6. (10pts) Consider the simple linear regression model Y = Bo + BX + e, with normal error, so e are iid N(0,02) random variables. Given n data points {(X,Y)=1, let bo and by be the least square estimates for 30 and 3. The i-th residual, e, is e; = Y - Y = Y-bo-bX. (a) Given a fixed i, say i = 1, derive the distribution for e,. Hint: Write e; as e; = , cY; for some choice of C, C2, Cn. (b) Are the residuals independent? Given i #j, are e, and e, independent random variables ? Hint: Note that , ei = 0 always.