The American Association of University Professors (AAUP) reports yearly on faculty salaries for all types of higher education institutions across the United States. Regard Salary as the response variable, Gender as the explanatory variable, and Academic Rank as the control variable. A regression analysis using these data could include an indicator variable for Gender and an indicator variable for Rank. The estimated coefficients are -13 (thousands of dollars) for Gender (x1 = 1 for female and x1 = 0 for male) and -40 (thousands of dollars) for a lesser assistant Rank (x2 = 1 for assistant professor and x2 = 0 for professor).
a. Interpret the coefficient for gender.
b. At particular settings of the other predictors, the estimated mean salary for female professors was 96.2 thousand dollars. Using the estimated coefficients, find the estimated means for
(i) Male professors and
(ii) Female assistant professors.