(5 points) Let S* and S be the least square estimates of S* and 3 respectively. True or false: 3* is always equal to 3. (10 points) Let B and y be the least square estimates of B and y in model (2). Show that 3 and y are independent if and only if X'Z = 0. Hint: You may find the linear algebra result on the inverse of a block matrix useful see Equation 2.50 on page 23 of the textbook).Problem 4. (25 points) Consider the following two models : y = X3* +E (1) and y = XB+Zyte, (2) where y is of size n and 3*, B and y are parameters. X and Z are n x p and n x k e~ N(0, o2 I). full-rank design matrices with p