You are interested on the relation between wages (y), education (z) and age (x). Your econometrician friend tells you that a well known estimator is defined by the solution of the following minimization problem: n minab(yi-azi - bx;) i=1 (1) (a) [8 marks] Write down the first order condition of the minimization problem (1). (b) [8 marks] The first order conditions form a linear system of two equations in a and b. Write them in matrix format AB = B where 3 = [a, b]T. (c) [8 marks] Write down the Hessian matrix. Is the objective function globally convex? (Hint: (z) ([x) - ( xizi) > 0) (d) [8 marks] Given that x = 1 and = = 2, = Zixi 1, yizi = 4, yixi = 5; what is the rank of A? Are the columns of A linearly independent? (e) [8 marks] Is there a unique solution for 3, how do you know? If there is, use Cramer's rule to find the solution for a. (f) [4 marks] Verify your answer to the previous question by finding A- and solv- ing for B. (g) [6 marks] Assume now that i = ax; for all i. Is there now a unique solution to ABB? If there is not, are there infinite solutions or none?