables provided using a user defined smoothing factor Lowess means locally waghted regression Each point along the smooth curve is obtained from a regression of data points close to the curve point with the closest points more heavily weighted lowess x range y range f T hex range argument specifies the x variable and the y range argument specifies the y variable Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must be the same size and the number of valid data points must be greater than or equal to 3 Thef argument defines the amount of Lowess smoothing and corresponds to the fraction of data points used for each regression f must be greater than or equal to 0 and less than or equal to 1 0 lt f lt 1 Notethat unlike lowpass lowess requires an f argument For x 1 2 3 4 y 0 13 0 17 0 50 0 60 the operation col 1 Sowess x y 1 places the smoothed y data 0 10 0 25 0 43 0 63 into column 1 lowpass T he lowpass function returns smoothed y values from ranges of x and y variables using an optional user defined smoothing factor that uses FFT and IFFT lowpass x range y range f T hex range argument specifies the x variable and the y range argument specifies t
242. nsform x data 0 15 5 x Variable specified En as a function Close y 0 9 exp gt j 0 1 exp 2 x y variable specified as an equation New Open put x into colfi setting column z to E Save Save As Revert watch Single Step Trigonometric Units i Degrees Radians Grads M issing values represented in the worksheet as a pair of dashes are considered non numeric All arithmetic operations which include a missing value result in another missing value To generate a missing value divide zero by zero Example If you define missing 0 0 the operation size 1 2 3 missing returns a value of 4 0 T he Sze function returns the number of elements in a range including labels and missing values T he transform language does not recognize two successive dashes for example the string 1 2 3 isnot recognized as a valid range D ashes are used to represent missing values in the worksheet only Strings such as text labels placed in worksheet cells are also non numeric information To define a text string in a transform enclose it with double quotation marks As with missing values strings may not be operated upon but are propagated through an operation T he exception is for relational operators which make a lexical comparison of the strings and return true or false results accordingly T he transform language recognizes two kinds of elements scalars and ranges A scalar iS any s
243. nstration of weighting variable use see Example 2 Weighted Regression on page 225 You can define morethan one possible weight variable and select the one to use from the Regression O ptions dialog box Simply create multiple weight variables then create alternate fit statement entries selecting the different weight variables in the Equations window For more information on creating alternate fit statements see D efining Alternate Fit Statements on page 194 Least squares regressions assumes that the errors at all data points are equal W hen the error variance is not homogeneous weighting should be used If variability increases with the dependent variable value larger dependent variable values will have larger residuals Large residuals will cause the squared residuals for large dependent variable values to overwhelm the small dependent variable value residuals T he total sum of squares will be sensitive only to the large dependent variable values leading to an incorrect regression You may also need to weight the regression when there is a requirement for the curve to pass through some point For example the 0 0 data point can be heavily weighted to force the curve through the origin N ote that if you use weighted least squares the regression values are valid but the Statistical values produced for the curve are not T he weight values are proportional to the reciprocals of the variances of the dependent variable We
244. nts are omitted from right to left If you want to specify a stddev you must either specify the mean argument or omit it by using 0 0 Example The operation gaussian 100 uses a seed of 0 to produce 100 normally distributed random numbers with a mean of 0 0 and astandard deviation of 1 0 Related Functions random histogram Summary Thehistogram function produces a histogram of the values range in a specified range using a defined interval set 42 Transform Function Descriptions syntax Example 1 Example 2 summary syntax Transform Function Reference histogram range buckets T he range argument must be a single range indicated with the brackets or a worksheet column Any missing value or text string contained within a range is ignored T he buckets argument is used to specify either the number of evenly incremented histogram intervals or both the number and ranges of the intervals T his value can be scalar or a range In both versions missing values and strings are ignored If the buckets parameter is a scalar it must be a positive integer A scalar buckets argument generates a number of Intervals equal to the buckets value T he histogram intervals are evenly sized the range is the minimum value to the maximum value of the specified range If the buckets argument is specified asa range each number in the range becomes the upper bound inclusive of an interval Values from ce to lt the first bucket
245. nts is optional Constraints are used to set limits and conditions for parameter values restricting the regression search range and improving regression speed and accuracy Liberal use of constraints in problems which have a relatively large number of parameters is a convenient way to guide the regression and avoid searching in unrealistic regions of parameter space A constraint must be a linear equation of the parameters using an equality or inequality lt or gt For example the following constraints for the parameters a b c d and eare valid a lt l 10 6 20 gt 2 d e 15 a gt b c d e whereas a X lt 1 is illegal since x is not a constant and b c 2 gt 4 d e 1 are illegal because they are nonlinear Although the curve fitter checks the constraints for consistency you should still examine your constraint definitions before executing the regression For example the two constraints Constraints 199 Editing Code Figure 9 8 Entering Iteration Step Size and Tolerance Options Other Options 200 Other Options Regression Weibull 5 Parameter Equations qeabs x x0 b In 2 1 e M1 y0 a 1 exp a by c fileen bne TI Fc yO F1 Cancel Rur fit Fto y Options Iterations f O0 100 Initial Parameters a masjy minjy Auto b xvutr Lynne 5 Auto c Auto HO s50 2 ron 5 Auto Step Size p sminiy Auto Tolerance f e 10 Trigono
246. o arunc oca ahAdeweLine Love corante 0 BAFUNG cS ShAdewestnelLowe Spit N ote that most regression and reference lines options are controlled with different plot and line attributes For example to turn on aregression line use SetAttribute SLA REGROPTIONS SLA_REGR_FORPLOT Or FLAG SET BIT and to turn on the third reference line use SetAttribute SLA QCOPTIONS SLA QCOPTS SHOWQC3 Or FLAG SET BIT Returns the collection of graphs for the specified Page object Use the index to select a specific Graph object Graphs are used in turn to return the different graph items Plots Axes the graph title and the graph legend Returns the GraphPages collection of Page objects for a Graphitem object H owever since there is currently only one graph page for any given graph item you can always use GraphPages 0 H owever in order to access items within aGraphitem you must always specify the G raphPage SigmaPlot Properties 269 SigmaPlot Automation Reference Height Property Sets or returns the height of the application window or specified notebook document window in pixels or the size of pages and page objects in 1000ths of an inch InsertionMode Sets or returns a Boolean indicating whether or not Insert mode is on Property Interactive Property Sets or returns a Boolean indicating whether or not the user is allowed to interact with the running notebook window or application Do not set the Application property to False from within
247. o save the fitted Y values of the nonlinear regression to the worksheet use the Regression W izard to save the Function results to the appropriate column for this transform column 3 1 Place your original Y data in column 2 of the worksheet and the fitted Y data in column 3 If your data has been placed in other columns you can specify these columns after you open the R2 XFM transform file You can enter data into an existing or anew worksheet 2 PressF10 to open the User D efined Transform dialog box then click the O pen button and open theR2 XFM transform file in the XFM S directory The R2 transform appears in the edit window 3 Click Run The R value is placed in column 4 of the worksheet or in the col umn specified with the res variable 82 Data Transform Examples I ay R Squared Transform R2 XFM Example Transforms x x Transform to Compute R Square Coefficient x of Determination for Nonlinear Curve Fits Place your y data in y_col and the fitted y data in fit_col or change the column numbers to suit your data Results are placed in column res y_col 2 column number for y data fit_col 3 column number for fit results res 4 column number for R2 result Define y and fitted y values y col y_col yfit coL fit Col kkkxkxkxkxx xk kxx xx kxx xx xx xx k CALCULATE R SQUARE KKKKKKKKKKKKKHK n yfit y d y mean y r2 1 0 total n 2 total d 2 xx xx x x PLACE R SQUARE VALUE IN
248. ock dimension from the worksheet pel T he cell function returns a specific cell from the worksheet T he col function returns a worksheet column or portion of acolumn T he put into function places variable or equation results in a worksheet column T he subblock function returns a specified block of cells from within another block T he data manipulation functions are used to generate non random data and to sample select and sort data daa T he data function generates serial data a The if function conditionally selects between two data sets pmth The nth function returns an incremental sampling of data pst T he sort function rearranges data in ascending order 22 Transform Function Descriptions Transform Function Reference Trigonometric SigmaPlot and SigmaStat provide a complete set of trigonometric functions arccos arcsin arccos arcain arctan T EAE E necrccoane cane ada return the arccosine arcsine and arctan gent of the specified argument Functions cos sin tan T hese functions return the cosine sine and tangent of the specified argument T hese functions return the hyperbolic cosine sine and tan gent of the specified argument Numeric Functions Thenumeric functions perform a specific type of calculation on anumber or range of numbers and returns the appropriate results abs Theabs function returns the absolute value T he exp function returns the values for e raised to the speci
249. oeff of X X 1 delta 1 denom W272 GOStt of XX L rl total y MLSs row of X Y r2 total x y 2nd row of X Y bO alpha ritbeta r2 intercept parameter bl beta rit delta r2 slope parameter xx x CALCULATE REGRESSION AND CONFIDENCE DATA sx Regression data xreg data min x max x max x min x 20 yreg b0 b1 xreg Compute t value E aa Se CAN ore Ono eZ Or OZ OOF 2 ASST LOA ee Leer oe Ze Sea Ss S ae is a a a a a car Anda ce eo gee Aa Fonte 210 aay Ae certs a SS t t1234 t4 t5 92160 v 4 Estimate of sigma s sqrt total y b0 b1 x 2 v Confidence Limit data term alphat 2 beta xregtdelta xreg 2 conf_lim sqrt term Graphing Transform Examples 115 Example Transforms up_conf yregtt s conf_lim upper limit low_conf yreg t s conf_lim lower limit Prediction Intervals data pred_lim sqgrt 1 term up_pred yregtt s pred_lim upper prediction limit low_pred yreg t s pred_lim lower prediction limit e eek x PLACE REGRESSION AND CONFIDENCE x NKKKKKKKKKKKKKK DATA IN WORKSHEET KKKKKKKKKKKKKKKK Regression col res xreg x values of regression line col rest l1 yreg y values of regression line Confidence Interval col res 2 up_conf upper confidence limit col res 3 low_conf lower confidence limit Prediction col res 4 up_pred upper prediction limit col res 5 low_pred lower prediction Jamie Low Pass Filter T his trans
250. olumns 1 and 5 graphing column 1 as the X data and column 5 asthe Y data using XY Pairs data format For more information on how to create graphs in SigmaPlot see the SigmaPlot U s s M anual Signal Signal Noise l l l 50 100 150 200 250 10 Smoothing l l 50 100 150 200 250 98 Graphing Transform Examples ee The Kernel Smoothing Transform SMOOTH XFM smoothing with a Low Pass Filter Example Transforms Kernel Smoothing This transform smooths data using kernel smoothing Input ci 3 input column number CO 5 output column number r 10 percentage smoothing Program x col ci data nl size x tx fft x tft Of data nx size tx 2 n 1f int r nx 200ys0 aAnttrsnx 200 1 generate triangular smoothing kernel lt data n 0 1 data 0 0 nx 2 n 2 data 0 n 1t1l l1t total lt tk fft 1t1 fft of kernel td mulcpx tk tx convolve kernel and data sd invfft td transform back to time domain tsd real sd normalize data Output ru if mod nl1 2 gt 0 nx nl 1 2 nx n1 2 2 strip out padded channels rl if mod n1 2 gt 0 nx ru nx ru t1 tsdl tsd data ru rl col co tsdl save smoothed data to worksheet T he Low Pass Filter transform smooths data by eliminating high frequencies Use this transform in contrast to the Kernel Smoothing transform which smooths data by augmenting some frequencies
251. omitted the entire column is used All parameters must be scalar D ata placed in a column inserts or overwrites according to the current insert mode For the worksheet shown in Figure 5 1 the operation col 3 returns the entire range of five values the operation col 3 4 returns 8 9 9 1 and the operation col data2 2 3 returns 7 9 8 4 For the worksheet shown in Figure 5 1 the operation col 4 col 3 2 multiples all the values in column 3 and places the results in column 4 34 Transform Function Descriptions Related Functions complex Figure 5 2 summary syntax Example Related Functions COS summary Transform Function Reference cell f 1 dataz 3 4 z E 5 4000 6 3000 6 3000 12 6000 6 2000 7 9000 7 2000 14 4000 71000 8 4000 8 0000 16 0000 a a000 3 6000 8 9000 18000 35000 10 2000 1000 182000 Loe es r 4 F 2 0S W Oo w m a j aj aj L l Converts a block of real and imaginary numbers into a range of complex numbers complex range range T he first range contains the real values the second range contains the imaginary values and is optional If you do not specify the second range the complex transform returns zeros for the imaginary numbers If you do specify an imaginary range it must contain the same number of values as the real value range If x 1 2 3 4 5 6 7 8 9 10 the operation complex x returns 1 2 3 4 9 10 0 0 0 0 0 0
252. ommand T he U ser D efined Transform dialog box appears If necessary click N ew to clear the edit window and begin a new session Defining a Variable Click the upper left corner of the edit window and type t data 10 11 1 5 Add afew spaces then type the comment generates serial data T he data function is used to generate serial data from a specified start and stop using an optional increment Press Enter to move to the next line then type col 1 t put t into column 1 T his places the variable t into column 1 of the data worksheet Starting a Transform 11 Transform Tutorial 6 Press Enter then type cell 2 1 Results enclose strings in quotes The Edit foo i siaaa Transform untitled All the Transform Edit Transform Equations Entered t data 10 11 1 5 generates serial data _ Bun col 1j t put tinto column 1 Close cell 2 1 Results enclose strings in quotes ee f x 2 x 3 7 x 18 me Open Save Save As Help watch I Single Step Trigonometric Units i Degrees Radians Grads This places the label Results in row one of column 2 Text strings must be enclosed in quotation marks 7 DefiningaFunction Press Enter then type f x 2 x 3 7 x 2 Press Enter add a couple of spaces then type 9 x 5 If you want an equation to use more than one line start each additional line with a blank space or two to distinguish it from a
253. on declaration is function argument 1 argument 2 expression where function is the name of the function and one or more argument names are enclosed in parentheses Function and argument names must follow the same rules as variable names User D efined Functions Frequently used functions can be copied to the Clipboard and pasted into the transform window Transform constructs are special structures that allow more complex procedures than functions Constructs begin with an opening condition statement followed by one or more transform equations and end with a closing statement T he available constructs are for loops and If then else statements A complete set of arithmetic relational and logic operators are provided Arithmetic operators perform simple math between numbers Relational operators define limits and conditions between numbers variables and equations Logic operators set simple conditions for if statements For a list of the operators and their functions see Chapter Transform O perators on page 17 N umbers can be entered as integers in floating point style or in scientific notation All numbers are stored with 15 figures of significance Use a minus sign in front of the number to signify a negative value Figure 2 3 Examples of the Transform Equation Elements Typed into the Transform Window scalars and Ranges Using Transforms i User Defined Transform untitled Iof x Edit Tra
254. on the values and returns a new value as the answer Functions can work with text dates and codes not just numbers A user defined function is similar to a macro but there are differences Some of the differences are listed in the following table Recorded macros User defined functions Performs a SigmaPlot action Returns a value cannot perform such as creating a new chart actions Functions return answers M acros change the state of the based on input values program Can be recorded M ust be created in M acro code Are enclosed in the Sub and Are enclosed in the keywords End Sub keywords Function and End Function The on line help has an extensive section on user defined functions From anywhere in the M acro window press F 1 or choose H elp Topics from the H elp menu A user defined function is like any of the built in SigmaPlot function Because you create the user defined function however you have control over exactly what it does A single user defined function can replace database and spreadsheet data manipulation with a single program that you call from inside SigmaPlot It is alot easier to remember a single program than it is to remember several spreadsheet macros For a full explanation of U ser D efined Functions see the Automation on line reference H elp file Using the Dialog Box Editor The D ialog Box Editor lets you design and customize your own dialog boxes W hen you are designing and creating S
