As of Version 7.0, ParameterConfidenceRegion has become a property of LinearModelFit and NonlinearModelFit.


is a possible value for the RegressionReport option which represents the elliptically shaped joint confidence region for parameter estimates.


  • To use ParameterConfidenceRegion, you first need to load the Regression Common Functions Package. You can do this by using Needs["LinearRegression`"] or Needs["NonlinearRegression`"], which will automatically load the Regression Common Functions Package, or you can load the package directly by using Needs["RegressionCommon`"].
  • ParameterConfidenceRegion gives a confidence region for all fitted parameters.
  • ParameterConfidenceRegion is based on CovarianceMatrix for linear regressions using Regress or DesignedRegress, and AsymptoticCovarianceMatrix for nonlinear regressions using NonlinearRegress.
  • The confidence level for the region can be specified via the ConfidenceLevel option.
  • ParameterConfidenceRegion is represented using an Ellipsoid object.
  • ParameterConfidenceRegion[{basis1,basis2,}]
    can be specified to obtain a confidence region for the basis functions basis1,basis2, in a linear regression.
  • ParameterConfidenceRegion[{par1,par2,}]
    can be specified to obtain a confidence region for the parameters par1,par2, in a nonlinear regression.


Basic Examples  (1)

Sample data:

ParameterConfidenceRegion for a linear regression: