In a study of faculty salaries in a small college in the Midwest, a linear regre

Question

In a study of faculty salaries in a small college in the Midwest, a linear regression model was fit, giving the fitted mean function E(Salary! Sex) 24697-3350Sex where Sex equals 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 mean function fit to these data with an additional term, Years, the number of years employed at this college, gives the estimated mean function E (Salary! Sex, Years) = 1 8065 + 201 Sex + 759 Years i. Give a sentence that describes the meaning of the three estimated coefficients ii. The important difference between these two mean functions is that the coefficient for Ser has changed signs. Explain how this could happen

Explanation / Answer

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

c)

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

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