Testing Linear Hypotheses about the Regression Coefficients

The LOGISTIC Procedure

Testing Linear Hypotheses about the 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 vector of regression coefficients ${\beta}$ includes slope parameters as well as intercept parameters. The Wald chi-square statistic for testing H₀ is computed as

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

where $\hat{V}(\hat{{\beta}})$ is the estimated covariance matrix. Under H₀, $\chi^2_{W}$ has an asymptotic chi-square distribution with r degrees of freedom, where r is the rank of L.

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