How much does education affect wage rates? The data file cps4_small.dat contains 1000 observations on hourly wage rates, education, and other variables from the 2008 Current Population Survey (CPS).

(a) Obtain the summary statistics and histograms for the variables WAGE and EDUC. Discuss the data characteristics.

(b) Estimate the linear regression WAGE ¼ b1 þ b2EDUC þ 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 WAGE ¼ a1 þ a2EDUC2 þ 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 14 years of education.

Compare these values to the estimated marginal effect of education from the linear regression in part (b).

82 THE SIMPLE LINEAR REGRESSION MODEL

(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 EDUC. Which model appears to fit the data better?

(g) Construct a histogram of ln(WAGE). Compare the shape of this histogram to that for WAGE from part (a). Which appears more symmetric and bell-shaped?

(h) Estimate the log-linear regression lnðWAGEÞ ¼ g1 þ g2EDUC þ

e. Estimate the marginal effect of another year of education on wage for a person with 12 years of education, and for a person with 14 years of education. Compare these values to the estimated marginal effects of education from the linear regression in part

(b) and the quadratic equation in part (e).