Question

In a study of faculty salaries in a small college in the Midwest, a linear regression model was fit, Y = Salary and x1 = Sex, giving the estimated regression function Yˆ = 24697 − 3340x1 where x1 = 1 if the faculty member was female and 0 if male. The response Salary is measured in dollars (the data are from the 1970s).

(a) Give a sentence that describes the meaning of the two estimated coefficients.

(b) An alternative model to the data set has an additional term, x2 = Years, i.e., the number of years employed at this college. The estimated regression function is Yˆ = 18065 + 201x1 + 759x2 The important difference between these two estimated regression functions is that the coefficient for x1 has changed signs. Provide an explanation as to how this could happen.

Answer 1

a)

Coeeficient of sex: when compared to male faculty, female faculty earns 3350 less

Intercept: 24695 is the salary, male faculty gets.

b)

Coeeficient of sex: For a given year, Female faculty earns 201 more than male faculty.

Coeeficient of year: For a given sex, for every one year increase, expected salary increases by 759

Intercept: Given the rest zero (year =0, sex =0), 18065 is the salary male faculty earns

This can happen if female faculties are working for longer than male faculty