C. [22 points] People with large student loan outstanding tend to invest in equity more cautiously. Therefore, their portfolio decisions (P) (percentage invested in equity) might be affect by the level of their student loan (L) in addition to their current income (I) as, P=1L+zI+g (a) Suppose 52 = Var() = 12, and we have surveyed 120 people with the following matrices, where X contains data on L and I, and Y contains data on P , _ 120 60 , _ 180 (X X) _ 60 300 ' (X Y) _ [540] Note:[\" b] 1 [d '5],3=(X'X)_1(X'Y),s =v(3)=gz(X'X)_1 C d adb(: c a (1) [6 points] If you run an OLS regression of Equation (a), what are the coefficient estimates 31 and 32? Do coefcient estimates make sense? (2) [5 points] Find the variance of OLS estimates, that is SE1 = V091) and 51%; = Vaiz) (3) [3 points] Test the hypothesis Ho: [31 = 0 (4) [5 points] Test the hypothesis H9: [31 = [32 (5) [3 points] Suppose one has a student loan of $50,000 and income of $60,000, what is her expected investment in equity? (note, both L and I are in million dollar in Equation (3)) D. [10 point] R Code