Question

A regression analysis of college faculty salaries included several predictors, including a dummy variable for gender (male = 1) and a dummy variable for race (nonwhite = 1). Assume gender takes on the values male and female, and race takes on the values nonwhite and white. For annual income measured in thousands of dollars, the estimated coefficients were 0.76 for gender and 0.62 for race. At particular settings of the other predictors, the estimated mean salary for white females was 30.2 thousand. Find the estimated means for the other three groups. What is the estimated mean for nonwhite males?

Answer 1

The regression model would be like below

average salary = constant + ax1+ bx2+ ..... + 0.76*gender + 0.62*race (assume that x1, x2 are other predictors)

Where gender and rance are the dummy variables, gender takes 1 for males and 0 for females. whereas, race takes 1 for nonwhite and 0 for white.

The four possible groups can be

White male white female

nonwhite male nonwhite female

given that salary = 30.2 for white females, i.e. the value gender takes = 0 and the value race takes = 0

==> constant + ax1+ bx2+ ..... = 30.2

group 1: white male ==> gender = 1 , rance = 0

==>constant + ax1+ bx2+ ..... + 0.76*1+ 0.62*0 = 30.2+0.76 = 30.96

Group 2: nonwhite male ==> gender = 1, race = 1

constant + ax1+ bx2+ ..... + 0.76*1+ 0.62*1 = 30.2+0.76+0.62 = 31.58

Group 3: nonwhite female ==> gender = 0, race = 1

==> constant + ax1+ bx2+ ..... + 0.76*0+ 0.62*1 = 30.2+0.62 = 30.82

Therefore, estimated mean for nonwhite males = 31.58