Hi, I have this question on modeling the salary on female and male Let X1 = GPA,

Question

Hi, I have this question on modeling the salary on female and male

Let X1 = GPA,
X2 = IQ,
X3 = Sex (1 for Female and 0 for Male),
X4 = Interaction between GPA and IQ,
X5 = Interaction between GPA and Gender.

Let the response be starting salary after graduation (in thousands of dollars). Suppose we use least squares to fit the model, and estimate

0 =50,
1 =20,
2 =0.07,
3 =35,
4 =0.01,
5 =10.

1. Which answer is correct, and why?
a) For a fixed value of IQ and GPA, males earn more on average than females.
b) For a fixed value of IQ and GPA, males earn more on average than females provided that the GPA is high enough.
c) For a fixed value of IQ and GPA, females earn more on average than males.
d) For a fixed value of IQ and GPA, females earn more on average than males provided that the GPA is high enough

2. Provide the estimated equation of a line for females. Simplify it as much as possible.

3. Predict the salary of a female with IQ of 110 and a GPA of 4.0.

4. True or false: Since the coefficient for the GPA/IQ interaction term is very small, there is very little evidence of an interaction effect. Justify your answer.

Explanation / Answer

The regressin equation is formed as

salary = 50 +20*GPA + 0.07*IQ + 35*gender+ 0.01*GPA*IQ -10*GPA*Gender

we know that females = 1 and male = 0

a) if iq and gpa are fixed , then females earn more than males , because all the coeffiecient terms are positive
when you put gender = 0

then all the coeffecients of gender , including interaction terms become zero . thereby reducing the overall value for salary

so for females put gender = 1 , hence the regression equation becomes

salary = 50 +20*GPA + 0.07*IQ + 35*1+ 0.01*GPA*IQ -10*GPA

= 85 +10*GPA + 0.07*IQ + 0.01*GPA*IQ

3)

prediction for female , put the given values

85 +10*4 + 0.07*10 + 0.01*10*4 = 126.1

4)

False , the evidence is usually calculated based on the p value of the interaction effect. if the p value is not less than 0.05 , then we can say that the interaction effect is not significant

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