Answer Happy

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.)