1. In a study of faculty salaries in a small college in the Midwest, a linear re
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Question
1. 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 Ý = 24697 – 3340.01 where r1 = 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, 12 = Years, i.e., the number of years employed at this college. The estimated regression function is Ý = 18065 + 201x1 + 759.22 The important difference between these two estimated regression functions is that the coefficient for xi has changed signs. Provide an explanation as to how this could happen.Explanation / Answer
a. If other independent variables remains zero then y will take the value of the intercept that is 24697.
If the member changes from male to female that means X1 changes by 1 unit then Salary will be changed ( in the opposite direction ) by 3340 units.
b. in the first regression only the impact of X1 was there on Y. But in the second equation both the impact of X1 and X2 are present in Y. Thats why the coefficient of X1 changes.
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