Question 5 Let, we are tting the following regression model, Y = X + 6 Under the Gauss-Markov assumptions. Let, H = X(X'X)_1X'. (a) [3 Marks] Show that Var(r | X) = 02H. Here 021 is the variancecovariance matrix of the random error. Show the detailed derivations. (b) [4 Marks] Show that given a dataset (or sample) the multiple coefcient of determination R2 can be written as the correlation squared between Y and Y, where, Y is the n X 1 vector of the tted values. Show the detailed derivations. Hint: Consider that the sample mean of (3)) = , and then think about what would be the sample variance of 332-. Show the detailed derivations