Are there differences in male and female educational attainment functions? This question has been answered by Exercise 6.16 but nevertheless it is instructive to investigate the issue using the dummy variable approach. Using your EAEF data set, define the following slope dummies combining MALE with the parental education variables:

MALESM = MALE*SM

MALESF = MALE*SF

and regress S on ETHBLACK, ETHHISP, ASVABC, SM, SF, MALE, MALEBLAC, MALEHISP (defined in Exercise 6.15), MALEASVC (defined in Exercise 6.12), MALESM, and MALESF. Next regress S on ETHBLACK, ETHHISP, ASVABC, SM, and SF only. Perform an F test of the joint explanatory power of MALE and the slope dummy variables as a group (verify that the F statistic is the same as in Exercise 6.16) and perform t tests on the coefficients of the slope dummy variables in the first regression.

Exercise 6.12

Is the effect of the ASVABC score on educational attainment different for males and females? Using your EAEF data set, define a slope dummy variable MALEASVC as the product of MALE and ASVABC: MALEASVC = MALE*ASVABC
Regress S on ASVABC, SM, SF, ETHBLACK, ETHHISP, MALE and MALEASVC, interpret the equation and perform appropriate statistical tests.

Exercise 6.15

Are there ethnic variations in the effect of the sex of a respondent on educational attainment? A special case of a slope dummy variable is the interactive dummy variable defined as the product of two dummy variables. Using your EAEF data set, define interactive dummy variables MALEBLAC and MALEHISP as the product of MALE and ETHBLACK, and of MALE and ETHHISP, respectively:

MALEBLAC = MALE*ETHBLACK
MALEHISP = MALE*ETHHISP

Regress S on ASVABC, SM, SF, MALE, ETHBLACK, ETHHISP, MALEBLAC and MALEHISP. Interpret the regression results and perform appropriate statistical tests.