Regression Options

This help page describes the options that may be provided to the regression commands in the Statistics package. See the Statistics/Regression help page for an overview of the regression commands.


Options for General Fitting



When the output = solutionmodule option is provided, a module with two exports, Settings and Results, is returned. Each export is a procedure that queries the values of the problem settings or solution. The output option can also take as a value one of the following names (or a list of these names): AtkinsonTstatistic, confidenceintervals, CookDstatistic, degreesoffreedom, externallystandardizedresiduals, internallystandardizedresiduals, leastsquaresfunction, leverages, parametervalues, parametervector, residuals, residualmeansquare, residualstandarddeviation, residualsumofsquares, standarderrors, variancecovariancematrix. Any of these names may also be provided as a string.


Some of these results are not available for all regression commands. Full details about how to use the solution module and descriptions of the setting and result values are provided in the Statistics/Regression/Solution help page.


Provide weights for the data points. If there are k data points, then a Vector of dimension k may be provided through the weights option. The ith data point is then weighted by the ith value of the weights Vector. By default, all data points are weighted equally, except for particular models as specified in the help pages for the commands associated with them. All weights must be positive values.



Options for Linear Fitting



confidencelevel = realcons


Specify the confidence level used in computing confidence intervals for the parameters.


svdtolerance = realcons(nonnegative)


Set the tolerance that determines whether a singularvalue decomposition (SVD) is performed. This option is available only for the linear regression commands. Normally, a method using QR decomposition is applied. If it is determined that the system does not have full rank, then an SVD is performed. The smaller the svdtolerance value, the stricter the criteria for performing an SVD. A value of 0.0 means that an SVD is never performed. The default value for the svdtolerance option is 1.0e12.



Options for Nonlinear Fitting



initialvalues = set(equation), list(equation), list(realcons), or 'Vector'(realcons)


Provide an initial point. Usually, the initial point is specified as a set or list of equalities $\mathrm{varname}\=\mathrm{value}$ when the most common form of input, algebraic form, is used. When operator form or Matrix form is used, the initial point is specified as a list or Vector of values.


Because the solvers in the Optimization package only compute local solutions, it is strongly recommended that you provide an appropriate initial point through this option. All solvers use initialpoint information, except the quadratic interpolation method of Optimization[NLPSolve]. The initial point is ignored in this case. For more information, see the Optimization/Methods help page.


This option only has an effect on nonlinear fitting, but it is accepted by Statistics[Fit] even in the case where linear fitting is used.


modelfunctiongradient = list(procedure)


Specify the gradient of the model function. This option is used only with the Matrix form of the NonlinearFit command. The gradient is represented by a list of procedures, with the jth procedure computing the derivative of the model function with respect to the jth parameter, at a given data point. The form of each procedure is the same as that required for the residual. For more information, see the Statistics/NonlinearFitMatrixForm help page.


parameternames = list(name)


Specify the order of parameter names in the model function. This determines the order in which values are placed in Vector results such as standarderrors or parametervalues. (See the Statistics/Regression/Solution help page for more information about results returned by the regression commands.)


parameterranges = list(name=range), list(range) or [Vector, Vector]


Specify the allowable range for each parameter. When the input is in algebraic form, the parameter ranges must be given as a list containing one or more equations of the form nm=r where nm is the name of a parameter and r is its range. When the input is in operator form, the parameter ranges must be given as a list of exactly m ranges where m is the number of parameters. The order of the ranges must correspond to the order of the parameters as specified in the procedure representing the model function. When the input is in Matrix form, the parameter ranges consists of two Vectors, each of dimension m. The first contains lower bounds and the second contains upper bounds on the parameters.


For all forms, infinity or infinity may be provided as values, meaning that the parameter is not bounded in the associated direction. See Statistics/Regression/InputForms for more information about the different input forms accepted by the regression commands.


