Documentation

# coefTest

Linear hypothesis test on generalized linear regression model coefficients

## Syntax

p = coefTest(mdl)
p = coefTest(mdl,H)
p = coefTest(mdl,H,C)
[p,F] = coefTest(mdl,...)
[p,F,r] = coefTest(mdl,...)

## Description

p = coefTest(mdl) computes the p-value for an F test that all coefficient estimates in mdl are zero, except for the intercept term.

p = coefTest(mdl,H) performs an F test that H*B = 0, where B represents the coefficient vector.

p = coefTest(mdl,H,C) performs an F test that H*B = C.

[p,F] = coefTest(mdl,...) returns the F test statistic.

[p,F,r] = coefTest(mdl,...) returns the numerator degrees of freedom for the test.

## Input Arguments

 mdl Generalized linear model, specified as a full GeneralizedLinearModel object constructed using fitglm or stepwiseglm, or a compacted CompactGeneralizedLinearModel object constructed using compact. H Numeric matrix having one column for each coefficient in the model. When H is an input, the output p is the p-value for an F test that H*B = 0, where B represents the coefficient vector. C Numeric vector with the same number of rows as H. When C is an input, the output p is the p-value for an F test that H*B = C, where B represents the coefficient vector.

## Output Arguments

 p p-value of the F test (see More About). F Value of the test statistic for the F test (see More About). r Numerator degrees of freedom for the F test (see More About). The F statistic has r degrees of freedom in the numerator and mdl.DFE degrees of freedom in the denominator.

## Examples

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Test a generalized linear model to see if its coefficients differ from zero.

Create a generalized linear regression model of Poisson data.

X = 2 + randn(100,1);
mu = exp(1 + X/2);
y = poissrnd(mu);
mdl = fitglm(X,y,'y ~ x1','distr','poisson');

Test whether the fitted model has coefficients that differ significantly from zero.

p = coefTest(mdl)
p = 3.1394e-36

There is no doubt that the coefficient of x1 is nonzero.

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## Alternatives

The values of commonly used test statistics are available in the mdl.Coefficients table.