Mincer studied the relationship of returns to schooling based on a cross-section of 31,093 individuals. The following bivariate regression was reported in his study (estimated standard errors are in parenthesis): In Y, = 7.58 + 0.070 Xi + e, R = 0.067 (0.00160)where Y; is income for individual i, X; is education level in years, and e; is the OLS residual. (a) Making explicit your assumptions, discuss the properties of these coefficient esti- mates. (b) What is the interpretation of the coefficient on X? In particular why was the log of education not used as the explanatory variable? (c) Considering the sample size, which tables should be consulted in testing the null hypothesis that the coefficient on X; is zero? Conduct the test and report your results. (d) Construct a 95% confidence interval for the coefficient on Xi. What informations does this interval provide us with regard to hypothesis testing? (e) Precisely what does the R in this regression measure? Could this measure be used to choose between Y, and In Y, as the dependent variable in the regression