Linear hypotheses for are expressed in matrix form as
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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
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where is the estimated covariance matrix in the section Variance Estimation. Under , has an asymptotic chi-square distribution with r degrees of freedom, where r is the rank of .