Consider the (multiple) linear regression model 3; = X+5, 5 ~ N(0, U21\"), X = [1,. |m1 | | gap] 6 BMW\"). (1) As usual 3 = (1'31) is the LSE of 13, E = (Iii) = X3 the vector of tted values and e = (31-) = y IE is the vector of residuals. H = (kg) = X (X TX )'1X T is the hat matrix. Answer the following questions, giving a brief justication in each case: 1. (True False) :8; is always independent of B} for 11 3% j. 2. (True False) (eTy)/(n p 1) is an unbiased estimate of a2. 3. (True False) H5 and (I H) are independent. 4. (True False) \"Hell2 ~ X12)\". Consider adding a covariate u E R\" to get the model, y=X+7u+, and assumeXTu=O, 761R. Let (anew, r) be the LSE of parameters (, qr) in this new model. Answer the following: 5. (True False) anew = E where F is LSE of in the original model (1). 6. (True False) 5} and fine... are independent. \f