Question

You have a data set with three predictors: X1 = GPA, X2 = IQ, and X3 = Gender (1 for female, 0 for male). The response is starting salary after graduation (in $ thousands). We use least squares to fit the model, and we get b0 = 50, b1 = 20, b2 = 0.07, and b3 = 35.

a. Predict the salary of a woman with an IQ of 110 and a GPA of 4.0 (for calculation please use Excel.)

b. True or False: For a fixed value of GPA and IQ, men earn on average more than women. Explain.

Answer 1

prediction formula :

starting salary (thousand $) = b0 + b1*x1 + b2*x2 b3*x3

= 50 + 20*x1 + 0.07*x2 + 35*x3

a.

salary of a woman with an IQ of 110 and a GPA of 4.0

x1 = 4 , x2 = 110 , x3=1(female)

starting salary (thousand $) = 50 + 20*x1 + 0.07*x2 + 35*x3

= 50 + 20*4 + 0.07*110 + 35*1

= 172.7 thousand $

b.

for same x1 and x2

x3 = 1 for female and 0 for males

for males :

starting salary (thousand $) = 50 + 20*x1 + 0.07*x2 + 35*0

= 50 + 20*x1 + 0.07*x2

starting salary (thousand $) = 50 + 20*x1 + 0.07*x2 + 35*1

= 50 + 20*x1 + 0.07*x2 + 35

we can see females have 35 thousand $ more salary with same x1 and x2

so , the statement " For a fixed value of GPA and IQ, men earn on average more than women " is FALSE

(please UPVOTE)