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=lL+2I+g (3,) Suppose 02 = Var(e) = 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) ' 6(1) 301d (X Y) ' 540 a b _ 1 d b 1 1 1 A , 1 Note:[ d] = [ ],=(XX) (XY),s =V( )=02(XX) C adbc '5 '1 (1) [6 points] If you run an OLS regression of Equation (a), what are the coefcient estimates B1 and z? Do coefcient estimates make sense? (2) [5 points] Find the variance of OLS estimates, that IS 531 = \"31) and SE2 = 170.02) (3) [3 points] Test the hypothesis Ha: I31 = 0 (4) [5 points] Test the hypothesis Ho: [3] = [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))