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ConfidenceLevel

is an option for LinearModelFit and other fitting functions that specifies the level to use in various confidence and prediction intervals and bands.

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ConfidenceLevel

ConfidenceLevel

is an option for LinearModelFit and other fitting functions that specifies the level to use in various confidence and prediction intervals and bands.

Details

  • ConfidenceLevel affects values of properties related to confidence intervals.
  • The default setting gives 95% confidence intervals.
  • The value should be a number between 0 and 1.
  • For certain types of models, model[…][prop,ConfidenceLevel->c] can be used to extract properties for a specified confidence level. »

Examples

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Basic Examples  (2)

Perform a linear fit and set the default confidence level to 99%:

Wolfram Language code: lm = LinearModelFit[{...}, x, x, ConfidenceLevel -> 0.99]

Obtain the mean prediction bands at this level:

Wolfram Language code: lm["BestFitAround"]

Set the confidence level when querying the prediction bands after fitting:

Wolfram Language code: nlm = NonlinearModelFit[{...}, a Exp[b x], {a, b}, x]
Wolfram Language code: nlm["BestFitAround", ConfidenceLevel -> 0.9]

Scope  (3)

Compute the parameter confidence intervals at various confidence levels:

Wolfram Language code: data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}};
Wolfram Language code: lm = LinearModelFit[data, x, x]

Estimates at the default 95% level:

Wolfram Language code: lm["ParameterEstimates"]//Query[All, {"BasisFunction", "ConfidenceInterval"}]

Estimates at the 90% level:

Wolfram Language code: lm["ParameterEstimates", ConfidenceLevel -> .9]//Query[All, {"BasisFunction", "ConfidenceInterval"}]

Set confidence level for a nonlinear model:

Wolfram Language code: data = Table[{x, 3 Sin[2x] + RandomReal[{-.2, .2}]}, {x, RandomReal[5, 10]}];
Wolfram Language code: nlm = NonlinearModelFit[data, a Sin[b x], {a, b}, x, ConfidenceLevel -> .9]
Wolfram Language code: nlm["ParameterConfidenceIntervalTable"]

Using the usual default level:

Wolfram Language code: nlm["ParameterConfidenceIntervalTable", ConfidenceLevel -> .95]

For a generalized linear model:

Wolfram Language code: data = {{0, 1}, {1, 1.5}, {3, 2}, {5, 4}};
Wolfram Language code: glm = GeneralizedLinearModelFit[data, x, x, ExponentialFamily -> "InverseGaussian"]
Wolfram Language code: glm["ParameterConfidenceIntervalTable", ConfidenceLevel -> .99]

Applications  (1)

Fit some data:

Wolfram Language code: SeedRandom[1]; data = Table[{x, 1.2 Sin[2 x] + RandomReal[{-.2, .2}]}, {x, 10}]
Wolfram Language code: nlm = NonlinearModelFit[data, a Sin[b x], {a, b}, x]

Obtain confidence intervals at several levels for comparison:

Wolfram Language code: intervals = Table[Thread@{p, Interval /@ nlm["ParameterConfidenceIntervals", ConfidenceLevel -> p]}, {p, {.8, .85, .9, .95, .99}}]

Plot the intervals versus the confidence levels:

Wolfram Language code: ListPlot[Transpose[intervals], PlotLegends -> {a, b}, PlotTheme -> "Detailed", FrameLabel -> {"ConfidenceLevel", "ConfidenceInterval"}]

Properties & Relations  (1)

ConfidenceLevel affects all confidence intervals in FittedModel properties:

Wolfram Language code: lm = LinearModelFit[Range[5], x ^ 2, x]

Intervals using default 95% level:

Wolfram Language code: Query[All, All, "ConfidenceInterval"]@lm[{"MeanPredictions", "SinglePredictions", "ParameterEstimates"}]

Intervals using 99% level:

Wolfram Language code: Query[All, All, "ConfidenceInterval"]@lm[{"MeanPredictions", "SinglePredictions", "ParameterEstimates"}, ConfidenceLevel -> .99]
Wolfram Research (2008), ConfidenceLevel, Wolfram Language function, https://reference.wolfram.com/language/ref/ConfidenceLevel.html.

Text

Wolfram Research (2008), ConfidenceLevel, Wolfram Language function, https://reference.wolfram.com/language/ref/ConfidenceLevel.html.

CMS

Wolfram Language. 2008. "ConfidenceLevel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ConfidenceLevel.html.

APA

Wolfram Language. (2008). ConfidenceLevel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ConfidenceLevel.html

BibTeX

@misc{reference.wolfram_2026_confidencelevel, author="Wolfram Research", title="{ConfidenceLevel}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ConfidenceLevel.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_confidencelevel, organization={Wolfram Research}, title={ConfidenceLevel}, year={2008}, url={https://reference.wolfram.com/language/ref/ConfidenceLevel.html}, note=[Accessed: 12-June-2026]}