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

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The Residuals E Yi Gi Have A Natural Correlation Structure When The Linear Model Assumptions Are Met In Particular 1 (160.02 KiB) Viewed 466 times

The residuals e; = 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) Assume ei is independent of ô2. What is the distribution of the studentized residual ri defined above? Justify your answer using properties already established in the course - no need to derive the distribution from first principles. (Hint: Recall that ne-2ĝ2 ~ X-p-1 and a t distribution can be obtained from independent standard normal and chi-square random variables.)