題組內容

5. (15%) An OLS regression has the following data: $\bar{X} = 3$; $\bar{Y} = 4$;

$$\Sigma(X - \bar{X})^2 = 32; \Sigma(Y - \bar{Y})^2 = 29; \Sigma(X - \bar{X})(Y - \bar{Y}) = 28;$$

The sample observation size is 10. Please calculate:

(2)(5%)The variance of residuals \( \hat{\sigma}^2 \)