The residuals ei = Yi - ĝi have a natural correlation structure when the linear model assumptions are met. In particular

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The Residuals Ei Yi Gi Have A Natural Correlation Structure When The Linear Model Assumptions Are Met In Particular 1 (143.28 KiB) Viewed 122 times

The residuals ei = Yi - ĝi have a natural correlation structure when the linear model assumptions are met. In particular, they have a variance that is proportional to 1 – hii, where hii is the ith diagonal of the hat matrix H = x(x'x)-'x'. So sometimes studentized residuals are used instead for diagnostics: ei ri= Vô2(1 – hii) Let e denote the residual vector Y - Ỹ. Note that û = xß = x(x'x)-'x'Y = HY Show that vare = 02(I – H). (Hint: first write Y – û in terms of I – H; then the problem should be a one-liner.) Are r1, ..., In independent for general x? Why or why not? Answer in 1 sentence. (Hint: refer to part i.)