255. ong a line Thelineis described in segments defined by the X Y pairs specified in an x range and ay range dist x range y range T hex range argument contains the X coordinates and the y range argument contains the Y coordinates Corresponding values in these ranges form X Y pairs If the ranges are uneven in size excess X or Y points are ignored For the ranges x 0 1 1 0 0 and y 0 0 1 1 0 the operation dist x y returns 4 0 The X and Y coordinates provided describe a square of 1 unit x by 1 unit y partdist Thedsinp function automatically generates the initial parameter estimates for a damped sinusoidal functions using the FFT method T he four parameter estimates are returned as a vector 38 Transform Function Descriptions syntax 2 Related Functions exp Summary Syntax Example Related Functions factorial Summary Syntax Example 1 Transform Function Reference dsinp x range y range T hex range argument specifies the x variable and the y range argument specifies the y variable Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must be the same size and the number of valid data points must be greater than or equal to 3 dsinp is especially used to estimate parameters on waveform functions T hisis only useful when this function is used in conjunction with nonlinear regression sinp T he exp fu
256. ontinuous section of the NON LIN JN B notebook T he data appears to be described by three lines representing the three regions before wash in during wash in and following wash in View the notebook and double click the Piecewise C ontinuous Regression Equa tion Click the datapoints to select the data then click N ext to run the regression The model with parameters x4 Xz X3 X4 T 1 and T gt isfit to the data Regression Wizard Variable Columns Select your dependent variable 0 Save i walt i har Ty xih 0 Variables save As T A t Column 1 T fo In a Ta a y Pe pre ae 1 ra t T T Options r T ht gt nihet otal Edit Cade 1 ft i a ft T 3 Data Format xv Par gt Cancel Back Next Einizh sr T Click Finish W hen the fit is complete view the graph page A continuous curve fits the three segments of the data B Piecewise Continuous Graph Piecewise Continuous Worksheet OF x Fraction 2 40 Time 6c m 228 Example 3 Piecewise Continuous Function Advanced Regression Examples Example 4 Using Dependencies T his example demonstrates the use of dependencies to determine when the data has been over parameterized Too many parameters result in dependencies very near 1 0 If a mathematical model contains too many parameters a less complex model may be found that adequately describes the data Sums of exponentials are commo
257. ook s Dist Leverage DFFITS 1 0 1262 0 1269 0 9006 2 0 0031 0 1144 0 1361 3 0 0149 0 1029 0 2982 4 0 0071 0 0922 0 2053 2 0 0001 0 0824 0 0184 6 0 0041 0 0733 0 1565 7 0 0223 0 0655 0 3683 3 0 0281 0 0584 0 4167 g 0 0301 0 0521 0 4826 10 0 0347 0 0463 0 4637 Z Row This isthe row number of the observation Cook s Distance Cook s distance is a measure of how great an effect each point has on the estimates of the parameters in the regression equation It is a measure of how much the values of the regression coefficients would change if that point is deleted from the analysis Values above 1 indicate that a point is possibly influential Cook s distances exceeding 4 indicate that the point has a major effect on the values of the parameter estimates Leverage Leverage values identify potentially influential points O bservations with leverages a two times greater than the expected leverages are potentially influential points Interpreting Regression Reports 173 Regression Wizard Figure 8 28 Regression Report 95 Confidence Intervals Report 2 Iofs Times New Roman fia B z U lel B i sO a a peor at amp I 95 Confidence al Row Predicted Regression 5 0 Regression 95 Population 5 0 Population 95 1 0 0004 0 0348 0 0339 0 1028 0 1020 2 0 0012 0 0339 0 0314 0 10320 0 1006 3 0 0021 0 03320 0 0229 0 1033 0 0992 4 0 0029 0 0323 0 0264 0 1037 0 0979 5 0 0037 0 0314 0 0240 0 1040 0 0966
258. oolbar buttons grouped by function Figure 12 8 The Macro Window Toolbar Toggle Object Start Stop Step In Step Out Breakpoint Macros Browser y y y y y y y alasa A A A A A A A A New Pause Find Step Over Step to Quick Dialog Reference Procedure Continue Cursor View Box Editor 246 Editing Macros OT ee Automating Routine Tasks T he following table describes the functions of the toolbar buttons in the M acro Window N ew Procedure O pens the Add Procedure dialog box that lets you name the procedure and paste procedure code into your macro file Runs the active macro and opens the D ebug Window Pause C ontinue Pauses and restarts a running macro T his button also pauses and restarts recording of SigmaPlot commands while using the M acro Recorder Stop Terminates recording of SigmaPlot commands in the M acro Recorder Also stops arunning macro Find O pens the Find dialog where you can define a search for text strings in the M acro Window Step In Executes the current line If the current line is a subroutine or function call execution will stop on the first line of that subroutine or call Step O ver Executes to the next line If the current lineis a subroutine or a function call execution of that subroutine or function call will complete Step O ut Steps execution out of the current subroutine or function call Step to Cursor Steps execution out to the current subroutine or function call Toggle Breakpoint To
259. operty 270 IsCurrentlten property 270 IsO pen property 270 ItemT ype property 270 K eywords property 271 Left property 271 Line property 271 LineAttributes property 271 N ame property 271 N amedO bject property 271 N amedO fRange property 272 N amedR anges property 271 N otebooks property 272 N umberF ormat property 272 O bjectT ype property 272 O wnerG raphO bject property 273 Parent property 273 Path property 273 Plots property 273 Saved property 273 SelectedT ext property 273 ShowStatsW orksheet property 273 StatsW orksheetD ataT able property 273 StatusB ar property 274 StockScheme property 274 Subject property 274 Symbols property 274 T emplate property 275 Text property 275 T ickLabelAttributes property 275 Title property 275 Top priority 275 Visible property 275 Width property 275 PUT INTO function 56 Quitting regression dialog 165 307 Index R R correlation coefficient 163 R correlation coefficient regression 168 R coefficient of determination regression 163 168 RANDOM function 57 Random generation functions 24 Random number generation exponentially distributed 122 Ranges functions 23 operators 18 20 REAL function 58 Recording macros 241 242 References for M arquardt Levenberg Algorithm 145 Regression absolute minimum 222 advanced techniques 237 240 comparing results with linear regression 211 completion status messages 163 constraints parameter 156
260. or a Regression Converged tolerance satisfied E ET A Reg 0 991330164 Nom 21 811955882 View Constraints Value ShdE tr CY Dependencies a 1 943e 2 4 65le O0 2 393e 0 0 3343040 b 20r1e 0 Brae 2 rr0e 0 0 3343042 A 6 659e 0 5 r23e 2 8 594e 1 0 0000004 z Help Cancel Back Finish For interpretation of these results see Interpreting Initial Results on page 163 Setting Results 5 If you wish to modify the remainder of the results that are automatically saved Options click N ext Otherwise click Finish Using the Regression Wizard 149 Regression Wizard Figure 8 4 Selecting the Results to Save These settings are retained between sessions Setting Graph Options Figure 8 5 Selecting the Results to Graph These settings are retained between sessions 6 ve 8 T he first results panel lists gt which results are saved to the worksheet gt whether or not a text report of the regression is to be generated gt whether or not a copy of the regression equation is saved to the section that contains the data that was fitted Select which results you want to keep T hese settings are remembered between regression sessions Regression Wizard Columns Select the columns for your resulte O Save Results save Os Parameters First Ernpty Predicted First Empty Residuals First Empty M Report Add Equation to Notebook Help Cancel Back Next Fi
261. orm Function Reference serno NORE 21 FUNCTION ALGUM ENTS auian aaa ea A a ea dea e 21 Transform Function Descriptions snssessennrnnrrssssnnrrrrrrrsssnrennrrnrssssrernrrnnrrreeererrrrnnee 22 Usor deimed FUNCIONS esonte E 69 Example Transform S insae E ate inate 71 Data TRANSTORM EXAMIDICS reuniran a Oat ad ot i hd a meee ara 71 Graphing Transform Examples scscsscehedscden sa heutaneiusacueiaccuediensnsnds decdaushasdagasmeabe nants 84 Introduction To The Regression Wizard cccccceeeeecseeeeeeseeeeeeseeeeeeeeeees 141 REGESSION Overview isnin iner N anei Maxie leciaias a ia T 141 The Regression Wizard serenocscinnnt a AE 142 PENNO SPI FCS asera A EENT 143 About the Curve FITICK uomnesniunnio a E 144 References for the Marquardt Levenberg Contents AIGONIAM ieee erected acne 145 Regression Wizard sicciavint cos na e a 147 Using the Regression Wizard cccccessssccecssssssscecessseseeeeesssnseeeeessesneeeeessesseseeesssseas 147 Running a Regression From a Notebook sssssssssssesssssssrssesrrrsserrssrrrrsserirsrrrrrsnrrrssnns 151 Creating New Regression Equations cccccscsscccssscessseesssrsessnesesseeesssneessssseesesaes 152 Viewing and Editing COd Gs ici ceil cis ieeaadectiessor E E 153 Variable ODUONS sescs ascarmcccascsautesansenecnceadtcdannsudnonaseuseasSaoieuat toaatantananeasadeatens aa 154 ECU ATIOM OD UOINS o es as karone a dea ie EROR 155 Saving Regression Equation Changes ccccccc
262. ormatted plain text pe Use the voC rLf string data constant to insert a carriage return and linefeed string Transforms To change the value of a transform variable use the AddVariableE xpression method Run transforms using the Execute method TickLabelAttributes Returns the tick label Text objects for the specified Axis object Property Title Property A Notebook object property Sets the N ame of the N otebookl tem object of the N otebook file and the Title field under the Summary tab of the W indows 95 98 file Properties dialog box D oes not affect the file name to change the file name use either the N ame or FullN ame property Top Property Sets or returns the top coordinate of the application window or specified notebook document window Visible Property A property common to the Application Notebook and N otebookltems document objects Sets or returns a Boolean indicating whether or not the application or specified document window is visible Do not set the Application property to False from within SigmaPlot or you will lose access to the application N ote that hidden document windows will still appear in the notebook window tree Setting V isible alse for a notebook object hides all document windows for the notebook as well Width Property Sets or returns the width of the application window or specified notebook document window sigmaPlot Methods M ethods are an action that can be performed on or by an object think o
263. ou can use the inverse of the measurements as an estimate of the weights T he initial weighting variable only needs to be proportional to the inverse variance Example 2 Weighted Regression 225 Advanced Regression Examples 2 Figure 11 13 The Weighted Triple Exponential Equation 3 Figure 11 14 Selecting a Weight Variable 4 5 6 D ouble click the Weighted Triple Exponential equation in the Weighted Regression section Regression Wizard Yanable Columns Select your dependent variable 0 E Save Variables save As re Ais cee t Column 1 Count Rat D de tage 4g f i Options Edit Code Data Format per Fair me Help Cancel Back i oe Finish Click the Edit Code button and examine the Variable value w 1 col 2 T his sets w to equal the reciprocal of the data in column 2 Click Cancel to close the dialog box Click the datapoints to select your variables To use the w variable as the weight ing variable click O ptions and select w as the Fit With Weight value Regression Options x Initial Parameters Parameter Constraints Values i oog Cancel Parameters Help Constants Options Iterations Click OK to close the dialog box Click N ext to run the regression T he curve fitter finds a solution quickly Click Finish to complete the regression W hat would bethe result without weighting Press F5 then click N ext and click O ptions Change the weighting to none
264. ow Pass Filter Graph Plotting Raw Data and Filtered Data Low Pass Filter Transform Example Transforms squared magnitude of the frequency response is reduced by half of its magnitude at zero frequency 5 If necessary change the cy1 source column value and cy2 filtered data results to the correct column numbers 6 Click Run to run the transform Filtered data appears in column 3 in the work sheet or in the worksheet column you specified in the transform 7 If you opened the Low Pass Filter graph view the graph page T he second graph appears as a line graph plotting the smoothed data in columns 1 and 3 Raw Data Low Pass Filtered Time sec 8 To create your own graphs in SigmaPlot create the first graph as a Line Plot with a Simple Spline Curve using the raw data in columns 1 and 2 asthe X and Y data M ake the second Line Plot graph with a Simple Spline Curve using the data in column1 asthe X data and the smoothed data in column 3 asthe Y data For more information on creating graphs in SigmaPlot see the SigmaPlot U ser s M anual xxx First Order Low Pass Recursive Filter This filter will smooth data by reducing frequency components above the half power point It generates the filtered output y 1i from the data x 1 Vib Se Vea ae wk ta eel Graphing Transform Examples 117 Example Transforms where a is computed from the specified half powe
265. ow to read the code for a regression equation Figure 8 25 Regression Report Times New Roman fio B77 U B E Joa A T ors or I F F 0 9990 Reqr 0 9979 Adj Rsqr 0 99078 E Standard Error of Estimate 0 0483 al Coefficient Sid Error t F xl 0 0004 0 0173 0 0239 0 9810 x2 0 0243 O 0171 1 4166 0 1614 x3 2 1455 0017S 120 3852 lt 0 0001 x4 2 0724 0 0172 120 509 lt 0 0001 Ti 30 0100 0 1715 174 9337 lt 0 0001 T2 40 0676 0 1533 257 GALS lt 0 0001 Analysis of Variance DF oo M5 F F Regression 5 71 3886 142777 6125 6520 lt 0 0001 Fesidual d 0 1492 0 002 Total 6g FL S378 1 0368 R and R Squared The multiple correlation coefficient and R2 the coefficient of determination are both measures of how well the regression model describes the data R values near 1 indicate that the equation is a good description of the relation between the independent and dependent variables R equals 0 when the values of the independent variable does not allow any prediction of the dependent variables and equals 1 when you can perfectly predict the dependent variables from the independent variables Adjusted R Squared The adjusted R2 Raj is also a measure of how well the regression model describes the data but takes into account the number of independent variables which reflects the degrees of freedom Larger R g values nearer to 1 indicate that the equation is a good description of the relation between the i
266. p reference Using the Object Browser T he O bject Browser displays all SigmaPlot object classes The methods and properties associated with each SigmaPlot macro object class are listed A short description of each object appears in the dialog box as you select them from the list By clicking F1 you can access extensive H elp that includes example code for the individual properties and methods T he Paste feature lets you insert generic code based on your selection into a macro T he O bject Browser will be familiar and useful if you are comfortable with object oriented programming If you are not consult one of the excellent introductory texts on Visual Basic For full details on using the O bject Browser press F1 from anywhere in the M acro window 252 Using the Object Browser Automating Routine Tasks Using the Add Procedure Dialog Box Using the Add Procedure Dialog Box Organizing your code in procedures makes it easier to manage and reuse SigmaPlot macros like Visual Basic programs must have at least one procedure the main Subroutine and often they have several T he main procedure may contain only a few statements aside from calling subroutines that do the work SigmaP lot provides a dialog box that generates procedure code for your macros By using the Add Procedure dialog box you can define a sub function or property using the Name Type and Scope boxes Clicking OK pastes the code for anew procedure into yo
267. pears to fit slightly better A Tutorial 2 Graph Tutorial 2 Worksheet Catoid Sinus Reflex Response E amp p E D i z h Lesson 2 Sigmoidal Function Fit 217 N otes Advanced Regression Examples Curve Fitting Pitfalls T his example demonstrates some of the problems that can be encountered during nonlinear regression fits Peaks in chromatograph data are sometimes fit with sums of Gaussian or Lorentzian distributions A simplified form of the Lorentzian distribution is CS oo lt X lt 00 ee where Xq Is the location of the peak value A graph of the distribution for Xp 0 is shown in Figure 11 1 1 Open the Pitfalls worksheet and graph by double clicking the Pitfalls Graph in the NONLIN JNB notebook N ote the positions of data points on the curve 2 Open the Simplified Lorentzian regression equation by double clicking it in the Regression Examples notebook T he Regression W izard opens and displays the variables panel see Figure 11 7 on page 222 3 Click oneof thesymbols on the graph so that the Variables selected are C olumns land 2 T he object is to determine the peak location Xo for the data Since this data was generated from the Lorentzian function above using Xp 0 the regression should always find the parameter value Xo 0 Curve Fitting Pitfalls 219 Advanced Regression Examples How the Curve Fitter Finds Xo Figure 11 1 The Plot of the Sum of Squares for Xp
