The manager of a human resources department wishes to predict the salary of an employee based on years of experience,x,and gender,g.(g = 1 for a male employee and 0 for a female employee.)A random sample of 50 employees results in the following least-squares regression equation: $\text { Salary } = 40,000 + 2,500 x + 1,500 \mathrm {~g} + 1,000 \mathrm { xg }$ Interpret the value of the coefficient of gender (g).
A)We predict that a woman with 0 years of experience will make $1,500 more than a man with 0 years of experience.
B)We predict that a man with 0 years of experience will make $1,000 more than a woman with 0 years of experience.
C)We predict that a man with 0 years of experience will make $2,500 more than a woman with 0 years of experience.
D)We predict that a man with 0 years of experience will make $1,500 more than a woman with 0 years of experience.
E)We predict that a woman with 0 years of experience will make $2,500 more than a man with 0 years of experience.

Question

Quizplus · Accepted Answer

The coefficient of gender is the difference in predicted salary between a male (g=1) and female (g=0) employee with the same years of experience (x). In this case, the coefficient of gender is not given in the question, so we need to look at the least-squares regression equation provided:

ŷ = 30000 + 1000x - 1500g

The coefficient of gender is -1500, which means that, holding years of experience constant, the predicted salary of a female employee is $1500 more than that of a male employee on average. Therefore, we predict that a man with 0 years of experience will make $1500 less than a woman with 0 years of experience. The correct choice is D.

The Manager of a Human Resources Department Wishes to Predict Salary =40,000+2,500x+1,500 g+1,000xg\text { Salary } = 40,000 + 2,500 x + 1,500 \mathrm {~g} + 1,000 \mathrm { xg } Salary =40,000+2,500x+1,500 g+1,000xg

The Manager of a Human Resources Department Wishes to Predict $\text { Salary } = 40,000 + 2,500 x + 1,500 \mathrm {~g} + 1,000 \mathrm { xg }$