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The Homoskedasticity Only F-Statistic Is Given by the Formula

Question 61

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The homoskedasticity only F-statistic is given by the formula The homoskedasticity only F-statistic is given by the formula where SSR<sub>restricted</sub> is the sum of squared residuals from the restricted regression, SSR<sub>unrestricted</sub> is the sum of squared residuals from the unrestricted regression, q is the number of restrictions under the null hypothesis, and k<sub>unrestricted</sub> is the number of regressors in the unrestricted regression. Prove that this formula is the same as the following formula based on the regression R<sup>2</sup> of the restricted and unrestricted regression: where SSRrestricted is the sum of squared residuals from the restricted regression, SSRunrestricted is the sum of squared residuals from the unrestricted regression, q is the number of restrictions under the null hypothesis, and kunrestricted 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: The homoskedasticity only F-statistic is given by the formula where SSR<sub>restricted</sub> is the sum of squared residuals from the restricted regression, SSR<sub>unrestricted</sub> is the sum of squared residuals from the unrestricted regression, q is the number of restrictions under the null hypothesis, and k<sub>unrestricted</sub> is the number of regressors in the unrestricted regression. Prove that this formula is the same as the following formula based on the regression R<sup>2</sup> of the restricted and unrestricted regression:

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Note that SSR = TSS - ESS. Hen...

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