ln(earningssi)=(.135)7.059+(0.008)0.147educ+(0.007)exp(0.036)0.201femaleR2=0.179,n=1801 a) Interpret the coefficient estimate on female. In answering parts b) and c), you must write down: (i) the null and alternative hypotheses; (ii) the test statistic; and (iii) the rejection rule. b) Test the hypothesis that there is no difference in expected earnings between black men and black women at the =0.05 level. c) Dropping exp and female from the regression gives: ln(earnings)=(0.182)6.703+(0.012)educR2=0.153,n=1801 Are exp and female jointly significant in the original equation at the =0.05 level? d) Suppose we run a regression of educ =0+1exp+2female+ and find a high R2 value. What problem does that cause for our regression? What effect is it likely to have on inference (Rejecting or failing to reject H0 ). e) Suppose we find evidence of heteroskedasticity in our error terms for the original model. Further, we note that the models residuals are divided into clusters between men and women, and that if we isolate the residuals based on sex, the residuals appear to be homoskedastic. How can you use this pattern to your advantage to mitigate the effects of heteroskedasticity? f) Now suppose that the residuals of men and women are clustered, but each group's residuals remain heteroskedastic. Can you still solve the problem of heteroskedasticity in the same way you did in part e)? If not, propose an alternative solution. ln(earningssi)=(.135)7.059+(0.008)0.147educ+(0.007)exp(0.036)0.201femaleR2=0.179,n=1801 a) Interpret the coefficient estimate on female. In answering parts b) and c), you must write down: (i) the null and alternative hypotheses; (ii) the test statistic; and (iii) the rejection rule. b) Test the hypothesis that there is no difference in expected earnings between black men and black women at the =0.05 level. c) Dropping exp and female from the regression gives: ln(earnings)=(0.182)6.703+(0.012)educR2=0.153,n=1801 Are exp and female jointly significant in the original equation at the =0.05 level? d) Suppose we run a regression of educ =0+1exp+2female+ and find a high R2 value. What problem does that cause for our regression? What effect is it likely to have on inference (Rejecting or failing to reject H0 ). e) Suppose we find evidence of heteroskedasticity in our error terms for the original model. Further, we note that the models residuals are divided into clusters between men and women, and that if we isolate the residuals based on sex, the residuals appear to be homoskedastic. How can you use this pattern to your advantage to mitigate the effects of heteroskedasticity? f) Now suppose that the residuals of men and women are clustered, but each group's residuals remain heteroskedastic. Can you still solve the problem of heteroskedasticity in the same way you did in part e)? If not, propose an alternative solution