Question 3 [4+=1 points]: In the standard linear model Y = X33 + s with X xed the vector of residuals can he expressed compactly,r as =(IH)y, 1where H = X[X'X]_1X' is the hat matrix. The otwarianoe matrix of the residuals is therefore equal to [I H ]E(I H j', where E is the covariance matrix of the error vector e. Assume that the errors are independent and identically,r distributed with error 0'2. 3.1 Show that H is idempotent. 3.2 Show that the covariance matrix of the residuals reduces to [I H )02.l