all four question please

Consider the multiple regression model Y = XO +

Consider thc multiple regression model Y = + With = O and = addition, if wc have a set Of linear constraints Of the form = wc showed that = Answer the following questions: a. Show that = b. Let be the residuals. Show that = Where is the Sum Of the matrix C is k x (k + l), and the vector = O. For example, if k = 5, the matrix C is as folltyws: 0 0 10 c. IS Of the constrained least squares larger or smaller than the Of the unconstrained least squares? Please explain your answer mathematically. d. Under the hypothesis = find the unbiased estimator Of in the case Of constrained least squares.