A dean claims that the salaries of humanities professors Y are determined solely by the number of years of teaching experience X. To see if there is a statistically significant difference in the salaries of male and female professors, the equation Y = α + β₁D + β₂X + β₃DX + ε was estimated, using the variable D = 0 if male, 1 if female.

a. Interpret each of the parameters α, β₁, β₂, and β₃.

b. What advantages does a regression model have over a simple comparison of the average men’s and women’s salaries?

c. Describe a specific situation in which a comparison of men’s and women’s average salaries shows discrimination against women while a regression equation does not.

d. Describe a specific situation in which a comparison of men’s and women’s average salaries shows no discrimination while a regression equation indicates discrimination against women.