Linear hypothesis test on generalized linear regression model coefficients
p = coefTest(mdl)
p = coefTest(mdl,H)
p = coefTest(mdl,H,C)
[p,F] = coefTest(mdl,...)
[p,F,r] = coefTest(mdl,...)
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.
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.
p-value of the F test (see Definitions).
Value of the test statistic for the F test (see Definitions).
Numerator degrees of freedom for the F test (see Definitions). The F statistic has r degrees of freedom in the numerator and mdl.DFE degrees of freedom in the denominator.
The p-value, F statistic, and numerator degrees of freedom are valid under these assumptions:
The data comes from a model represented by the formula mdl.Formula.
The observations are independent conditional on the predictor values.
Suppose these assumptions hold. Let β represent the (unknown) coefficient vector of the linear regression. Suppose H is a full-rank matrix of size r-by-s, where s is the number of terms in β. Let v be a vector the same size as β. The following is a test statistic for the hypothesis that Hβ = v:
Here is the estimate of the coefficient vector β in mdl.Coefs, and C is the estimated covariance of the coefficient estimates in mdl.CoefCov. When the hypothesis is true, the test statistic F has an F Distribution with r and u degrees of freedom.
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 = 1.2461e-30
There is no doubt that the coefficient of x1 is nonzero.
The values of commonly used test statistics are available in the mdl.Coefficients table.