The *p*-value, *F* statistic, and numerator
degrees of freedom are valid under these assumptions:

Suppose these assumptions hold. Let *β* represent the unknown
coefficient vector of the linear regression. Suppose *H* is a
full-rank numeric index matrix of size *r*-by-*s*,
where *r* is the number of linear combinations of coefficients
being tested, and *s* is the number of terms in
*β*. Let *c* be a vector the same size as
*β*. The following is a test statistic for the hypothesis that
*Hβ* = *c*:

Here $$\widehat{\beta}$$ is the estimate of the coefficient vector *β* in
`mdl.Coefs`

, and *V* 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.