Let the ith residual of the regression model be ei = yi yi . Prove that

Let the ith residual of the regression model be ei = yi − yˆi . Prove that Var(ei) = s 2 (1 − hii), where s 2 is the mean square error of the regression model and hii is the ith diagonal element of the HAT matrix.

.7361 0.11564 0.94022 1.0921 0.13904 10 0.3972 0.6555 0.39405 -1.92210 -3.2833 0.41459 11 0.6429 0.7600 0.15403 -0.17736 -0.2103 0.15660 12 6.7240 8.0934 0.16919 6.76184 8.1389 0.16920 13 2.8625 3.4654 0.17397 1.35393 1.6565 0.18266 14 0.9210 1.0521 0.12456 1.09787 1.2542 0.12468 15 -8.3857 -9.1765 0.08619 -4.94225 -5.6903 0.13146