An economist would like to estimate a regression relating monthly salary to the

Question

An economist would like to estimate a regression relating monthly salary to the highest level of education (high school or college and above) and gender (male or female):

yˆ = b0 + b1x1 + b2x2 + b3x1(x2)

x1: 1-college and above, 0: otherwise; x2: 1-female, 0-male.

(a) What is the estimated salary of a male employee with high school as the highest degree?

(b) What is the estimated salary for a female employee with college degree?

(c) What is the estimated salary difference between a female employee with college degree and a male employee with college degree?

Explanation / Answer

The regression equation is yˆ = b0 + b1x1 + b2x2 + b3x1(x2)

x1: 1-college and above, 0: otherwise; x2: 1-female, 0-male.

(a) What is the estimated salary of a male employee with high school as the highest degree?

Estimated Salary of male employee (1) and high school as highest degree (0)

y^ = b0 + b1x1 + b2x2 + b3x1(x2) = b0 + b1 *0 + b2 * 0+ b3 * 0 = b0

(b) What is the estimated salary for a female employee with college degree?

y^ =  b0 + b1x1 + b2x2 + b3x1(x2) = b0 + b1 *1 + b2 *1+ b3 *1*1 = b0 + b1 + b2 + b3

(c)  What is the estimated salary difference between a female employee with college degree and a male employee with college degree?

Estimated salary of female employee with college degree

y^ = b0 + b1 + b2 + b3

Estimated salary of male employee with college degree

y^ = b0 + b1x1 + b2x2 + b3x1(x2) = b0 + b1

difference between salary = (b0 + b1 + b2 + b3 ) - ( b0 + b1 ) = (b2 + b3)

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