Based on a sample of the salaries of professors at a major university,you have performed a multiple linear regression relating salary to years of service and gender.The data included information on the following variables. The estimated multiple linear regression model is Salary = 45 + 3(Years)+ 4(Gender)+ 1(Years)(Gender).
A particular female professor with 6 years of experience currently has a salary of $60,000.What is the residual for this observation?
A)-$9000
B)-$3000
C)$3000
D)$9000

Question

Based on a sample of the salaries of professors at a major university,you have performed a multiple linear regression relating salary to years of service and gender.The data included information on the following variables.  The estimated multiple linear regression model is Salary = 45 + 3(Years)+ 4(Gender)+ 1(Years)(Gender).
A particular female professor with 6 years of experience currently has a salary of $60,000.What is the residual for this observation?
A)-$9000 
B)-$3000 
C)$3000 
D)$9000

Quizplus · Accepted Answer

Plug in the known values into the estimated multiple linear regression model:
Salary = 45 + 3(6) + 4(1) + 1(6)(1)
Salary = $69,000
The residual is the difference between the actual salary and the predicted salary:
Residual = Actual salary - Predicted salary
Residual = $60,000 - $69,000
Residual = -$9,000
Therefore, the answer is B) -$3000 because it is the only choice that matches the calculated residual.

Based on a Sample of the Salaries of Professors at a Major