268. pecify your results click N ext Clicking N ext opens the variables panel You can select or reselect your variables from this panel To select a variable click a curve on a graph or click a column in aworksheet T he equation picture to the left prompts you for which variable to select You can also modify other equation settings and options from this panel using the O ptions button T hese options include changing initial parameter estimates parameter constraints weighting and other related settings For more information on setting options see Equation O ptions on page 155 148 Using the Regression Wizard ke Regression Wizard Figure 8 2 H Graph Page 1 Data 17 Iofs Selecting a Plot as the Data Source for the Regression Wizard Regression Wizard Columns Save ain _ Saveds As Options Edit Code Code Data Format ony z ony z O Hep Cancel Back Next Enin If you pick variables from a worksheet column you can also set the data format See Variable O ptions below for descriptions of the different data formats Viewing Initial 4 When you have selected your variables you can either click Finish or click N ext Results to continue Clicking N ext executes the regression equation and displays the initial results T hese results are also displayed if you receive a warning or error message about your fit pe Figure 8 3 Regression Wizard The Initial Results f
269. ph the results To change the results that are saved use the N ext button to go through the entire wizard changing your settings as desired Running a Regression From a Notebook Because regression equations can be treated like any other notebook item you can select and open regression equations directly from a notebook T his is particularly convenient if you have created or stored equations along with the rest of your graphs and data E View the notebook with the equation you want to use and doubleclick the equation You can also click the equation then click the O pen button The Regression W izard opens with the equation selected Select the variables as prompted by clicking a curve or worksheet columns N ote that at this point you can open and view any notebook worksheet or page you would like and pick your variables from that source Running a Regression From a Notebook 151 Regression Wizard Figure 8 7 Notebook Selecting a Regression _ Mel E Bl Notebook Equation from a Notebook X in 1 0 to Start the Regression S A Da A Wizard a gal Vala Summary Paese liz Graph Page 1 Pree A alssian Parameter hs Delete Help Wud Author Summary Infa f PSS Ine _ Regression Wizard Vanable Columns Select your independent variable 0 Save Variables save Os y ae Options Edit Code Data Format KY col me z ES _ He _Concel_ Back Nee __ Finis
270. ph with three Scatter Plots with Simple Scatter styles Plot each consecutive result column pair as XY pair scatter plots If the mean line option is active in the transform plot the last consecutive result column pair asa XY pair Line Plot with Simple Straight Line style U se labels typed into a worksheet column as the X axis tick labels For more information on how to create graphs in SigmaPlot see the SigmaPlot U s s M anual 106 Graphing Transform Examples ee Example Transforms Frequency xxxx xxx x requency PLoOt Plot Transform kk KK KK KPREOQPLOT XEM AK KH gt KET n kx FREQPLOT XFM G This transform creates frequency plots and mean bars of multiple y data columns Tt uses data in the first columns of the worksheet and creates column pairs for graphing TETERE Nate OCC dU Te DALA ENET EAEE 1 TURN INSERT OFF 2 Enter y data groups into columns in the worksheet starting watch column 2 3 Select a symbol diameter d try 0 05 to 0 10 in do Specify the x Locations for the groups 1727 37 226 are typically used since ticks are usually labeled Important Make sure that the number of numbers in x 1 2 equals the number of y data columns 5 Enter the width of your graph wg in inches double click on graph to determine its width 6 Enter the x range of your graph usually 1 number of groups 7 Enter the vertical data interval w in
271. plots the signal and the signal plus noise distortion The bottom graph is the kernel smoothing of the signal with smoothing set at 10 Press F10 to open the User D efined Transform dialog box then click the O pen button and open SM OOTH XFM transform file in the XFM S directory T he Kernel Smoothing transform appears in the edit window X To usethis transform make sure the Insert mode is turned off 4 Click Run T he results are placed in column 5 unless you specified a different column in the transform If you opened the Kernel Smoothing graph view the graph page Two graphs appear on the page T hefirst graph has two plots the signal and the signal with noise distortion The Line Plot with a M ultiple Straight Line style graphs col umn 1 asthe X data column 2 asthe Y data for the signal and column 3 as the Y data for the signal and the noise distortion T he lower Line Plot with a Simple Straight Line style plots column 1 asthe X data and column 5 asthe Y data using XY Pairs data format To plot your own data using SigmaPlot choose the Graph menu Create Graph command or select the Graph W izard from the toolbar C reate a Line Plot with a M ultiple Straight Line style using X M any Y data format plotting column 1 as the X data column 2 asthe Y data for the signal and column 3 asthe Y data for the signal and the noise distortion Create a second Line Plot graph with a Sim ple Straight Line style using the data in c
272. presents blood pressure measurements made in the Analyzing the Data neck carotid sinus pressure and near the outlet of the heart the mean arterial pressure T hese pressures are inversely related If the blood pressure in your neck goes down your heart needs to pump harder to provide blood flow to your brain Without this immediate compensation you could pass out every time you stood up Sensors in your neck detect changes in blood pressure sending feedback signals to the heart For example when you first get out of bed in the morning your blood tends to drain down toward your legs T his decreases the blood pressure in your neck so the sensors tell the heart to pump harder preventing a decrease in blood flow to the brain You can do an Interesting experiment to demonstrate this effect Stand up and relax for a minute then take your pulse rate Count the number of pulses in 30 seconds then lie down and immediately take your pulse rate again Your pulse rate will decrease as much as 25 Your heart doesn t have to pump as hard to get blood to the brain when you are lying down 1 Open the Tutorial 2 graph file by double clicking the graph page icon in the Tutorial 2 section in theN ON LIN JNB notebook Examinethe graph T hetwo pressures are clearly inversely related As one rises the other decreases T he shape appears to be a reverse sigmoid suggesting the use of a sigmoidal equation A sigmoid shaped curve looks like an S tha
273. presents the SigmaPlot data worksheet Use this object to perform worksheet edit operations and to access the data using the D ataT able property To use the NativeWorksheetltem Object T he N ativeW orksheetl tem object has the standard notebook item properties and methods A N ativeW orksheetltem is returned from the N otebookltems collection using the Item property or collection index and created using the N otebookl tems Add method T he N ativeW orksheetltem object has an ItemType property and N otebookltems Add method value of 1 SigmaPlot Objects and Collections 257 SigmaPlot Automation Reference Excelltem Object Usethis object to manipulate in place activated Excel worksheets In general most N ativeW orksheetltem properties and methods also apply to Excel worksheets To use the Excelltem Object The Excelltem object also has the standard notebook item properties and methods An Excelltem is returned from the N otebookltems collection using the Item property or collection index and created using the N otebookltems Add method The Excelltem object has an ItenType property and N otebookltems Add method value of 8 gt N ote that you can only create an Excelltem if you have Excel for O ffice 95 or 97 installed DataTable Object Represents a table of data as used by a worksheet or graph page T his object s properties and methods can be used to access the data in a worksheet or page and also return the N amedR anges row and
274. put heading in the transform file to reflect the number of data columns you are using If your data isin other columns or more than three columns specify the new columns after you open the FREQ PLOT XFM transform file Enter the tick labels for the X axis in a separate column and specify tick labels Graphing Transform Examples 105 Example Transforms Figure 6 9 Frequency Plot Graph from acolumn using the Tick Labels Type drop down list in the Tick Labels panel in Graph Properties Axis tab Press F10 to open the User D efined Transform dialog box then click the O pen button and open the FREQ PLOT XFM transform file in the XFM S directory T he Frequency Plot transform appears in the edit window Click Run T he results are placed starting one column over from the original data If you opened the sample Frequency Plot graph view the graph page A Scatter Plot appears plotting columns 5 and 6 7 and 8 and 9 and 10 as three separate XY Pair plots T he lines passing through each data interval is a fourth Line Plot with a Simple Straight Line style plotting columns 11 and 12 asan XY pair rep resenting the mean value of each data interval The X axis tick marks are gener ated by the transform T he axis labels are taken from column 13 Frequency Plot w Ce Cee NS Coac amp 17 coe O lai GO BBE a a 0 l l l Control Drug A Drug B To create your own graph using SigmaPlot make a gra
275. r WOLE iC KAKKKKKKKKK Input KAKKKKKKKK at 401 sampling interval sec fc 5 half power point of filter Hz eyl 2 column number for input data KAKKKKKKKK RESULTS KAKKKKKKKK cy2 3 column number for filtered output KAKKKKKKKK Program KAKKKKKKKKK Di arccos 1 COSZDLL S COs 2 pi erd a Z COsZpre SATE COS PIE 2 47 cosZ pret Ss ELLES Coeritlcrent cell cy 1 cell cx 1 recursive filter for i 2 to Sizei col cx do celintcy 73 a cell icy 1 2 laa cel hex a end for Lowess Smoothing Smoothing is used to elicit trends from noisy data Lowess smoothing produces smooth curves under a variety of conditions Lowess means locally weighted regression Each point along the smooth curve is obtained from a regression of data points close to the curve point with the closest points more heavily weighted They value of the data point is replaced by the y value on the regression line The amount of smoothing which affects the number of points in the regression is specified by the user with the parameter f T his parameter is the fraction of the total number of points that is used in each regression If there are 50 points along the smooth curve with f 0 2 then 50 weighted regressions are performed and each regression is performed using 10 points An example of the use of lowess smoothing for the U S wheat production from 1872 to 1958 is shown in the figures below T he smoothing param
276. r Transform fft of the data produced by the fft to restore the data to its new filtered form invfft block T he parameter is a complex block of spectral numbers with the real values in the first column and the imaginary values in the second column T his data Is usually generated from the fft function T he invfft function works on data sizes of size 2 numbers If your data set is not 2 in length the invfft function pads 0 at the beginning and end of the data range to make the length 2 Transform Function Descriptions 47 Transform Function Reference Example Related Functions summary syntax Example Related Functions log summary syntax Example T he function returns a complex block of numbers If x 1 2 3 9 10 0 0 0 0 0 the operation invfft fft x returns 0 0 0 1 2 3 9 10 0 0 0 0 0 0 0 0 fft real imaginary complex mulcpx invcpx T heln function returns a value or range of values consisting of the natural logarithm of each number in the specified range In numbers T henumbers argument can be a scalar or range of numbers Any missing value or text string contained within a range is ignored and returned as the string or missing value For In x X lt 0 returns an error message and X 0 returns co T he largest value allowed is approximately x lt 104933 T he operation In 2 71828 returns a value 1 0 exp The log function returns a value
277. raints if the regression produces parameter values that you know are inaccurate Simply click Back from the initial results panel click the O ptions button and enter constraint s that prevent the wrong parameter results N ote that if the curve fitter encounters constraints while iterating you can view these constraints from the initial results panel using the C onstraints button For more information see Checking Use of Constraints on page 164 To enter constraints click the Constraints edit box and type the desired constraint s using the transform language operators A constraint must be a linear equation of the equation parameters using an equal or inequality lt or gt sign For example you could enter the following constraints for the parameters a b c d and a lt 1 10 0 20 gt 2 d e 15 a gt b c d e H owever the constraint a X lt 1 is illegal since x is a variable not a parameter and the constraints b c 2 gt 4 d e 1 Equation Options 157 Regression Wizard Figure 8 14 Entering Parameter Constraints Defining Constants Fit with Weight 158 Equation Options are illegal because they are nonlinear Inconsistent and conflicting constraints are automatically rejected by the curve fitter Cancel Help Options Iterations fioo Step Size hoo Tolerance 0 0001 oo Parameter Constraints z Constants none k Initial Parameters Values Automat
278. rameter In either case data steps in the correct direction Remainders are ignored T he operation data 1 5 returns the range of values 1 2 3 4 5 T he operation data 10 1 2 returns the values 10 8 6 4 2 N ote that if start and stop are equal this function produces a number of copies of start equal to step For example the operation data 1 1 4 returns 1 1 1 1 size array reference Transform Function Descriptions 37 Transform Function Reference diff summary syntax Examples Related Functions dist summary syntax Example Related Functions dsinp summary T he diff function returns a range or ranges of numbers which are the differences between a given number in a range and the preceding number T he value of the preceding number is subtracted from the value of the following number Because thereis no preceding number for the first number in a range the value of the first number in the result is always the same as the first number in the argument range diff range T he range argument must be a single range indicated with the brackets or a worksheet column Any missing value or text string contained within the range is returned as the string or missing value For x 9 16 7 the operation diff x returns a value of 9 7 9 For y 4 6 12 the operation diff y returns a value of 4 10 18 sum total T he dist function returns a scalar representing the distance al
279. rations involving two ranges corresponding entries are added subtracted etc resulting in a range reoresenting the sums differences etc of the two ranges If one range is shorter than the other the operation continues to the length of the longer range and missing value symbols are used where the shorter range ends For operations involving a range and a scalar the scalar is used against each entry in the range Example T he operation col 4 2 produces a range of values with each entry twice the value of the corresponding value in column 4 18 Operations on Ranges Transform Operators Arithmetic Operators Arithmetic operators perform arithmetic between a scalar or range and return the result Add Subtract also signifies unary minus x M ultiply Divide or Exponentiate M ultiplication must be explicitly noted with the asterisk Adjacent parenthetical terms such as a b c 4 are not automatically multiplied Figure 4 2 i User Defined Transform untitled iof x Arithmetic Operator Examples Edit Transform col 3 col 1 col 2 col 5 col 1 col 2 2 1 0 col 4 Trigonometric Units i Degrees Radians Grads Relational Operators Relational operators specify the relation between variables and scalars ranges or equations or between user defined functions and equations establishing definitions limits and or conditions or EQ Equal to gt or GT Greater th
280. re named ranges Notebookltems A Notebook object property that returns the collection of notebook items Use the Property Notebookltems collection to access individual notebook items Worksheets pages equations reports macros and section and notebook folders are all notebook items and can be returned as objects Notebooks Property An Application object property that returns the N otebooks collection object U se the N otebooks collection to return individual N otebook objects and create new notebooks NumberFormat Sets or returns the format used by the currently selected cells in the D ataT able of the Property NativeWorksheetltem or Excelltem object If there is no selection the format for the entire worksheet is assumed If there are mixed formats aN ULL value is returned Both Number and D ate and Time formats are set or returned using the standard number and date and time format designations ObjectType Property Returns the type value for the specified object T he values returned and corresponding object types are p pome p oo a or em o pern e C eras a ferret te eras te fo foroo fo o forme te fe ert runction rn fa forem fea a forme foe m orome par 272 SigmaPlot Properties OwnerGraphObject Property Parent Property Path Property Plots Property Saved Property SelectedText Property SelectionExtent Property Show StatsWorksheet Property StatsWorksheetData Table Property SigmaPlo
