A dummy variable takes on only the values 0 and 1..

A dummy variable takes on only the values 0 and 1. It is used for categorical data, such as an individual's gender. Let Di and Do be vectors of 1's and 0's, with the i th element of D, equaling 1 and that of D, equaling 0 if the person is a man, and the reverse if the person is a woman. Suppose that there are m1 men and n, women in the sample. Consider the three regressions Y = mit Dimi+ Dgazte (1) = Dial + Droz te (2) Y = mit Didte (3 (a) Can all three regressions (1), (2), and (3) be estimated by OLS? Explain if not. (b) Compare regressions (2) and (3). Is one more general than the other? Explain the relationship between the parameters in (2) and (3). (c) Compute 'D, and 'Do, where & is an n x1 vector of ones. (d) write equation (2) as Y = Xote. Consider the assumption E(e|X ) = 0. Is there any content of to this assumption in this setting? (e) What is the form of E(ee'| X) in this setting? (f) Compute Var (a|X )