Consider the (multiple) linear regression model y = X +5, 5 ~ N03, 021...), X = [1\" | $1 | | mp] 6 BMW\"). (1) As usual (3" = (3;) is the LSE of , = (g) = XE the vector of tted values and e = (as) = y II is the vector of residuals. H = (ht-j) = X (X TX )'1X T is the hat matrix. Answer the following questions, giving a brief justication in each case: 1. (True False) 36 is always independent of 33 for i % j. 2. (True False) (eTy)/(n p 1) is an unbiased estimate of 02. 3. (True False) H e and (I H )5 are independent. 4. (True False) \"HE'II2 w x3)\". Consider adding a covariate u E R\" to get the model, y=X+7u+, and assumeXTu=0, 761R. Let (anew, I?) be the LSE of parameters (13, qr) in this new model. Answer the following: 5. (True False) 3...... = E where 3 is LSE of [3' in the original model (1). 6. (True False) 3} and fine... are independent