The Homoskedasticity Only F-Statistic Is Given by the Formula

question 61

Essay

The homoskedasticity only F-statistic is given by the formula where SSR_restricted is the sum of squared residuals from the restricted regression, SSR_unrestricted is the sum of squared residuals from the unrestricted regression, q is the number of restrictions under the null hypothesis, and k_unrestricted is the number of regressors in the unrestricted regression. Prove that this formula is the same as the following formula based on the regression R² of the restricted and unrestricted regression:

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Definitions:

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