1. An economist specifies the relation between earnings y; and an employee's sex using the linear regression model y = Bo + Bila + 82liz + E;, where ra is a dummy variable which equals 1 for females and 0 otherwise, and T,2 is a dummy variable which equals 1 for males and 0 otherwise. She collects a sample of 5 employees, of which observations i = 1, 2, 4 are females and i = 3,5 are males. (a) Write down explicitly the 5 x 3 regressor matrix X of the matrix formulation of the linear regression model y = XB + E. (b) Find a non-zero vector a = (do, (1, a2)' such that do + alfa + a2;2 = 0 for all i. Equivalently, find a non-zero solution a to the linear system of equations Xa = 0, where 0 is a 5 x 1 vector of zeros. (c) Which of the Gauss-Markov assumptions is being violated here? (d) How could the economist overcome this issue