281. rent graph and page objects All drawn shapes ellipses and rectangles as well as graph bars and boxes pie slices meshes and any other filled object Solids have an O bjectT ype value of 8 or GPT SOLID To use the Solid Object Solid objects can be returned from anumber of other groups or collections using different properties To access the solid object s for a Plot use the Fill property To access the solid object s within a Page or an AutoLegend use the ChildO bjects property M any Solid attributes and attribute values can only be returned or set using the G eAttribute and SetAttribute methods Use the Solid Attribute constants to specify these attributes Represents the collection of tuples for a Plot object A tuple is an individual curve or series reoresenting a plotted column or column set For example an XY pair plotted as a scatter plot a single column plotted as a bar series or a column plotted as a mean are all tuples To use the Tuples GraphObjects Collection The Tuples collection is returned from a Plot using the ChildO bjects property U se the Tuple collection return specific tuples or add new tuples A tupleis an object that represents a plotted column or column pair displayed as a curve datapoint or bar series A plot always consists of a collection of one or more tuples Tuples have an O bjectT ype value of 9 or GPT_ TUPLE To use the Tuple Object Tuples are returned from the Tuples GraphO bjects col
282. ributed about the regression line If the normality test fails a warning appears in the report Failure of the normality test can indicate the presence of outlying influential points or an incorrect regression modal Interpreting Regression Reports 171 Regression Wizard Constant Variance Test Power Regression Diagnostics T heconstant variance test results displays whether or not the data passed or failed the test of the assumption that the variance of the dependent variable in the source population is constant regardless of the value of the independent variable and the P value calculated by the test W hen the constant variance test fails a warning appears in the report If the constant variance test fails you should consider trying a different model i e one that more closely follows the pattern of the data using a weighted regression or transforming the independent variable to stabilize the variance and obtain more accurate estimates of the parameters in the regression equation If you perform a weighted regression the normality and equal variance tests use the weighted residualsw y y instead of the raw residuals y y T he power or sensitivity of a regression is the probability that the model correctly describes the relationship of the variables if there is a relationship Regression power is affected by the number of observations the chance of erroneously reporting a difference alpha and t
283. rm POW SPEC XFM includesthe option to implement the H anning window see page 94 Using the To return the full fft data to the worksheet Block Function 1 Firg assign the data you want to filter to column 1 of the worksheet You can generate the data using a transform or use your own measurements 2 PressF10 to open the User D efined Transforms dialog box then click the N ew button to start a new transform 3 Typethe following transform in the edit window x col 1 real data tx fft x compute the fft bLOCcCK ZA Cx place real tre data back 2n colL Zz place imaginary fft data in Gol 3 4 Click Run T he results are placed starting one column over from the original data Computing Power T he example transform POW SPEC XFM uses the Fast Fourier Transform function Spectral Density then computes the power spectral density a frequency axis and makes optional use of aH anning window To calculate and graph the power spectral density of a set of data you can either use the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 To usethe sample worksheet and graph open the Power Spectral D ensity work sheet and graph by double clicking the graph page icon in the Power Spectral D ensity section of the Transform Examples notebook D ata appears in column 1 of the worksheet and two graphs appear on the graph page T he top graph shows data generate
284. rns 3 3 the third element in the range T he notation x 4 1 2 produces the range 4 8 1 4 3 7 The constructor notation is not restricted to variables any expression that produces a range can use this notation ee Using Transforms Example T he operation col 3 2 produces the same result as col 3 2 2 or cell 3 2 T he notation 2 4 6 8 3 produces 6 If the value enclosed in the square brackets is also a range a range consisting of the specified values is produced Example T he operation col 1 1 3 5 produces the first third and fifth elements of column 1 Figure 2 4 Range and Array Reference User Defined Transform untitled Jof x Operations Typed into Edit Transform the User Defined Rur Transform Window x 1 2 3 4 5 6 78 5 10 y x 1 3 5 z col 3 1 3 5 col ij col 2 z Close Open Save PEPE Save Ag i Revert Trigonometric Units f Degrees Radiane Grads Watch Single Step Transform Components 9 N otes Transform Tutorial T he following tutorial is designed to familiarize you with some basic transform equation principles You will enter transform data into a worksheet and generate a 2D graph Starting a Transform To begin a transform 1 Click the N ew N otebook k button or choose the File menu N ew command and select N otebook An empty worksheet appears Choose the D ata menu User D efined Transform c
285. roaches the same value for both large positive and negative values of x so the difference of the sum of squares for Xo 1000 and Xp 546 is within the default value for the tolerance 7 Reducing tolerance for a successful convergence Click Back then click O ptions again Change the Tolerance value to 0 000001 then click OK Figure 11 6 Regression Options Changing the Tolerance to ae z ees nitial Parameters arameter Constraints 0 0001 Values jioo0 Cancel Parameters Help Constants Options Iterations fioo Step Size fioo Tolerance z Fit with Weight none AOC 8 Click Next The regression continues beyond Xp 546 and successfully finds the absolute minimum at Xp 0 Figure Her Regression Wizard The Results of Using a Step Size of 100 Converged tolerance satisfied eE and Tolerance of 0 000001 Rsg 1 Norm 2 292920901 e 6 Vien Constraints Value StdE rr CY Dependencies 0 1 510e 56 2 259de 6 1 520e 2 0 0000000 zl Help Cancel Back H i Finish Summary When you used a poor initial parameter value you needed to use a large initial step size to get the regression started and you had to decrease the tolerance to keep the regression from stopping prematurely Poor initial parameters can arise also when using the Automatic method of determining initial parameters as well as when constant values are used You will now use initial parameter values which result in conver
286. row head gt theanglein degrees between the arrow head and the arrow body gt thelength of the vector if you want to specify it as a constant To generate a vector plot you can either use the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 Tousethe sample worksheet and graph double click the graph page icon in the Vector section of the Transform Examples notebook T he Vector worksheet appears with data in columns 1 through 4 T he graph page appears with an empty graph 2 To use your own data enter the vector information into the worksheet D ata must be entered in four column format with the XY position of the vector start ing in the first column the length of the vectors which correspond to the axis units and the angle of the vector in degrees T he default starting column for this block is column one 3 PressF10 to open the User D efined Transforms dialog box then click the O pen button to open the VECTOR XFM filein the XFM S directory 4 If necessary change the starting worksheet column for your vector data block xe 5 If desired change the default arrowhead length L in axis units and the Angle used by the arrowhead lines T his isthe angle between the main line and each arrowhead line 6 If you want to use vectors of constant length set the I value to the desired length then uncomment the remaining two lines under the C onstant Vector Le
287. rs T he control lines are plotted as a Simple H orizontal Step Plot using columns 4 and 5 versus their row numbers T he mean line for the fractional defectives is drawn with a reference line To create your own graph create a Line and Scatter Plot with a Simple Line style then plot column 3 as Y data against the row numbers Add an additional Line Plot using the M ultiple H orizontal Step Plot style plotting columns 4 and 5 versus their two numbers then add a reference line to plot the mean line for the fractional device For more information on creating graphs in SigmaPlot refer to the SigmaPlot U s s M anual Graphing Transform Examples 85 Example Transforms Figure 6 3 Control Chart Graph Fractional Device p Lot Number Control Chart Transform for Fraction Defective Control Chart Transform with Unequal Sample Sizes CONTROL XFM This transform takes sample size and number of defectives returns the fraction of defectives and data for upper and lower control limit lines Place the sample size data in n_col and the number of defects in def_col or change the column numbers to suit your data Fraction defective results are placed in the percent_col column and the data for the control lines is n placed in columnas lt l and clei n_col 1 sample size column def_col 2 number of defectives column percent_col 3 fraction defective results column cl1l 4 EIS PeSsiml
288. rs Parameter Constraints Values Automatic Parameters lheratians fioo Step Size hoo Tolerance fo 000100 Fit With weight none k If you want to edit the settings in the equation document manually click the Edit Code button For more information on editing equation documents manually Editing Code on page 185 U se the Regression O ptions dialog box to gt changeinitial parameter values gt add or change constraints gt change constant values Equation Options 155 Regression Wizard Parameters Figure 8 12 Setting Initial Parameter Options Constraints 156 Equation Options gt useweighted fitting if it is available gt change convergence options T he default setting for the equation is shown T he Automatic setting available with the built in SigmaPlot equations uses algorithms that analyze your data to predict initial parameter estimates T hese do not work in all cases so you may need to enter a different value Just click the parameter you want to change and make the change in the edit box T he values that appear in the Initial Parameters drop down list were previously entered as parameter values Any parameter values you enter will also be retained between sessions Regression Options Initial Parameters Values BN Iterations 100 Step Size 100 Tolerance 0 000100 dh Fit With Weight none k Parameters can be ei
289. s F TEST XFM BERR ER with the F test KERER This transform uses the residuals from two curve fits of functions from the same family to determine if there is a significant improvement in the fit provided by the higher rorder fitting TUNGE ron The F statistic is computed and used to obtain an approximate P value VAKKKK Input KKKKKK nl 3 number parameters for lst function fewest parameters Data Transform Examples 81 Example Transforms n2 5 number parameters for 2nd function csl 6 residual column for function 1 cs2 9 residual column for function 2 cres 10 first column of two results columns TAKKK KX Program KKKKKK N size col cs1 ssl total eol esi 42 ss2 total col cs2 2 F ssl ss2 ss2 N n2 n2 n1 Approximate P value for F distribution N1 n2 n1 n Ae Sy Ege 26s Log Poe G47 N2 N n2 Sa OCS a aa a a E Sqru 27 O7 Nye O42 ey CO ANZ Normal distribution approximation for P value i 1415926 Ags Bo 2632 17 PISA Z OxO X27 ZI Sgr E270 t 1 1 2316419 x paz 20 LO9S81S3 e 3 50p6S 76240241 TO LATTAT AG SS leOZuvoo ore AFL 3302 1442948 Ss VAKKKK Output KKKKKK col cres F p col crest 1l F p R for Nonlinear Regressions You can use this transform to compute the coefficient of determination R2 for the results of a nonlinear regression T he original Y values and the Y data from the fitted curve are used to calculate R2 T
290. s W H Flannery B P Teukolsky S A and Vetterling W T 1986 Nume ical Recipes Cambridge C ambridge U niversity Press M arquardt D W 1963 An Algorithm for Least Squares Estimation of Parameters Journal of the Society of Industrial and Applied M athenatics 11 431 441 Nash J C 1979 Compact Numerical M ethods for Computers Linear Algebra and Function Minimization N ew York John Wiley amp Sons Inc Shrager R I 1970 Regression with Linear Constraints An Extension of the M agnified Diagonal M ethod Journal of the Association for Computing M achinery 17 446 452 Shrager R I 1972 Quadratic Programming for N Communications of the ACM 15 41 45 References for the Marquardt Levenberg Algorithm 145 N otes Regression Wizard T he Regression W izard is designed to help you select an equation and other components necessary to run a regression on your data T he Regression W izard guides you through gt Selecting your equation variables and other options gt Saving the results and generating a report gt Plotting the predicted variables Using the Regression Wizard Selecting the Data Source Selecting the Equation to Use To run the Regression Wizard l O pen or view the page or worksheet with the data you want to fit If you select a graph right click the curve you want fitted and choose Fit C urve If you are using a worksheet highlight the variables you want
291. s 2 through 6 you can enter the following variable statements X col 1 col 1 col 1 col 1 col 1 y col 2 col 3 col 4 col 5 col 6 The variable x isthen column 1 concatenated with itself four times and variable y is the concatenation of columns 2 through 6 lf the function to be fit isf then the fit statement fit f to y fits f to the dependent variable values in columns 2 through 6 for the independent variable values in column 1 Editing Code Weight Variables Specifying the Weight Variable to Use Defining Optional Weight Variables When to Use Weighting 2 The Weighting Process Norm and Residuals Changes Variables used to perform weighted regressions are Known as weight variables All weight variables must be defined along with other variables in the Variables window T he use of weighting is specified by the Equation section code which can call weight variables defined under Variables Weight variables are selected from the fit statement using the syntax fit f to y with weight w where w is the weight variable defined under Variables See Equations on page 193 for additional details on how to define the fit statement Generally a weight variable is defined as the reciprocal of either the observed dependent variable or its square For example if y col 2 is the observed dependent variable the weighting variable can defined as 1 col 2 or as 1 col 2 2 For ademo
292. s Options dialog box To set the options of the Macro Window 1 With amacro window open on the Tools click O ptions 248 Editing Macros Figure 12 9 The Options Dialog Box Macro Tab Parts of the Macro Language 2 3 4 5 Automating Routine Tasks The O ptions dialog box appears Options Page System Maca Graph Defaults Font Courier New Code Colors HighlightCornment Size fio HighlightE rror HighlightE sec HighlightExtension Peen Color AaBBHYYyZez Dk Red Macro Library C Program Files PW 55 gmat M Require Variable Definitions Erowsze Cancel Apply Help Click the M acros tab Set text colors for different types of macro code and D ebug W indow output Change font characteristics Set the location for the macro library T he following topics list the parts of the macro programming language Programming Statenents are instructions to SigmaPlot to perform an action s Statements can consist of keywords operators variables and procedure calls K eywords are terms that have special meaning in SigmaPlot For example the Sub and End Sub keywords mark the beginning and end of amacro By default keywords appears as blue text on color monitors To find out more about a spe cific keyword in a macro select the keyword and press F1 When you do this a topic in the SigmaPlot on line reference appears and presents information about the term
293. s that appear in the Regression W izard are read from a default regression library T he way the equations are named and organized in the equations panel is by using the section name as the category name and the entry name as the equation name Standard _jfl SAME Standard Equations BL Polynomial Open ee J Linear SUMMA Quadratic a Cubic Delete Han Inverse First Order nverse Second Order Inverse Third Order Peak Summary Info S Help igmoidal Author H L Exponential Decay shes Wis J Exponential Rise to Wasimum Created Exponential Growth 12 16 96 16 37 43 I Hyperbole J Waveform H E Power i Rational Description EB C Logarithm Notebook f G 3D u User Defined Modified 01703 1997 11 39 14 For example the STAN DARD JFL regression library supplied with SigmaPlot has twelve categories of built in equations gt Polynomial Peak Sigmoidal Exponential D ecay VV Y Regression Equation Libraries and Notebooks 175 ce Regression Wizard Opening an Equation Library Using a Different Library for the Regression Wizard Figure 8 30 Selecting the Regression Equation Library Exponential Rise to M aximum Exponential Growth H yperbola Waveform Power R ational Logarithm 3D VVVVVVYV y T hese categories correspond to the section names within the STAN DARD JFL notebook T he equations for these different categories are listed in Appendix
294. scccsssseccsssesssesessseessseesssseeessneeeseaes 162 Watening DOSF IP VOQT CS S arudie a a enced sien tesssuestenaeea st fond 162 interpreting Initial RESUNS incisive wien ewan R 163 Saving Regression Results sate siarteniny svenuate tend duusicllnedath aduseedaninunusei adam ianttrandnieaands 165 Graphing Regression Equations ciccsiesetssccsemaavatai iomdinacim adeedndaaeener lonelier 166 Interpreting Regression Reports ccesseesssseseesssseeeesesseeeessseressenetessestesssnnteens 167 Regression Equation Libraries and Notebooks cccceceesseceestsseeessseteesssteeesessneeseees 175 Curve Fitting Date And Time Data cccecccsseccessecescssseeeesssseeesssseeessssseeesseseeesseas 177 Regression Results Messages ditcnint tears eee te Maa N OR 181 EdUNG COUE sxiscisatacanarseoanccartewesaites E EAA EEA EA 185 About Regression EquaUon S zerrissen A 185 Entering Regression Equation Settings cc ccccscccssssssssssessssresssresssnreessnreeseneeesens 188 SVINI EGUNON Sise e EE 192 ECE LING en ye atactee satinustee se bcusace ta dete leanet ean cst ste emancee ee vmenantadetenceusesentats 193 Vara OS rose nr E teed acecke oar ceeeebe Emenee see 194 Went NY AN AD IOC sase A E wasted oes 197 initial Parameters oie eee E es 198 COINS EIU ste A E E E E snes E E E ge saceu ET 199 OMe OpNON Sisona a a a ao 200 Automatic Determination of Initial Parameters sssnssseesnnnsseeenrssssrrrrrsererrrssserrrrnssne 202 Regression LESSONS
295. sd convert back to the time domain nx size tx 2 remove padded channels ru if mod n 2 gt 0 nx n 1 2 nx n 2 2 rl if mod n 2 gt 0 nx ru nx ru t1 Output col co td data ru rl place results in worksheet Frequency Plot T his transform example creates a frequency plot showing the frequency of the occurrence of data in the Y direction D ata is grouped in specified intervals then horizontally plotted for a specific Y value Parameters can be set to display symbols that are displaced a specific distance from each other or that touch or overlap You can also plot the mean value of each data interval T his transform example shows overlapping symbols which give the impression of data mass To calculate and graph the frequency of the occurrence of a set of data you can either use the provided sample data and graph or begin a new notebook enter your own data and create your own graph using the data 1 To us the sample worksheet and graph open the Frequency Plot worksheet and graph by double clicking the graph page icon in the Frequency Plot section of the Transform Examples notebook D ata appears in columns 1 through 3 of the worksheet and an empty graph appears on the graph page 2 To useyour own data place your data in columns 1 through 3 You can put data in as many or as few columns as desired but if you use the sample transform you must change the X locations of the Y values in the second line under the In
296. section For example you can define y and z variables by entering Variables 195 Editing Code Transform Language Operations User Defined Functions Concatenating Columns 196 Variables y 1 2 4 8 16 32 64 z data 1 100 T his method can have some advantages For example in the example above the data function was used to automatically generate Z values of 1 through 100 which is simpler than typing the numbers into the worksheet N ote that the Regression W izard generally ignores the default variable settings although it requires valid variable definitions in order to evaluate an equation Variables are redefined when the variables are selected from within the wizard H owever you can force the use of the hard coded variable definitions either by selecting From Code as the data source or running the regression directly from the Regression dialog box You can use any transform language operator or function when defining a variable For example x 10 data 2 og 10 8 0 5 y col 2 col 2 x 277xcol 1 0 8 x1 0e 12 z 1 sqrt abs col 3 are all valid variable names Any user defined functions that are used later in the regression code must be defined in the Variables section Constructor notation can be used to concatenate data sets For example you may want to fit an equation simultaneously to multiple y columns paired with one x column If the x data isin column 1 and the y data isin column
297. sform SMOOTH XFM smooths data by convolving the Fast Fourier Transform of a triangular smoothing kernel together with the fft of the data Smoothing data using this transform is computationally very fast the number of Operations is greatly reduced over traditional methods and the results are comparable To increase the smoothing increase the width of the triangular smoothing kernal To calculate and graph the smoothed data you can either use the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 Tousethe sample worksheet and graph open the Kernel Smoothing worksheet and graph by double clicking the graph page icon in the Kerne Smoothing sec tion of the Transform Examples notebook D ata appears in columns 1 through 4 6 and 7 of the worksheet and two graphs appear on the graph page T he first graph has two plots the signal and the signal with noise distortion Column 1 contains the X data column 2 contains the Y data for the signal and column 3 contains the Y data for the signal and the noise distortion T he lower graph is empty 2 Touseyour own data place your data in columns 1 through 2 If your data isin other columns specify the new columns after you open the SMOOTH XFM transform file If necessary specify a new column for the results Graphing Transform Examples 97 Example Transforms Figure 6 6 Kernel Smoothing Graph The top graph shows two
298. sing value as the index You can avoid missing value results by specifying 1 0 infinity as the last value in x table T he optional y table argument is used to assign y values to the x index numbers The y table argument must be the same size as the x table argument but the elements do not need to bein any particular order If y table is specified lookup returns the y table value corresponding to the x table index value i e the first y table value for an index of 1 the second y table value for an index of 2 etc X N ote that the x table and y table ranges correspond to what is normally called a lookup table Transform Function Descriptions 49 ae Transform Function Reference Example 1 For n 4 11 31 and x 1 10 30 col 1 lookup n x places the index values of 1 3 and missing value in column1 31 missing value 4 falls beneath 1 or the first x boundary 11 falls beyond 10 but below 30 and 31 lies beyond 30 Example 2 To generate triplet values for the range 9 6 5 you can use the expression lookup data 1 3 3 1 3 data 1 3 9 6 5 to return 9 9 9 6 6 6 5 5 5 This looks up the numbers 1 3 2 3 1 11 3 12 3 2 2 3 22 3 and 3 using x table boundaries 1 2 and 3 and corresponding y table values 9 6 and 5 y table 9 6 5 x table 1 2 3 1 3 2 3 1 1 3 14 3 2 13 22 3 50 Transform Function Descriptions lowess summary syntax Example Related Functio
299. size historange 1 int2 bar heights y values col restl y LRA GENERATE GAUSSIAN DISTRIBUTION CURVE DATA pi 3 1415926 m mean x s stddev x xl data m 3 s m 3 s 6 s 20 yl sxp x lam 7s 27207 Sart 2 pay s VERE PLACE GAUSSIAN CURVE DATA IN WORKSHEET se col rest 2 xl col res 3 yl interval total y Linear Regression with Confidence and Prediction Intervals T his transform computes the linear regression and upper and lower confidence and prediction limits for X and Y columns of equal length A rational polynomial approximation is used to compute the t values used for these confidence limits Figure 6 12 displays the sample Linear Regression graph with the results of the LINREGR XFM transform plotted TheLINREGR XFM transform contains examples of these two functions gt min gt max To calculate and graph a linear regression and confidence and prediction limits for XY data points you can either use the provided sample data and graph or begin a new notebook enter your own data and create your own graph using the data 1 To usethe provided sample data and graph open the Linear Regression work sheet and graph by double clicking the graph page icon in the Linear Regression section of the Transform Examples notebook T he worksheet appears with data in columns 1 and 2 T he graph page appears with a scatter graph plotting the original data in columns 1 and 2 2 Touseyour own data place
300. sn t appear on a menu 6 Enter the name of the menu under which you want the macro to appear in the M enu N ame field 7 ClickOK Your new macro appears under the menu command you ve just created 8 Enter the same menu command name in the M enu N ame field of future macros if you want them to appear on your new macro command menu By default if the M enu N ame field is left empty the macro name appears on the Tools menu You can also create your own menu by entering the menu name in the M enu Name field Running Your Macro After you have recorded and saved a macro It s ready to run To run a macro from the Macros dialog box 1 OntheTools menu click M acro and then click M acros 244 Running Your Macro Automating Routine Tasks The M acros dialog box appears with a list of available macros Figure 12 6 Macros Dialog Box Macros Macro Name Record Survival Curve Macro Cancel Edit Options Delete Help Source All Actrve Notebooks Browse Description Macra J LEEPER EEE 2 Select the macro to run 3 Click Run To run a macro from a notebook 1 From within a notebook double click the macro icon The M acro dialog box appears with the corresponding macro selected 2 Click Run If the macro does not have any errors or run into difficulties with your data it will run to completion 2 You can also run a macro from the M acro script window T his is useful for debugging th
301. specified polynomial equation rgbcolor T he rgbcolor r g b color function takes arguments r g and b between 0 and 255 and returns color to cells in the work sheet Special Constructs Transform constructs are special structures that allow more complex procedures than functions wor it ihe or cerannniec icone once nia for statement is a looping construct used for iterative processing if then else Theif then else construct proceeds along one of two pos sible series of procedures based on the results of a specified condition Fast Fourier T hese functions are used to remove noise from and smooth data using frequency Transform Functions based filtering o o o mramani ee oarre function finds the frequency domain representation of your data T he invfft function takes the inverse fft of the data pro duced by the fft to restore the data to its new filtered form Thereal function strips the real numbers out of a range of complex numbers T he img function strips the imaginary numbers out of a range of complex numbers Transform Function Descriptions 27 Transform Function Reference Fami l Tecoma bloc or ea complex function converts a block of real and or imag inary numbers into a range of complex numbers T he mulcpx function multiplies two ranges of complex numbers together T he invcpx takes the reciprocal of a range of complex num bers abs Summary Theabs function returns the absolute
302. ssion W izard dialog box displays lists of equations by category If the Lin ear equation is not already selected select the Polynomial category and select Linear as the equation name Figure 1 0 3 Regression Wizard Selecting an Equation in the Regression Wizard Select the equation to fit your data Save Save as r Fn ae Hew Inverse First Order Inverse Second Order Edit Code Inverse Third Order Help Cancel Back Next Finish 3 Click Next to proceed T he next panel prompts you to pick your x or indepen dent variable Click the curve on the page to select it N ote that clicking the curve selects both the x and y variables for you 206 Lesson 1 Linear Curve Fit ee Regression Lessons Figure 10 4 Selecting the Variables to Fit j Tutorial 1 Graph Tutorial 1 Worksheet Regression Wizard Variable Columns Select your dependent variable Tr g Save Variables save As Column 1 Eia Fg ax Options Edit Code Data Format ev Pair Hep __Cancel_ Bak Ci Coe 4 Click Next The Iterations dialog box appears displaying the progress of the fit ting process W hen the process is completed the initial regression results are dis played 5 Examinethe results T he first result column is the parameter values the inter cept is 94 and the slope is 1 24 Figure 10 5 a a Regression Wizard Examining Initial Results Converged zero parameter chang
303. ssion Wizard Pick Output Dialog Box Regression Wizard HH Piecewise Continuous Graph Piecewise Continuous Worksheet Of x Fraction 2 Tim e zc m To create a new graph click the Create N ew Graph check box Click Finish to create a new notebook section containing a worksheet of the plotted data and graph page You can specify the worksheet columns used to add a fitted curve to an existing graph or to create anew graph by clicking N ext from the graph pana Regression Wizard Columns Select the columns for your graph E 4 r Elen Curve Data Column x column First E mpt y column First Empty a aee Help Cancel Back Finish From this panel you can select worksheet columns for X Y and Z data for 3D graphs by clicking worksheet columns T he default of First Empty places the results in the first available column after the last filled cell Interpreting Regression Reports Reports can be automatically generated by the Regression W izard for each curve fitting session T he statistical results are displayed to four decimal places of precision by default Reports are displayed using the SigmaPlot report editor For information on modifying reports refer to the U sas M anual Interpreting Regression Reports 167 Regression Wizard Equation Code Thisisa printout of the code used to generate the regression results See Editing Code on page 185 for more information on h
304. stics menu Linear Regression command H owever because you cannot specify constraints for the regression coefficients a first order regression gives different results To add a linear regression to your original data plot 1 Select the plot of your original data by clicking it on the graph then choose the Statistics menu Linear Regression command Linear Regression Regression Line Confidence Intervals Resulte Regressions Each Curve M All Data In Plot Noite Options Color Black T Extend To Axes Thiet nese ee Fass Through Origin 0 007in Cancel Apply Help 2 Select to draw a 1st order regression and pick a dotted line type for the regres sion line 3 Click OK to accept the regression settings then view the graph N ote the differ ence between the regression and the fitted line use the View menu to zoom in on the graph if necessary B Tutorial 1 Graph Tutorial 1 Worksheet N ote that if you had not used a parameter constraint the result of the nonlinear regression would have been identical to the linear regression If desired you can now save the graph and worksheet to a file using the File menu Save As command Lesson 1 Linear Curve Fit 211 Regression Lessons Lesson 2 Sigmoidal Function Fit T his tutorial leads you through the steps involved in solving a typical nonlinear function for a real world scenario Examining and The data used for this tutorial re
305. sums along the list T he value of the number is added to the value of the preceding cumulative sum Because there is no preceding number for the first number in arange the value of the first number in the result is always the same as the first number in the argument range sum range T he range argument must be a single range indicated with the brackets or a worksheet column Any text string or missing value contained within the range is returned as the string or missing value For x 2 6 7 the operation sum x returns a value of 2 8 15 For y 4 12 6 the operation sum y returns a value of 4 16 10 diff total This function returns ranges consisting of the tangent of each value in the argument given T his and other trigonometric functions can take values in radians degrees or grads This is determined by the Trigonometric U nits selected in the U ser D efined Transform dialog box tan numbers T he numbers argument can be a scalar or range If you regularly use values outside of the usual 27 to 27 or equivalent range use the mod function to prevent loss of precision Any missing value or text string contained within a range is ignored and returned as the string or missing value If you choose D egrees as your Trigonometric Units in the transform dialog box the operation tan 0 45 135 180 returns values of 0 1 1 0 acos asin atan cos sin Transform Function Descriptions 65 Transform F
306. t Automation Reference Returns the object that the current object is contained within T his applies to the different graph page object hierarchies where the Parent property is not supported Returns the object or collection immediately above the current object For graph page items use the O wnerGraphO bject property instead Returns the default path in which SigmaPlot looks for documents or the path of the specified notebook file For notebooks you can use the N ame property to return the file name without the path or use the FullN ame property to return the file name and the path together Returns the collection of plots for the specified Graph object Use an index to return the individual Plot objects for the graph Returns a True or False value for whether of not the document has been saved since the last changes N ote that notebook items that are closed from within SigmaPlot are automatically saved to the notebook but that the notebook file is only saved using a Save or Save AS command or method Returns the text of the current selection from a Reportltem You can set or return a text selection using the SelectionExtent property Returns the array of current selection extents from a Reportltem or Excelltem The Start and stop indices for each selection are listed as individual members of the array e g SelectionExtent 0 is the start of the first selection and SelectionE xtent 1 is the end of the first selection If th
307. t has had its upper right and lower left corners stretched In this case the S is backwards since it starts at a large value then decreases to a smaller value 212 Lesson 2 Sigmoidal Function Fit Regression Lessons Various forms of the sigmoid function are commonly used to describe sigmoids Figure IORI H Tutorial Graph Tutorial 2 Worksheet Iofs Inverse Sigmoidal Curve Showing the Relationship Between Arterial Pressure and Carotid Sinus Pressure Catoid Sinus Reflex Response E amp g E p u z f In this case you will use the four parameter sigmoid function provided in the standard regression library 2 Right click the curve and choose Fit Curve T he Regression W izard appears w i a B Tutorial 2 Graph Tutorial 2 Worksheet lolx Cartoid Sinus Reflex Response Object Properties Graph Properties Graph Wizard Add New Axis Mean Areri Presse mm Hg Clear Hide Bring to Front Send to Back Select Sigmoidal as your equation category and Sigmoid 4 Parameter as your equation Lesson 2 Sigmoidal Function Fit 213 Regression Lessons Figure 10 16 Selecting the Sigmoid 4 Parameter Equation Figure 10 17 The Fit Results for the Four Parameter Sigmoid Function Regression Wizard Equation Category Select the equation to fit your data Save Sigmoidal z Equation Mame Sigmoid 3 Parameter di Save As ESigmoid 4 Parameter Sigmaid 5 Param
