# 2.13.3.1 Linear, Polynomial and Multiple Regression

In LabTalk scripts, three simple quick use X-Functions, fitLR, fitPoly, and fitMR, are available for performing linear regression, polynomial regression, and multiple linear regression, respectively. And the -h switch can be used to see the argument list.

## Linear Regression

fitLR finds a best fit straight line to a given dataset.

newbook;  // create a new book

// file name
string strFile$= system.path.program$ + "Samples\Curve Fitting\Linear Fit.dat";
impasc fname:=strFile$; // import the data wks.addcol(FitData); // add a column for fitted data, named FitData // perform linear fit on the first ten points of column 1 (X) and column 2 (Y) // and the fitted data is output to FitData column fitLR iy:=(1,2) N:=10 oy:=col(FitData); // a tree object named fitLR is created, and contains the output values fitLR.a = ; // output the fitted intercept fitLR.b = ; // output the fitted slope fitLR.= ; // output all the results, which include fitted intercept and slope More examples about linear regression can be found in Curve Fitting sample page, or under Fitting category in XF Script Dialog (press F11 to open). ## Polynomial Regression Polynomial fitting is a special case wherein the fitting function is mathematically non-linear, but an analytical (non-iterative) solution is obtained. In LabTalk, fitPoly is used to control polynomial fitting. newbook; // create a new book; // file name string strFile$ = system.path.program$+ "Samples\Curve Fitting\Polynomial Fit.dat"; impasc fname:=strFile$;  // import data

// perform polynomial fitting on column 1 (X) and column 3 (Y)
// polynomial order is 3
fitPoly iy:=(1,3) polyorder:=3 coef:=col(PolyCoef) oy:=(col(FittedX),col(FittedY));

// the results are stored in the tree named fitPoly, output it
fitPoly.= ;

Additionally, fitPoly provides the outputs for adjusted residual sum of squares, coefficient of determination, and errors in polynomial coefficients. For more detailed examples, please refer to Curve Fitting sample page, or Fitting category in XF Script Dialog (press F11 to open).

## Multiple Linear Regression

Multiple linear regression studies the relationship between several predictor variables and a response variable, which is an extension of simple linear regression.

// create a new book and import some data
newbook;
fn$= system.path.program$ + "Samples\Curve Fitting\Multiple Linear Regression.dat";
impasc fn$; wks.addcol(FitValue); // add a column for fitted values of dependent // perform multiple linear regression // column D is dependent, and column A, B, and C are independents // the output results are stored in a tree, tr fitMR dep:=col(D) indep:=col(A):col(C) mrtree:=tr odep:=col(FitValue); tr.= ; // output the result tree For more examples, please refer to Curve Fitting sample page, or Fitting category in XF Script Dialog (press F11 to open). ## Run Operation Classes to Perform Regression The X-Functions depicted above are for simple quick use only to perform linear, polynomial and multiple regression. That is to say, some quantities are not available when using these three X-Functions. For full access to all quantities, the X-Function xop is provided to invoke the internal menu commands (operation commands), so to run the corresponding operation classes to perform regression. The following example shows how to use the X-Function xop to perform linear fit, and generate a report. // create a new book and import data newbook; fname$ = system.path.program$+ "Samples\Curve Fitting\Linear Fit.dat"; impasc fname$;

tree lrGUI;  // GUI tree for linear fit
// initialize the GUI tree, with the FitLinear class
xop execute:=init classname:=FitLinear iotrgui:=lrGUI;

// specify the input data in the GUI tree
lrGUI.GUI.InputData.Range1.X$= col(A); lrGUI.GUI.InputData.Range1.Y$ = col(C);

// perform linear fit and generate a report with the prepared GUI tree
xop execute:=report iotrgui:=lrGUI;

xop execute:=cleanup;  // clean up linear fit operation objects after fitting