NonlinearRegress

• To use NonlinearRegress, you first need to load the Nonlinear Regression Package using Needs["NonlinearRegression`"].

• The data can have the form {{x₁, y₁, ..., f₁}, {x₂, y₂, ..., f₂}, ...}, where the number of coordinates x, y, ... is equal to the number of variables in the list vars.

• The data can also be of the form {f₁, f₂, ...}, with a single coordinate assumed to take values 1, 2, ....

• The model expr must yield a numerical value when pars and vars are all numerical.

• The estimates of the model parameters give a least-squares fit, minimizing the sum of squared residuals.

• NonlinearRegress returns a list of rules for results and diagnostics specified by the option RegressionReport.

• The model expr must yield a numerical value when pars and vars are all numerical.

• For constrained models, the constraints cons can contain equations, inequalities, or logical combinations of equations and inequalities.

• Parameters are specified using the same syntax as in FindFit.

• The results found by NonlinearRegress may correspond only to a local optimum.

• The following options can be given:

• The options AccuracyGoal, Compiled, Gradient, MaxIterations, Method, PrecisionGoal, and WorkingPrecision are the same as for FindFit.

• Possible settings for Weights are Automatic, a list of numbers with the same length as data, or a pure function.

• With the default setting Weights->Automatic, each data point is given a weight of 1.

• With the setting Weights->g, the weight associated with each point is g[f_i, x_i, y_i, ...].

• The default setting RegressionReport->SummaryReport includes the elements BestFitParameters, ParameterCITable, EstimatedVariance, ANOVATable, AsymptoticCorrelationMatrix and FitCurvatureTable.

• For constrained models, RegressionReport values based on approximate normality assumptions may not be valid. When such values are included, the values will be generated along with a warning message.