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ParameterConfidenceRegion

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

ParameterConfidenceRegion

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

Details and Options

  • 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.

Examples

Basic Examples  (1)Summary of the most common use cases

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https://wolfram.com/xid/0vxq7gvc5l6tyhlu-hs9w5q

Sample data:

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https://wolfram.com/xid/0vxq7gvc5l6tyhlu-uqe

ParameterConfidenceRegion for a linear regression:

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Wolfram Research (2007), ParameterConfidenceRegion, Wolfram Language function, https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html.
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Wolfram Research (2007), ParameterConfidenceRegion, Wolfram Language function, https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html.

Text

Wolfram Research (2007), ParameterConfidenceRegion, Wolfram Language function, https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html.

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Wolfram Research (2007), ParameterConfidenceRegion, Wolfram Language function, https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html.

CMS

Wolfram Language. 2007. "ParameterConfidenceRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html.

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Wolfram Language. 2007. "ParameterConfidenceRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html.

APA

Wolfram Language. (2007). ParameterConfidenceRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html

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Wolfram Language. (2007). ParameterConfidenceRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html

BibTeX

@misc{reference.wolfram_2025_parameterconfidenceregion, author="Wolfram Research", title="{ParameterConfidenceRegion}", year="2007", howpublished="\url{https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html}", note=[Accessed: 16-May-2025 ]}

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@misc{reference.wolfram_2025_parameterconfidenceregion, author="Wolfram Research", title="{ParameterConfidenceRegion}", year="2007", howpublished="\url{https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html}", note=[Accessed: 16-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_parameterconfidenceregion, organization={Wolfram Research}, title={ParameterConfidenceRegion}, year={2007}, url={https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html}, note=[Accessed: 16-May-2025 ]}

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@online{reference.wolfram_2025_parameterconfidenceregion, organization={Wolfram Research}, title={ParameterConfidenceRegion}, year={2007}, url={https://reference.wolfram.com/language/RegressionCommon/ref/ParameterConfidenceRegion.html}, note=[Accessed: 16-May-2025 ]}