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The parameter v is a list of the independent variable names used in f. If there is only one independent variable, then v can be a single name. The order of the names in the list must match exactly the order in which the independent variable values are placed in the columns of X.

The Fit command returns the model function, with the final parameter values, in terms of the independent variables. Additional results or a solution module that allows you to query for various settings and results can be obtained with the output option. The Fit command determines if the model function is linear or nonlinear in the model parameters.

Note that a model function can be nonlinear in the independent variables but linear in the model parameters. The most commonly used options are described below. Additional options accepted by LinearFit or NonlinearFit are passed directly to those commands. Note in particular the recommended use of the initialvalues option.

The Fit command accepts the model function only as an algebraic expression. Different input forms, allowing for greater flexibility and efficiency, are offered by the LinearFit and NonlinearFit commands. For more information, see the Input Forms help page. The options argument can contain one or more of the options shown below. The output option can take as a value the name solutionmodule , or 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 , rsquared , rsquaredadjusted , standarderrors , tprobability , tvalue , variancecovariancematrix.

This option is only available when the model expression is linear in the parameters. The underlying computation is done in floating-point; therefore, all data points must have type realcons and all returned solutions are floating-point, even if the problem is specified with exact values. Set infolevel[Statistics] to 2 or higher to see messages about the progress of the solvers.

In particular, these userinfo messages indicate whether the LinearFit command or the NonlinearFit command is being used. For fitting a data sample to a distribution, see MaximumLikelihoodEstimate. Fit a model that is linear in the parameters. It is also possible to generate a summary for models that are linear in the parameters. Note that the summary is not a part of the output that is assigned to ls :.

Standard Error. Adjusted R-squared:. Residual Sum of Squares. Residual Mean Square. Residual Standard Error. Degrees of Freedom. Five Point Summary. First Quartile. Third Quartile. Fit a model that is nonlinear in the parameters. Consider now an experiment where quantities x , y , and z are quantities influencing a quantity w according to an approximate relationship. Six data points are given by the following matrix, with respective columns for x , y , z , and w.

We compute both the model function and the residuals. Also, we select more verbose operation by setting infolevel. In NonlinearFit algebraic form. We note that Maple selected the nonlinear fitting method. Furthermore, the exponent on x is only about 1. However, this problem is conditioned well enough that Maple finds a good fit anyway.

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