2. The dataset wage.csv contains information on average hourly earnings (wage), years of education (educ), years potential experience(exper), years with current employer (tenure), and gender variable (female) with 1 for female, 0 for male.

1. (a)Suppose that the Least-Squares assumptions are satisfied and estimate the following regression model: log(wagei) = 0+1educi+2experi+3tenurei+4femalei+ui, i= 1, . . . , n.(2)
2. Report the estimated values of the regression coefficients and discuss their signs (if it is or it is not as expected, and interpret each of the coefficients), their (heteroskedasticity robust) standard errors, and significance level. Also, report theR2, the adjustedR2(R2) and the value of the F-statistics for the null hypothesis that all the slope coefficients are equal to0. Do you reject the null hypothesis? Explain. Notice that, the dependent variable islog(wage)instead ofwage, you need to create thelog(wage)variable
3. (b)We now introduce some additional variables and some nonlinearities in the model. We add the square of experience (expersq), the square of tenure (tenuresq). We thus estimate the following model. log(wagei) =0+1educi+2experi+3tenurei+4femalei +5expersqi+6tenuresqi+ui (3)
4. Obtain the OLS estimators of the regression coefficients and their (heteroskedas- ticity robust) standard errors. Compare the new estimators with those obtained in (a). How have they changed? Compare the adjustedR2in this model and in model (2). Obtain the F-statistic to test for the null hypothesis that5and6are jointly equal to0. Would you reject this null hypothesis? Based on the adjustedR2and these F-tests, would you prefer model (2) or model (3)? Notice that you need to createexpersqandtenuresq
5. (c)Derive the marginal effect ofexperienceonlog(wage), and explain its meaning. What is the effect of increasing experience of one unit onlog(wage)for a person with 5 years of experience? How about the same effect for a person with 17 years of experience?