Testing Linear Hypotheses about the Regression Coefficients

Linear hypotheses for are expressed in matrix form as

where is a matrix of coefficients for the linear hypotheses and is a vector of constants. The vector of regression coefficients includes slope parameters as well as intercept parameters. The Wald chi-square statistic for testing is computed as

where is the estimated covariance matrix in the section Variance Estimation. Under , has an asymptotic chi-square distribution with degrees of freedom, where is the rank of .