The homoskedasticity-only F-statistic is
A) $\frac{(R \hat{\beta}-\mathrm{r})^{\prime}\left[R^{\prime}\left(\mathrm{X}^{\prime} \mathrm{X}\right)^{-1} R\right]^{-1}(R \hat{\beta}-r) / q}{\mathrm{~s}_{\mathrm{u}}^{2}}$
B) $\frac{(R \hat{\beta}-\mathrm{r})^{\prime}\left[R^{\prime}\left(X^{\prime} X\right)^{-1} R\right]^{-1}(R \hat{\beta}-r)}{\mathrm{s}_{\mathrm{u}}^{2}}$
C) $\frac{(R \hat{\beta}-\mathrm{r})^{\prime}\left[R^{\prime} \hat{\Sigma}_{\beta} R\right]^{-1}(R \hat{\beta}-r)}{\mathrm{q}}$
D) $\frac{\hat{\mathrm{U}} \mathrm{P} Z \hat{\mathrm{U}}}{\hat{\mathrm{U}^{\prime} \mathrm{M}_{\mathrm{Z}} \mathrm{U}}}$

Question

Quizplus · Accepted Answer

The homoskedasticity-only F-statistic is $\frac{(R \hat{\beta}-\mathrm{r})^{\prime}\left[R^{\prime}\left(\mathrm{X}^{\prime} \mathrm{X}\right)^{-1} R\right]^{-1}(R \hat{\beta}-r) / q}{\mathrm{~s}_{\mathrm{u}}^{2}}$ because it is the ratio of the explained variation to the unexplained variation, and the denominator is the variance of the residuals.