Show that the Wald statistic in (4.15) does not depend on the specific equations used. Specifically, suppose that \(K\) and \(K^{\prime}\) are two equivalent systems of equations for a linear hypothesis, i.e., the row spaces generated by the rows of the two matrices are the same, then the corresponding Wald statistics are the same, i.e., \((K \widehat{\boldsymbol{\beta}})^{\top}\left(K \Sigma_{\beta} K^{\top}\right)^{-1}(K \widehat{\boldsymbol{\beta}})=\left(K^{\prime} \widehat{\boldsymbol{\beta}}\right)^{\top}\left(K^{\prime} \Sigma_{\boldsymbol{\beta}} K^{\prime \top}\right)^{-1}\left(K^{\prime} \widehat{\boldsymbol{\beta}}\right)\).

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T - Q = n (K b) (KK) (K b) - (4.15)