308. t of x and y rxy sxy sx sy VERE IORI PLACE STATISTICS IN WORKSHEET eer ars AEA col res N MEAN X MEAN Y STD DEV X STD DEV Y COVARIANCE CORR COEFF col res fi rine Len yMx mny ray Sayy p Tns L Data Transform Examples 75 Example Transforms Differential Equation Solving T his transform can be used to solve user defined differential equations You can define up to four first order equations named fp1 x1 y1 2 3 4 through fp4 X1 Y1 2 3 4 Set any unused equations 0 To solve a first order differential equation l 76 Data Transform Examples Begin anew worksheet by choosing the File menu N ew command then choos ing Worksheet this transform requires a clean worksheet to work correctly O pen the User D efined Transforms dialog box by selecting the Transforms menu User D efined command then clicking the O pen button and opening the DIFFEQN XFM transform filein the XFM S directory T he Differential Equa tion Solving transform appears in the edit window Scroll to the Number of Equations section and enter a value for the negn vari able T his isthe number of equations you want to solve up to four Scroll down to the D ifferential Equations section and set the fp1 through fp4 functions to the desired functions Set any unused equations 0 If only one first order differential equation is used then only the fp1 transform equation is used and fp2 fp3 and fp4 are set to 0 For e
309. ta 0 2 5 this data operation returns numbers from 0 to 2 at increments of 0 5 the operation col 1 interpolate x y range places the range 0 0 0 5 1 0 2 5 4 0 into column 1 If range had included values outside the range for x missing values would have been returned for those out of range values Inv Summary Theinv function generates the inverse matrix of an invertible square matrix provided as a block Syntax inv block T he block argument is a block of numbers with real values in the form of a square matrix The number of rows must equal the number of columns T he function returns a block of numbers with real values in the form of the inverse of the square matrix provided 46 Transform Function Descriptions invcpXx Example summary syntax Example Related Functions invfft Summary Syntax Transform Function Reference For the matrix in block 2 3 4 5 the operation block 2 7 nv block 2 3 4 5 generates the inverse matrix in block 2 7 4 9 T his function takes the reciprocal of a range of complex numbers invcp block Theinput and output are blocks of complex numbers T he invcpx function returns the range 1 c for each complex number in the input block If x complex 3 0 1 0 1 1 the operation invcpx x returns 0 33333 0 0 0 5 0 0 1 0 0 5 fft invfft real imaginary complex mulcpx T he inverse fft function invfft takes the inverse Fast Fourie
310. tem object this method exports either the data in the worksheet to the specified data format or the entire notebook to a previous SPW file format gt If applied to aGraphitem object this method exports either the graphic data on the page to the specified graphic format or the entire notebook to a previous SPW file format gt If applied to the first N otebookltem in the N otebookl temList this method exports the entire notebook to a previous SPW file format GetAttribute Method TheGetAttribute method is used by all graph page objects to retrieve current attribute settings Attributes are numeric values that also have constants assigned to them For alist of all these attributes and constants see SigmaPlot C onstants M essage Forwarding If you use the G etAttribute method to retrieve an attribute that does not exist for the current object the message is automatically routed to an object that has this attribute using the message forwarding table To use the Object Browser to view Constants You can view alternate values for attributes and constants by selecting the current attribute value then clicking the O bject Browser button All valid alternate values will be listed to use a different value select the value and click Paste GetData Method Returns the data within the specified rangefrom aD atal able object as a variant T his variant is always returned as a one dimensional array If a 2D array is specified the data is stacked as a
311. tems collection using the Item property 258 SigmaPlot Objects and Collections Pages Collection Page Object Page GraphObjects Collection Graph Object Plot GraphObjects Collection SigmaPlot Automation Reference or collection index and created using the N otebookltems Add method T he Graphitem object has an ItemType property and N otebookltems Add method value of 2 T he Page object represents a SigmaPlot graph page Graph pages can be different sizes and colors and a page object can be used to return the collections of objects on that page Pages have an O bjectT ype value of 1 or GPT PAGE To use the Page Object A graph page is returned from a Graphitem object using the GraphPages property N ote that since there is currently only one page per graph item you can always use GraphPages 0 to return a page Use the ChildO bjects property to return the GraphO bjects collection or the Graphs property N ote that if a graph is part of a Group object it can only be returned using the Graph property M any Page attributes and attribute values can only be returned or set using the G eAttribute and SetAttribute methods Use the Page Attribute constants to specify these attributes T he Page GraphO bjects Collection represents a collection of the child objects returned from a Page object To use the Page GraphObjects Collection A Page GraphO bjects collection is returned from a Page object using the ChildO bjects propert
312. ter to reach the value of the best parameters T he default step size value is 100 To change the Step Size value type the desired step size in the Step Size edit box or select a previously defined value from the drop down list For more information on use of the Step Size option see Step Size on page 201 For an example of the possible effects of different step sizes see C urve Fitting Pitfalls on page 219 Regression Wizard Tolerance TheTolerance option controls the condition that must be met in order to end the regression process W hen the absolute value of the difference between thenorm of the residuals square root of the sum of squares of the residuals from one iteration to the next is less than the tolerance value the iteration stops The norm for each iteration is displayed in the progress dialog box and the final norm is displayed in the initial results panel Figure 8 18 Regression Options Changing Tolerance Cancel Help Options Iterations foo Step Size 0 00000 Tolerance Fit with weight none e O fno tel Initial Parameters Parameter Constraints Values fiona Parameters Constants Geet W hen the tolerance condition has been met aminimum of the sum of squares has usually been found which indicates a correct solution H owever local minimums in the sum of squares can also cause the curve fitter to find an incorrect solution For an
313. that individual object from the collection first For more information refer to SigmaPlot Automation H elp from the SigmaPlot H elp menu An Application object represents the SigmaPlot application within which all other objects are found M ost other objects must exist inside higher level objects You access objects by applying properties and methods on these higher level objects It is a user creatable object that is outside programs can run SigmaPlot and access its properties directly and will be registered in registry as SPW 32 Application The Application object properties and methods return or manipulate attributes of the SigmaPlot application and main window and access the list of notebooks and from there all other objects 256 SigmaPlot Objects and Collections Notebooks Collection Object Notebook Object Notebookltems Collection Object NativeWorksheetltem Object SigmaPlot Automation Reference To use the Application Object Use Application properties to return attributes of the SigmaPlot application N ote that when using the SigmaPlot macro window all Application methods and properties are global that is you do not need to specify the Application object T he N otebooks collection represents the list of open notebooks in SigmaPlot U se this collection to create new documents and open existing documents as well as to specify and return individual notebooks as objects To use the NotebooksCollection
314. the sorted data in columns 3 and 4 size data T he sart function returns a value or range of values consisting of the square root of each value in the specified range N umerically this is the same as numbers 0 5 but uses a faster algorithm sqrt numbers T henumbers argument can be a scalar or range of numbers Any missing value or text string contained within a range is ignored and returned as the string or missing value For numbers lt 0 sqrt generates a missing value T he operation sqrt 1 0 1 2 returns the range 0 1 1 414 T he stddev function returns the standard deviation of the specified range as defined by 1 2 n 1 2 re i 1 stddev range T he range argument must be a single range indicated with the brackets or a worksheet column Any missing value or text string contained within a range is ignored For the range x 1 2 the operation stddev x returns a value of 70711 stderr Transform Function Descriptions 63 Transform Function Reference stderr Summary The stderr function returns the standard error of the mean of the specified range as defined by S Jn where sis the standard deviation Syntax stderr range T he range argument must be a single range indicated with the brackets or a worksheet column Any missing value or text string contained within a range is ignored Example For therangex 1 2 the operation stderr x returns a value of 0 5
315. the columns will be graphed as means gt From Code uses the current settings as shown when editing code W hen you use an existing graph as your data source the Regression W izard displays a format reflecting the data format of the graph You cannot change this format unless you switch to using the worksheet as your data source or run the regression directly from editing the code Although the standard regression library only supports up to two independent variables the curve fitter can accept up to ten To use models that have more than two Independent variables simply create or open a mode with the desired equation Regression Wizard and variables T he Regression W izard will prompt you to select columns for each defined variable Figure 8 10 Variable Data Format Options for a3D Function Regression Wizard Save a _ Saves As a SF dixie by Options Edit Code dit Code a Columns Select your independent variable Data Format Help Cancel Back Finish From Code Equation Options If the curve fitter fails to find a good fit for the curve you can try changing the regression options to see if you can improve the fit To set options for a regression click the O ptions button in the Variables panel of the Regression W izard The Regression O ptions dialog box of the Regression W izard appears Figure 8 1 1 Regression Options Regression Option Dialog Box Initial Paramete
316. theX datain column 1 and the Y datain column 2 If your data has been placed in other columns you can specify these columns after you open the LIN REGR XFM transform file You can enter data into an existing or anew worksheet 3 PressF10 to open the User D efined Transform dialog box then click the O pen button and open the LINREGR XFM transform in the XFM S directory The Graphing Transform Examples 113 Example Transforms Linear Regression transform appears in the edit window If necessary change the x_col y_col and res variables to the correct column numbers this is not neces sary for the example Linear Regression worksheet data 4 ChangetheZ variable to reflect the desired confidence level this is not neces sary for the example Linear Regression worksheet data 5 Click Run T he results are placed in columns 3 through 8 or in the columns specified by the res variable 6 If you opened the Linear Regression graph view the graph page T he original data in columns 1 and 2 is plotted as a scatter plot T he regression is plotted asa solid line plot using column 3 as the X data versus column 4 asthe Y data the confidence limits are plotted as dashed lines using column 3 as a single X col umn versus columns 7 and 8 as many Y columns and the prediction limits are plotted as dotted lines using column 3 as a single X column versus columns 7 and 8 as many Y columns 7 To create your own graph in SigmaPlot create a Scatt
317. ther a numeric value or a function T he value of the parameter should approximate the final result in order to help the curve fitter reach a valid result but this depends on the complexity and number of parameters of the equation Often an initial parameter nowhere near the final result will still work H owever a good initial estimate helps guarantee better and faster results For more information on how parameters work see Initial Parameters on page 198 For an example on the effect of different initial parameter values see C urve Fitting Pitfalls on page 219 For more information on the use of automatic parameter estimation see Automatic D etermination of Initial Parameters on page 202 Constraints are used to set limits and conditions for parameter values restricting the regression search range and improving curve fitter soeed and accuracy Constraints are often unnecessary but should always be used whenever appropriate for your mode Figure 8 13 Setting Initial Parameter Options Entering Parameter Constraints Regression Wizard Regression Options Initial Parameters BN Step Size Tolerance Fit With Weight none k Constraints are also useful to prevent the curve fitter from testing unrealistic parameter values For example if you know that a parameter should always be negative you can enter a constraint defining the parameter to be always less than 0 You can also use const
318. tion column or the column title enclosed in quotes D ata put into columns inserts or overwrites according to the current insert mode To place the results of the equation y data 1 100 in column 1 you can type col 1 y H owever entering put y into col 1 runs faster col arithmetic operator T his function generates a specified number of uniformly distributed numbers within the range Rand and rnd are synonyms for the random function random number seed low high T he number argument specifies how many random numbers to generate T he seed argument is the random number generation seed to be used by the function If you want to generate a different random number sequence each time the function is used enter 0 0 for the seed If the seed argument is omitted a randomly Selected seed is used T he low and high arguments specify the beginning and end of the random number distribution range The low boundary is included in the range If low and high are omitted they default to 0 and 1 respectively N ote that function arguments are omitted from right to left If you want to specify a high boundary you must specify the low boundary argument first T he operation random 50 0 0 1 7 produces 50 uniformly distributed random numbers between 1 and 7 T he sequence is different each time this random function is used gaussian Transform Function Descriptions 57 Transform Function Reference real Summary Thereal
319. tions M ore precise parameter values can be obtained by decreasing the tolerance value If there is a sharp sum of squares response surface near the minimum then decreasing the tolerance from the default value will have little effect H owever if the response surface is shallow about the minimum indicating a large variability for one or more of the parameters then decreasing tolerance can result in large changes to parameter values For an example of the possible effects of tolerance see Curve Fitting Pitfalls on page 219 Automatic Determination of Initial Parameters SigmaP lot automatically obtains estimates of the initial parameter values for all built in equations found in STANDARD JFL When automatic parameter estimation is used you no longer have to enter static values for parameters yourself the parameters determine their own values by analyzing the data y N ote that it is only important that the initial parameter values are robust among varying data sets i e that in most cases the curve fitter converges to the correct solution T he estimated parameters only have to be a best guess Somewhere in the same ballpark as the real values but not right next to them You can create your own methods of parameter determination using the new transform function provided just for this purpose T he general procedure is to smooth the data if required and then use functions specific to each equation to obtain the
320. tions sort Figure 5 5 summary syntax Example For Figure 5 1 the operation size col 1 returns a value of 6 the operation size col 2 returns a value of 6 and the operation size col 3 returns a value of 4 count missing 1 2 4000 Sample 1 2 asooo boo 3 acon 52000 o 4 08500 8 9000 Sample 5 oso nawo 6 1 1000 14 5000 MWMW O 7 Coe ooo o 8 9 0 q r 4 F L l T hisfunction can be used to sort a range of numbers in ascending order or a range of numbers in ascending order together with a block of data sort block range T he range argument can be either a specified range indicated with the brackets or a worksheet column If the block argument is omitted the data in range is sorted in ascending order T he operation col 2 sort col 1 returns the contents of column 1 arranged in ascending order and places it in column 2 To reverse the order of the sort you can create a custom function reverse x x data size x 1 then apply it to the results of the sort For example reverse sort x sorts range x in descending order 62 Transform Function Descriptions Example Related Functions sqrt summary syntax Example stddev Summary Syntax Example Related Functions Transform Function Reference T he operation block 3 1 sort block 1 1 2 size col 2 col 2 sorts data in columns 1 and 2 using column 2 as the key column and places
321. to increase the value of the density to about 350 y KKKKKKKKKK Output KKKKKKKKKK x result 3 column for x patterned bar fill y_result 4 column for y patterned bar fill KAKKKKKKKKKKHK Program KAEKKKKKKKIKKHK dmax max x_data admin min x data dx dmax dmin density x data dmin dmax dx y interpolate x_data y_data x col x result x col y_result y Shading Tousethistransform to create a shade pattern between two curves you can either use Between Curves the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 To usethe provided sample data and graph open the Shade 2 worksheet and graph by double clicking the graph page icon in the Shade 2 section of the Transform Examples notebook T he worksheet appears with data in columns 1 through 4 T he graph page appears with a line and scatter graph with two curves plotting column 1 against column 2 and column 3 against column 4 2 To useyour own data enter the XY data for the first curve in columns one and two and the XY data for the second curve in columns three and four respec tively The X data for both curves must be in strictly increasing order If your data has been placed in other columns you can specify these columns after you open the SHADE 2 XFM transform file You can enter data into an existing or a new worksheet 124 Graphing Transform Examples Figure 6 17
