Question

3.1 The output is the result of fitting an educational attainment function, regressing Son ASVABC, a measure of cognitive ability, SM, and SF, years of schooling (highest grade completed) of the respondent's mother and father, respectively, using EAWE Data Set 21. Give an interpretation of the regression coefficients. reg S ASVABC SM SF Source SS df MS Modell Residual 1235.0519 2518.9701 3 496 411.683966 5.07856875 Number of obs = FC 3, 496) - Prob > F R-squared Adj R-squared Root MSE 500 81.06 0.0000 0.3290 0.3249 2.2536 Total 1 3754.022 499 7.52309018 SI Coef. Std. Err. t P>t! [95% Conf. Interval] ASVABC SMI SF 1 cons 1.242527 .091353 . 2028911 10.59674 . 123587 . 0459299 . 0425117 .6142778 10.05 1.99 4.77 17.25 0.000 0.047 0.000 0.000 .999708 .0011119 . 1193658 9.389834 1.485345 . 1815941 .2864163 11.80365 3.2 Fit an educational attainment function parallel to that in Exercise 3.1, using your EAWE data set. Regress Son ASVABC, SM, and SF and interpret the regression results. There is a saying that if you educate a male, you educate an individual, while if you educate a female, you educate a nation. The premise is that the education of a future mother has a beneficial knock-on effect on the educational attainment of her children. Do your regression results support this view?

Answer 1

3.1

The regression coeefficient indicates the effect of a unit change in independent variable on dependent variables if all other independent variables are left constant.

If AVCABC increases by one unit, then S rises by 1.242527 units on an average, holding other variables constant.

If SM increases by one unit, then S rises by 0.091353 units on an average, holding other variables constant.

If SF increases by one unit, then S rises by 0.2028911 units on an average, holding other variables constant.

Also, all the above variables are significant at 5% level of significance. If we look at the p-values corresponding to each of the coefficients, then p-values < 0.05 (i.e. level of significane). Hence, all the variables significantly affecting the dependent variable S.

3.2

The results from the regression undoubtedly depict that female education, depicted by variable for years of schooling of respondent's mother (SM) positively affects the educational attainment (depicted by variable S). But the regression coefficients depict that years of schooling of respondent's father leads to more effect on educational attainment comparatively.

It can be seen from the values of regression coefficients of SF and SM. If years of schooling of respondent's mother increase by 1 year, then educational attainment rises by 0.091353 whereas if years of schooling of respondent's father increase by 1 year, then educational attainment rises by 0.2028911.

Hence, the regression results do support the idea that education of a future mother has a beneficial knock-on effect on the educational attainment of children but this effect is smaller in magnitude when compared to education of a future father, as depicted in regression results.