2. [12 points] In a study of faculty salaries in a community college, a linear regression model was fit, giving the fitted mean function E(Salary| Sex) = 24748.9 - 3338.4Sex, (1) where Sex equals 1 if the faculty member was female and 0 if male. The response Salary is measured in dollars. (a) Explain 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) = 18116.4 + 203.3Sex + 759.1Years. (2) The important difference between the two mean functions (1) and (2) is that the coeffi- cient for Sex has changed signs. Explain how this could happen.(c) By including the interaction term Sex x Years, the estimated mean function becomes E(Salary| Sex) = 18277.5 - 588.4Sex + 740.7Years + 173.3Sex x Years. (3) Give the estimated coefficients if Sex were coded as -1 for males and +1 for females