The regression equation relating y = education

(number of years completed) to race (z = 1 for whites, z = 0 for nonwhites) in a certain country isE(y) = 11+2z.

The regression equation relating education to race and to father’s education (x) is E(y) = 3 + 0.8x − 0.6z.

(a) Ignoring father’s education, find the mean education for whites, the mean education for nonwhites, and the difference between them.

(b) Plot the relationship between x and the mean of y for whites and for nonwhites.

(c) Controlling for father’s education, find the difference between the mean education of whites and nonwhites.

Illustrate by finding the mean education for each group when father’s education equals 12 years.