Testing Linear Hypotheses about Regression Coefficients

The PHREG Procedure

Testing Linear Hypotheses about Regression Coefficients

Linear hypotheses for ${\beta}$ are expressed in matrix form as

$H_{0}\colon{L}{{\beta}}=c$

where L is a matrix of coefficients for the linear hypotheses, and c is a vector of constants. The Wald chi-squared statistic for testing H₀ is computed as

$\chi^2_{W}=( L\hat{{\beta}}-c ) ' [ L\hat{V}(\hat{{\beta}})L' ] ^{-1} ( L\hat{{\beta}}-c )$

Under H₀, $\chi^2_{W}$ has an asymptotic chi-squared distribution with r degrees of freedom, where r is the rank of L.

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