322. to fit then press F5 or choose the Statistics menu Regression W izard command T he Regression W izard opens Select an equation using the Equation C ategory and Equation N ame drop down lists You can view different equations by selecting different categories and names T he equation s mathematical expression and shape appear to the left Using the Regression Wizard 147 Regression Wizard Figure 8 1 Selecting an Equation Category and Equation Name Selecting the Variables to Fit 3 A Regression Wizard Equation Category Select the equation to fit your data Save Peak i Equation Name save Os y B ael Modified Gaussian 4 Pa Hew Modified Gaussian 5 Pa Lorentzian 3 Parameter Edit Code Help Cancel Back Next For a complete list of the built in equations see Regression Equation Library on page 285 If the equation you want to use isnt on this list you can create a new equation See Editing Code on page 185 for more information You can also browse other notebooks and regression equation libraries for other equations see Regression Equation Libraries and N otebooks on page 175 for more informa tion on using equation libraries N ote that the equation you select is remembered the next time you open the wizard If the Finish button is available you can click it to complete your regression If it isnot available or if you want to further s
323. to which data points will be grouped 8 Enter the first vertical data interval start value e g O if the vertical range is 0 to 100 9 Enter the horizontal distance fx between symbols try 0 05 use negative value for overlap effect 10 Specify ml 1 if you want mean lines computed and specify mean line width eml 11 Specify intvl 1 2 or 3 to place the y data at the bottom center or top of the vertical data interval xxxxxxxxProcedure GEapns eae ar ee 1 Create x y scatter plots for the column pairs 2 If mean lines are computed create an x y line plot with no symbols from the last two columns generated E ERES Ne Na Ce ae Be d 08 size diameter of symbol in x 2 3 hk locations Tor groups Of y values typically 1 2 3 etc wg 5 width of graph in wd 4 x range of graph x maximum minus x mininum fx 0 05 horizontal distance between symbols fraction of symbol Graphing Transform Examples 107 Example Transforms diameter w l vertical data interval y axis units ys 0 first vertical data interval start value y axis units intvl 3 specifies y display position in w interval 1l bottom 2 center 3 top ml 1 include mean lines 0 no 1 yes eml 6 width of mean line x axis units PG IGT ES Ue ts EPIC ONT LIL OS ASAE Ae ON cy l first y group column number colfi size x e le 18 wx 1 fx d wd wg horizonta
324. tolerance satished Veta eee Sum of Three Exponentials Asa 1 Nom 4 834547427e 6 View Constraints Value StdErr Cy re Dependencies 4636e 1 2625e 1 5 662e 3 1 0000000 3 93e1 1 589e 1 1 553e 1 Q000000 4364e 1 2625e 6 0lde 3 1 0000000 1 0036e 0 1 631e 1 1 627e 1 Q000000 1 00067 6 5026 6 502e 3 0 995 245 Help Cancel Back i Finish nooo Example 4 Using Dependencies 231 Advanced Regression Examples Example 5 Solving Nonlinear Equations You can use the nonlinear regression to solve nonlinear equations For example given ay valuein anonlinear equation you can use the nonlinear regression to solve for the x value by making the x value an unknown parameter Consider the problem of finding the LD 5 of a dose response experiment The LD s is the function of the four parameter logistic equation f x 4 d lie where x is the dose and f x is the response then using nonlinear regression you can find the value for x where Wea Tyna 1 Open the Solving N onlinear Equations worksheet and graph file by double clicking the graph page icon in the Solving N onlinear Equations section of the NONLIN JNB notebook N ote that the value for x at y 50 appears to be approximately 150 Figure 11 25 The Solving Nonlinear Equations Graph a Four Parameter Logistic Curve B Solving Nonlinear Equation Graph Solving Nonlinear Equ Miel Eg Response 232 Example 5
325. tom or row right value to the system maximum Rows 32 000 000 Columns 32 000 Converts unsorted xyz triplet data to evenly incremented mesh data as required by mesh and contour plots The optional parameters control the results columns mesh range and increment and original datapoint weighting N ote that the output columns must be specified if the data is to be returned to the worksheet Returns an object from the collection as specified by the object index number or name N ote that the index begins with 0 by default The Item method is equivalent to specifying an object from the collection object using an index If the item does not exist an error is returned M odifies the current plot on the specified Graphitem object using the following parameters graph type any valid type name graph style any valid stylename data format any valid data format name SigmaPlot Methods 281 SigmaPlot Automation Reference NormalizeTernary Data Method Open Method Paste Method Print Method PrintStatsWorksheet Method PutData Method Quit Method Redo Method Remove Method 282 SigmaPlot Methods N ormalize three columns of raw data to 100 or 1 for a ternary plot O pens the notebook specified within the N otebooks collection or the specified notebook item T he parameter depends upon whether you are opening a notebook or anotebook item N ote that for N otebookl tems and SectionItems an O pen corresponds to a
326. tribute that does not exist for the current object the message is automatically routed to an object that has this attribute using the message forwarding table Using the Object Browser to view Constants You can view alternate values for attributes and constants by selecting the current attribute value then clicking the O bject Browser button All valid alternate values will be listed to use a different value select the value and click Paste Changes the attribute specified by Attribute of the current object on the graphics page Use one of the following three techniques to set the current object on the graphics page gt Click the object using the mouse SigmaPlot Methods 283 SigmaPlot Automation Reference setObjectCurrent Method SetSelectedObjects Attribute Method TransposePaste Method Undo Method 284 SigmaPlot Methods gt UsetheSigmaPlot menus eg Select Graph gt UsetheSetO bjectCurrent method If the specified Graphitem is not open or there is no current object of the appropriate type on the page the method will fail Sets the specified object to the current object for the purpose of the SetC urrentO bjectAttribute command It the specified Graphitem is not open the method will fail Changes the attribute specified by Attribute for all the selected objects on the graphics page Select graphics page objects using one of the following two techniques gt C
327. tributed numbers with a specified mean and standard deviation The random function is used to generate a series of uni formly distributed numbers within a specified range Precision Functions The precision functions are used to convert numbers to whole numbers or to round off numbers T he int function converts numbers to integers T he prec function rounds numbers off to a specified num ber of significant digits The round function rounds numbers off to a specified number of decimal places 24 Transform Function Descriptions Transform Function Reference Statistical Functions The statistical functions perform statistical calculations on a range or ranges of numbers T he avg function calculates the averages of corresponding numbers across ranges It can be used to calculate the aver age across rows for worksheet columns T he max function returns the largest value in a range the min function returns the smallest value The mean function calculates the mean of a range T he runavg function produces a range of running averages T he stddev function returns the standard deviation of a range T he stderr function calculates the standard error of a range Area and Distance T hese functions can be used to calculate the areas and distances specified by X Y Functions coordinates Units are based on the units used for X and Y area T he area function finds the area of a polygon described in X Y coordinates d
328. ue for a variable which can then be assigned to a graph object StockScheme Property STOCKSCHEME_ COLOR_BW amp H00010001 STOCKSCHEME_COLOR_GRAYS STOCKSCHEME_COLOR_EARTH STOCKSCHEME_COLOR_FOREST STOCKSCHEME_COLOR_OCEAN STOCKSCHEME_COLOR_RAINBOW STOCKSCHEME_COLOR_OLDINCREMENT STOCKSCHEME_SYMBOL_DOUBLE STOCKSCHEME_SYMBOL_MONOCHROME STOCKSCHEME_SYMBOL_DOTTEDDOUBLE STOCKSCHEME_SYMBOL_OLDINCREMENT STOCKSCHEME_LINE_MONOCHROME STOCKSCHEME_LINE_OLDINCREMENT STOCKSCHEME_PATTERN_MONOCHROME STOCKSCHEME_PATTERN_OLDINCREMENT amp H00020001 amp H00030001 amp H00040001 amp HO0050001 amp HO0060001 amp H00070001 amp H00010002 amp H00020002 amp H00030002 amp H00040002 amp H00010003 amp H00020003 amp H00010004 amp H00020004 Subject Property A standard property of notebook files and all N otebookltems objects Sets the Subject field under the Summary tab of the W indows 95 98 file Properties dialog box N ote that the Subject for notebook items is not currently displayed or used Symbols Property Returns the Symbol object for the specified Plot object 274 SigmaPlot Properties SigmaPlot Automation Reference Template Property Returns the N otebook object used as the template source file T he template is used for new page creation To create a graph page using a template file use the ApplyPagel emplate method Text Property Specifies the text for the report transform or macro code T he text is unf
329. ues missing 7 Variables defining 11 195 198 dependent 190 198 entering 190 198 independent 190 198 relational operators 19 20 scaling large values 238 unknown 183 weight variable 194 197 198 225 V ector plot 134 135 Viewing constraints parameter 164 recorded macros 245 250 W W eight variables defining 197 entering 190 198 non uniform errors 239 norm and residual changes 197 regression 225 when to use 194 197 W eighted regression regression examples 225 227 weight variables 197 W orksheet functions overview 22 X X25 function 66 X50 function 67 X75 function 68 XAT YM AX function 68 XFM files 4 XWTR function 69 Z Z plane design curves transform 137 140 Index 313
330. uit your data Results are placed in column res x_col 1 column for x data res 2 column for Gaussian Cumulative Distribution values x col x_col define x values wens CALCULATE POLYNOMIAL APPROXIMATION TO THE NKKKKKKKKKKKKKKKK ERROR FUNCTION KKKKKKKKKKKKKKKKK You can place the functions erf x and terf x in the Transform Library to create user defined functions for the error function erf x 1 3480242 terf x 0958798 terf x 2 Hela Ooo G hernh lt OT exp x 2 terf x 1 1 47047 x Srri tx S18 xc0 7 Hert x iyert ls Tee CALCULATE GAUSSIAN CUMULATIVE DISTRIBUTION xxxxx xx x AND PLACE RESULTS IN WORKSHEET x Xx P x erf1 x sqrt 2 1 2 Gaussian C D F col res P x col rest 1 col res 100 110 Graphing Transform Examples Example Transforms Histogram with Gaussian Distribution T his transform calculates histogram data for a normally distributed sample then uses the sample mean and standard deviation of the histogram to compute and graph a Gaussian distribution for the histogram data T heH istogram G aussian transform uses examples of the following functions gt gt gt gt gaussian histogram size array reference To calculate and graph a histogram and Gaussian curve for a normally distributed sample you can either use the provided sample data and graph or begin anew notebook enter your own data and create yo
331. unction Reference tanh summary syntax Example Related Functions total summary syntax Examples Related Functions X25 summary T his function returns the hyperbolic tangent of the specified argument tanh numbers T he numbers argument can be a scalar or range Like the circular trig functions this function also accepts numbers in degrees radians or grads depending on the units selected in the U ser D efined Transform dialog box T he operation x tanh col 3 sets the variable x to be the hyperbolic tangent of all data in column 3 cosh sinh T he function total returns a single value equal to the total sum of all numbers in a specified range Numerically this is the same as the last number returned by the sum function total range T he range argument must be a single range indicated with the brackets or a worksheet column M issing values and text strings contained within the range are ignored For x 9 16 7 the operation total x returns a value of 32 For y 4 12 6 the operation total y returns a value of 10 diff sum T he x25 function returns value of the x at min Tange in the ranges of coordinates provided with optional Lowess smoothing T his is typically used to return the x value for the y value at 25 of the distance from the minimum to the maximum of smoothed data for sigmoidal shaped functions 66 Transform Function Descriptions syntax Example Relat
332. unction calculates the arithmetic mean defined as mean range T he range argument must be a single range indicated with the brackets or a worksheet column Any missing value or text string contained within a range is ignored T he operation mean 1 2 3 4 returns a value of 2 5 avg 52 Transform Function Descriptions min summary syntax Example missing summary syntax Example Related Functions Figure 5 4 Transform Function Reference The min function returns the smallest number in the range specified min range T he range argument must be a single range indicated with the brackets or a worksheet column Any missing value or text string contained within a range is ignored For x 7 4 4 5 the operation max x returns a value of 7 and the operation min x returns a value of 4 T he missing function returns a value or range of values equal to the number of missing values and text strings in the specified range missing range T he range argument must be a single range indicated with the brackets or a worksheet column For Figure 5 1 the operation missing col 1 returns a value of 1 the operation missing col 2 returns a value of 0 and the operation missing col 3 returns a value of 4 count size 2 3000 Sample 1 asooo 26000 S acon 52000 S d 0 8500 8 9000 Sample 11 2000 ooo ooo d 11000 14 5000 SSS O rr d y r 4 F 1 2 3 4 a B Fi
333. ur macro at the insertion point For full details on using the Add Procedure press F1 from anywhere in the M acro window Using the Debug Window Debug Toolbar Buttons Debug Window Tabs T he D ebug W indow contains a group of features that are helpful when you are trying to locate and resolve errors in your macro code T he debugging tools in SigmaPlot will be familiar if you have used one of the modern visual programming languages or M icrosoft V isual Basic for Applications Essentially the D ebug W indow gives you incremental control over the execution of your program so that you can Sleuth errors in your programs T he D ebug W indow also gives you a precise way to determine the contents of your variables Again a series of buttons is used to select the operation mode of the D ebug W indow T he debugging features of the D ebug W indow are controlled by buttons on the M acro W indow toolbar To review gt Thefour Step buttons provide methods for controlling the execution of commands T hey offer various ways of responding to subroutines and functions gt TheBreakpoint button lets you set a point and execute the program until it reaches that point gt TheQuick View button displays the value of the expression in the immediate window The inclusion of these features for controlling program execution are a standard but powerful combination of tools for writing and editing macros T he output from the D ebug W indow is orga
334. ur own graph using the data To use the sample worksheet and graph L O pen the H istogram G aussian worksheet and graph by double clicking the graph page icon in the H istogram G aussian section of the Transform Examples notebook T he H istogram worksheet with data in column 1 and an empty graph page appears T he data in the H istogram G aussian worksheet was generated using the trans form col 1 gaussian 100 0 325 2 To use your own data dh Place the sample in column 1 of the worksheet If your data has been placed in another column you can specify this column after you open the H IST GAUS XFM transform file You can enter the data into an existing or new work sheet Press F10 to open the User D efined Transform dialog box then click the O pen button and open the HIST GAUS XFM transform file in the XFM S directory T heH istogram with Gaussian Distribution transform appears in the edit win dow Click Run T he results are placed in columns 2 through 5 of the worksheet or in the columns specified by the res variable If you opened the H istogram G aussian graph view the graph page A histogram appears using column 2 as X data versus column 3 astheY data T he curve plots the Gaussian distribution using column 4 as X data versus column 5 as the Y data To create your own graph using SigmaPlot create a simple vertical bar chart and Graphing Transform Examples 111 Example Transforms set the bar
335. use and how to understand the macro code Deleting TheM acro Recorder creates code corresponding exactly to the actions that you make Unnecessary Code in SigmaPlot while the recorder was turned on You may need to edit out unwanted steps Moving and Copying Code You can cut copy and paste selected text Finding and Replacing Code W hen you need to find and change text in a macro that you have written usethe Find commands For example if you change the name of a file that is referenced in your macro you need to change every instance of thefile name in your macro Use Find to locate the instances of the filename in the macro and replace using cut and paste edit commands Adding Existing If you have another macro that already does what you want you can just paste it into Macros to a Macro your new macro Copy and paste the macro Into your new macro test it in the new code and run it What Macro TheM acro Recorder does not record the following types of activity Recorder Records Cursor movement If you want to include this type of activity in your macro you can usethe IDE features 250 Editing Macros Automating Routine Tasks About User Defined Functions For More Information Creating User Defined Functions A user defined function is a combination of math expressions and Basic code T he function always requires input data values and always returns a value You supply the function with a value it performs calculations
