Hi, could you please help me answer three STAT question, thank you.

1. Studentized Residuals When we compute the studentized residuals, Ti 32 V (I _ PX)i,iSSres/(n _ p _1)1 as long as n p 1 is large, then we claim that 5.5 has a t(n p 1) distribution which is close to a N(U, 1). Show that actually 3%- can't have a t (n p 1) distribution by showing that Isi] 3 V1), p 1. Hint: write $87.33 as 211:1 1:52 and use the fact that (I PX)\"- E (0, 1] for all i. 2. The Outlier E'ect Consider the linear regression setting where we have n sample points with s N N(0, of) and m sample points with 8 ~ N(0, (73).1 (a) Show that for some 6 6 [0,1], n+m Z Var (sz) = 603 + (1 (5)03. i=1 1 n+m (b) Assuming that (I? 2 (c) Var (Y) = e\" ((0 WHY) = V2 1 Here, the m points could represent a few outliers in the dataset which will effect the hypothesis tests and condence intervals