How much does education affect wage rates? The data file cps5_small contains 1200 observations on hourly wage rates, education, and other variables from the 2013 Current Population Survey (CPS). 

a. Obtain the summary statistics and histograms for the variables \(W A G E\) and \(E D U C\). Discuss the data characteristics.

b. Estimate the linear regression \(W A G E=\beta_{1}+\beta_{2} E D U C+e\) and discuss the results.

c. Calculate the least squares residuals and plot them against EDUC. Are any patterns evident? If assumptions SR1-SR5 hold, should any patterns be evident in the least squares residuals?

d. Estimate separate regressions for males, females, blacks, and whites. Compare the results.

e. Estimate the quadratic regression \(W A G E=\alpha_{1}+\alpha_{2} E D U C^{2}+e\) and discuss the results. Estimate the marginal effect of another year of education on wage for a person with 12 years of education and for a person with 16 years of education. Compare these values to the estimated marginal effect of education from the linear regression in part (b).

f. Plot the fitted linear model from part (b) and the fitted values from the quadratic model from part (e) in the same graph with the data on WAGE and \(E D U C\). Which model appears to fit the data better?