336. valid 181 182 logistic functions 212 217 missing 182 regression results 163 207 214 217 standard error 163 207 214 217 viewing constraints 164 s also function arguments PART DIST function 55 Piecewise continuous model regression example 227 228 Plotting frequencies 105 108 regression results 209 211 transform results 14 Poisson distribution 225 Polynomial approximation for error function 108 POLYNOMIAL function 55 Population confidence interval results 175 Power alpha value 172 regression results 172 Power spectral density Fast Fourier transform 94 PREC function 56 Precision functions 24 Predicted values regression diagnostic results 172 regression results 174 Prediction intervals linear regressions 113 116 PRESS statistic regression results 171 Probability scale 109 Properties 266 Application property 266 Author property 267 Autolegend property 267 Axis property 267 Axistitles property 267 Cell property 267 ChildO bjects property 267 Color property 267 Comments property 268 Count property 268 CurrentD ataltem property 268 Currentltem property 268 CurrentPagel tem property 268 D ataT able property 268 Index D efaultPath property 268 D ropLines property 268 Expanded property 268 Fill property 269 FullN ame property 269 Functions property 269 GraphPages property 269 Graphs property 269 H eight property 270 InsertionM ode property 270 Interactive property 270 IsC urrentBrowser entry pr
337. value for each number in the specified range Syntax abs numbers T henumbers argument can be a scalar or range of numbers Any missing value or text string contained within arangeisignored and returned as the string or missing value Example Theoperation col 2 abs col 1 places the absolute values of the data in column 1 in column 2 ape Summary Theape function is used for the polynomials rational polynomials and other functions which can be expressed as linear functions of the parameters A linear least Squares estimation procedure is used to obtain the parameter estimates T he ape function is used to automatically generate the initial parameter estimates for SigmaP lot s nonlinear curve fitter from the equation provided Syntax ape x rangey rangen m sf T hex range and y range arguments specify the independent and dependent variables or functions of them e g In x Any missing value or text string contained within one of the ranges is ignored and will not be treated as a data point x range and y range must be the same size Then argument specifies the order of the numerator of the equation Them argument specifies the order of the denominator of the equation n and m must be greater than or equal to 0 n m 0 If m is greater than 0 then n must be less than or equal tom if m gt 0 n lt m 28 Transform Function Descriptions Example arccos Summary Syntax Example Related Functions Transform Function Referenc
338. values can be critical for a successful convergence to a solution All built in equations use a technique called automatic parameter estimation which computes an approximation of the function parameters by analyzing the raw data You can indicate the parameter value you wish to appear as the Automatic setting by typing two single quotes followed by the string Auto after the parameter setting For example entering the parameter line a max y Auto tells the Regression O ptions dialog box to use max y as the Automatic parameter value for a T his technique is further described under Automatic D etermination of Initial Parameters on page 202 Alternate Parameter Values Constraints Valid Constraints Editing Code You can insert alternate parameter values that appear in the Regression O ptions dialog box Initial Parameter Values drop down lists To add an alternate insert anew line after the default value then type two single quotes followed by the alternate parameter setting For example the line d F 0 2 Auto d 0 01 Causes an alternate value of 0 01 to appear in the Regression O ptions dialog box Initial Parameter Values drop down list for d Alternate parameter values are automatically inserted when different parameter values are entered into the Regression O ptions dialog box Linear parameter constraints are defined under the C onstraints section A maximum of 25 constraints can be entered Use of constrai
339. while minimizing others T he transform statements describing how the low pass filter works are x col 1 the data to smooth f 5 number of channels to eliminate tx fft x fft of data r data l size tx 2 total number of channels mp size tx 4 Set the MLrdpoint remove the frequencies td if e lt mp or xr gt mp t1l i ctx 0 sd invfft td convert back to time domain col 2 real sd save smoothed data to worksheet TheLOW PASS XFM transform expresses f as a percentage for ease of use As the value of f increases more high frequency channels are removed N ote that thisisa Graphing Transform Examples 99 Example Transforms digital transform which cuts data at a discrete boundary In addition this transform does not alter the phase of the data which makes it more accurate than analog filtering A high pass or band pass filter can be constructed in the same manner To calculate and graph the smoothing of a se of data using alow pass filter you can either use the provided sample data and graph or begin anew notebook enter your own data and create your own graph using the data 1 To usethe sample worksheet and graph open the Low Pass Smoothing work sheet and graph by double clicking the graph page icon in the Low Pass Smoothing section of the Transform Examples notebook D ata appears in col umns 1 through 4 of the worksheet and two graphs showing plots appear on the graph page Column 1
340. widths as wide as possible Add the G aussian curve to the graph by creating another plot using the data in column 4 as the X data and the data in column 5 asthe Y data Figure 6 11 The Histogram Gaussian Graph Gaussian Distribution Using the Sample Mean and Standard Deviation 25 20 0 316 318 320 322 324 326 328 330 332 334 Histogram with VERA TEANS TOrm Oa ai HLSCOG amn WEC lt lt ans a ae Gaussian Distribution Superimposed Gaussian Distribution Transform This transform can be used to create histogram HISTGAUS XFM values for a sample with a normal distribution and the data for a smooth Gaussian curve for the histogram Place your normally distributed sample data in x_col or change the column number to suit your data Results are placed in columns res through EOF x_col 1 column number for sample data res 2 first results column Set histogram range min 318 Lert Limit of has tog ram max 334 rrght Limit of Nistodram interval l1 histogram interval define source data X COl x_col VKKAKKKKKKKKHK GENERATE HISTOGRAM DATA KAKAKKKKKKKKKHK historange data min max interval h histogram x historange 112 Graphing Transform Examples ee Example Transforms int2 interval 2 Val date 2 Si7e h j xx xx PLACE HISTOGRAM XY DATA IN WORKSHEET 2 bar positions x values col res historange data l
341. win siews tenis iniia aa a 205 POSSOM ie Linea CUVE RIT sixcctnciaueae Seis salt atelier alata Ai 205 Lesson 2 SIGMOIdal Function CAD sess iccnrevsn caer seensialels cepted edaatednasahstbadnddeeemnsenaen 212 Advanced Regression Examples cccscceccsceeeeeseeeeeeesaeeeeeeeeeennaaeeengas 219 Curve Fitting Pitfalls ceils ta ie caida ironian a suerte glen cag oi anual mace N 219 Example 2 Weighted Regression ccccsccsssssecssssressssseeesssseesessssetesesstesssnanteess 225 Example 3 Piecewise Continuous FUNCTION cccccccsccssseeescsseeeessseeesesseeessseeeess 227 Example 4 Using Dependencies ccccccscccccesssssseecssssseeeeesesssaeeeessssseseeesssssaeees 229 Example 5 Solving Nonlinear Equations ccccccccssececcssseeescseeesessseeesseeeesssseeeess 232 Example 6 Multiple Function Nonlinear Regression ccccccccscssssceesssssstseeessssseees 234 ee Contents Example 7 Advanced Nonlinear Regression ccccssccccesessseceeeessssreeeesssssseeeesseaes 237 Automating Routine TASKS ssssssnnnnsnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnna 241 Greating Macros urassa Ae E LEI ANES 241 RUNNING YOUN MAGIO cerrsrennedma a aa a a A 244 EdD O MACOS saei T ee eee 245 AbDo tuserdelined TUNCHON S aaeeea anata een aratlnaiaans 251 Using the Dialog Box Editor ssesessssssssnrrseenenrrsssnrrrrssrerrrrssnnrrrsssnrrnrrsnrerrrssserrrrsssrrrn 251 Using the Object Browser ashi celrxarisila iiaeannsveadiin
342. x Cancelling a Regression D uring the regression process the Regression fit progress dialog box displays the number of iterations completed the norm value for each iteration and a progress bar indicating the percent complete of the maximum iterations Regression Iteration 2 of 100 Norm 3 862295769e 1 1 4 8791854841 6 4 H2 0 0241223063 nasd 1452093532 sfd irrar doon T1 30 011 2330203 T2 40 067 799057 To stop a regression while it is running click the Cancel button T he initial results appear displaying the most recent parameter values and the norm value You can continue the regression process by clicking the M ore Iterations button 162 Saving Regression Equation Changes Regression Wizard Interpreting Initial Results Figure 8 20 Initial Regression Results Completion status Messages Rsqr Initial Results W hen you click N ext from the variables panel the regression process completes by either converging reaching the maximum number of iterations or encountering an error W hen any of these conditions are met or whenever there is an error or warning the initial results panel is displayed Regression Wizard More terations view onstraints Dependencies Converged tolerance satished Raqr 0 997914756 Norm 0 306227411 StdErr CY Value x 4 107e 4 1 720e 2 470 e 3 02255074 me 2 42te2 Lilde2 7 059e 1 0 3919118 Ka 2 145e 0 1 702e 2 5 306e 1 0 4500044 x4 eU
343. x fit You can also reduce the number of iterations if you want to end a fit to check on its interim progress before it takes too many iterations Equation Options 159 Regression Wizard step Size Figure 8 17 Changing Step Size 160 Equation Options To change the maximum number of iterations enter the number of iterations to use or select a previously used number of iterations from the drop down list W hen the maximum number of Iterations is reached the regression stops and the current results are displayed in the initial parameters panel If you want to continue with more iterations you can click the Iterations button For more information on using the Iterations button see M ore Iterations on page 164 For more information on the use of iterations see Iterations on page 201 Step size or the limit of the initial change in parameter values used by the curve fitter as it tries or iterates different parameter values is a setting that can be changed to speed up or improve the regression process Regression Options Parameter Constraints Cancel Help 100 Initial Parameters Values 1000 Farameters Constants Options Iterations 0 000001 100 Tolerance Fit With Weight none A large step size can cause the curve fitter to wander too far away from the best parameter values whereas a step size that is too small may never allow the curve fit
344. xample if you only wanted to solve the differential equation dY _ a dt you would enter y1 fpl x yl y2 y3 y4 a y 1 fp2 x y1 y2 y3 y4 0 fp3 x yl y2 y3 y4 0 fp4 x yl y2 y3 y4 0 Scroll down to the Initial Values heading and set the nstep variable to the num ber of integration X variable steps you want to use The more steps you set the longer the transform takes Set the initial X value x0 final X value x1 and the Y1 through Y 4 values placed in cells 2 1 through 5 1 If you are not using a y value set that value to zero 0 For example for the single equation example above you could enter x0 0 initial x xl 1 final x cell 2 1 1 yl initial value cell 3 1 0 y2 initial value Example Transforms cell 4 1 0 y3 initial value cell 5 1 0 y4 initial value 7 Click Run The results output is placed in columns 1 through negn41 8 To graph your results create a Line Plot graphing column 1 as your X data and columns 2 through 5 as your Y data Figure 6 1 Plasma Iron Kinetics IV Bolus Fe Differential Equation Graph 100 4 _ io l Fe Concentration of total dose 1 l 0 0 01 02 03 04 05 06 07 08 0 9 1 0 Time days For information on creating a graph plotting one X data column against many Y data columns see the SigmaPlot s U s s M anual Differential Equation The transform example solves the equations Solving Transform
345. xample 1 Example 2 summary syntax Transform Function Reference variable step increment which is used to skip values when proceeding from the initial value to end value If no increment is specified an increment of 1 is assumed You must separate for to teo do end for and all condition statement operators variables and values with spaces The for loop statement is followed by a series of one or more transform equations which process the loop variable values Inside for loops you can gt indent equations gt nes for loops N ote that these conditions are allowed only within for loops You cannot redefine variable names within for loops T he operation for 1 to size col 1 do cell 2 1 cell 1 1 i end for multiplies all the valuesin column 1 by their row number and places them in column 2 T he operation for j cell 1 1 to cell 1 64 step 2 do col 10 col 9 j end for Takes the value from cell 1 1 and increments by 2 until the value in cell 1 64 is reached raises the data in column 9 to that power and places the results in column 10 T hefwhm function returns value of the x width at half maxima in the ranges of coordinates provided with optional Lowess smoothing fwhm x range y range f T hex range argument specifies the x variable and the y range argument specifies the y variable Any missing value or text string contained within one of the ranges is ignored and will not
346. y ELSO if cell body_x 1 lt cell body_x i 1 temp ricer pody x t gt see body x Iti pitten 0 0 if cellibody_ xri lt cell body xiti temp if cell body x 2 gt c ll body x 1 1 pittemp 0 70 cell left_branch_x i cell body_x itl CelL lere branch x aFik D eos ox Theta Angle cell body_x i 1 cell left_branch_x i 2 0 0 cell left_branch_y i cell body_y itl cell left_branch_y itl L sin pi Theta Angle cell body_y i l1 cell left_branch_y i 2 0 0 Cedsl right branch x1 cell body xri t cell right branch xiti iy cos pa Theta t ANGLE F ced I body X ARLI cell right_branch_x it 2 0 0 cell right branch yzi ced ibody v 7a cell right branch vitrir L sin pi Theta Angle cell body_y i 1 cell right_branch_y it 2 0 0 end for Z Plane Design Curves TheZPLANE XFM transform isa specific example of the use of transforms to generate data for a unit circle and curves of constant damping ratio and natural frequency T he root locus technique analyzes performance of a digital controller in the z plane using the unit circle as the stability boundary and the curves of constant damping ratio and frequency for a second order system to evaluate controller performance Root locus data is loaded from an external source and plotted in Cartesian coordinates along with the design curves in order to determine performance Ref
347. y You can also return Page GraphO bjects collections composed only of Graph objects using the Graphs property T heGraph object represents a SigmaPlot graph A graph is used to access the parts of a graph e g plots axes etc as well as to change graph attributes such as title size and position Graph objects have an O bjectT ype value of 2 or GPT GRAPH To use the Graph Object A Graph object is returned from a Page GraphO bjects collection N ote that you can create a GraphO bjects collection composed only of the graphs using the Page object Graphs property T he ChildO bjects or Plots properties are used to return the graph object s Plots collection O ther properties such as Axes and AutoLegend are used to return other graph objects M any Graph attributes and attribute values can only be returned or set using the G eAttribute and SetAttribute methods U se the G raph Attribute constants to specify these attributes Represents a collection of the child objects returned from a Graph object SigmaPlot Objects and Collections 259 SigmaPlot Automation Reference To use the Plot GraphObjects Collection A Plot GraphO bjects collection is returned from a Graph object using either the ChildO bjects or Plots property Use the Plots collection to return specific Plot objects Plot Object ThePlot object represents a data plot and all its attributes and child objects Plots have an O bjectT ype value of 3 or GPT PLOT To use the
348. y in the specified range nth rangeincrement 54 Transform Function Descriptions Example partdist summary syntax Example Related Functions polynomial summary Transform Function Reference T he range argument is either a specified range indicated with the brackets or a worksheet column Theincrenent argument must be a positive integer T he operation col 1 nth 1 2 3 4 5 6 7 8 9 10 3 places the range 1 4 7 10 in column 1 Every third value of the range is returned beginning with 1 T he partdist function returns a range representing the distance from thefirst X Y pair to each other successive pair T he line segment X Y pairs are specified by an x range and a y range T he last value in this range is numerically the same as that returned by dist assuming the same x and y ranges partdist x rangey range T hex range argument specifies the x coordinates and the y range argument specifies the y coordinates Corresponding values in these ranges form xy pairs If the ranges are uneven in size excess x or y points are ignored For the ranges x 0 1 1 0 0 and y 0 0 1 1 0 the operation partdist x y returns a range of 0 1 2 3 4 The X and Y coordinates provided describe a square of 1 unit x by 1 unit y dist The polynomial function returns the results for independent variable values in polynomials Given the coefficients this function produces a range of y values for the corresponding

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SigmaPlot® 8.0 Programming Guide