A resercher is trying to explain the choice to attend college by high-school graduates.

2. A researcher is trying to explain the choice to attend college by high-school graduates. Define college = 1 if a high-school graduate chooses either a 2-year or 4-year college, and zero otherwise. The researcher uses explanatory variables faminc, denoting gross family income; the binary variable black that is equal to one if the high-school graduate is black and zero otherwise, and finally the binary variable mocoll that is equal to one if the mother has attended college and zero otherwise. Using a sample of N = 1000 graduates the researcher first estimated a linear probability model (LPM) of the form: college = Bo + Bifaminc + Byblack + B3faminc x black + BAmocoll + u The estimated coefficients of the LPM had the following signs: Bo, B1, B4 were positive, and B2, B3 were negative. The researcher then estimated a probit model of the form: P(college = 1) = @(70 + 71faminc + 72black + 73 faminc x black + yamocoll) The estimated coefficients of the probit had the following signs: 70, 71, 74 were positive, and 72, 73 were negative 2.1. How can one compare results from the LPM and the probit model? [20%] 2.2. Using the probit model, what is the marginal effect of the mother having attended college on the graduate's probability of attending college? [10%] 2.3. Using the probit model, what is the marginal effect of family income on the gradu- ate's probability of attending college? Is this effect constant across different levels of income, while keeping the mother's college attendance constant? [10%] 2.4. Using the probit model, what is the effect of race on the graduate's probability of attending college? Is this effect constant across different levels of income while keeping the mother's college attendance constant? [10%]