Question

Q5. 20% An Economics department at a large university keeps track of its majors' starting salaries. Let SAL = salary in dollars, GPA = grade point average on a 4.0 scale, COURSE = 1 if student took econometrics, and 0 otherwise. The model is estimated using information on randomly sampled 50 graduates (standard errors in parentheses): SAL=24200 + 1643 GPA +5033 COURSE, R2 = 0.74. (1078) (352) (456) The errors are assumed to be normally distributed and homoskedastic. (a) What is the economic interpretation of the two slope coefficients? Are they statistically significant at the 5% level? (b) Test the model for the overall goodness of fit. Why is it not sufficient in this case to test each coefficient separately for significance? (c) How would you test a hypothesis that the intercept and the effect of taking a class in econometrics are the same for men and women? Assume that the effect of GPA is the same for both groups. Carefully specify the regression (regressions) that you will estimate to answer this question. Explain how you will use the estimates to test this hypothesis: provide the formula for the test statistic, explain what distribution is used for critical values, specify the critical value(s), and describe the decision rule.

Answer 1

Answer:-

Given That:-

An Economics department at a large university keeps track of its major's starting salaries.

(a) What is the economic interpretation of the two slope coeeficients?

SAL = 24200 + 1643GPA + 5033 METRICS

Interpretation:

i) When GPA is zero & econometrics has not been taken then average salary is 24200.

ii) When GPA Rises by '1' grade point, salary raises by 1643 on average.

iii) When econometrics has been taken, average salary is 5033 higher.

(b) Why is it not sufficient in this case to test each coefficient seperately for significance?

In order to see impact of gender, a dummy variable can be created taking values of '1' for females and '0' for makes

Let its name be FEMALE.

Eqn : SAL = A + B* GPA + C* METRICS + D* FEMALE

D = Coefficient of FEMALE dummy variable.

(c) How would you test a hypothesis that the intercept and the effect of taking a class in econometrics are the same for men and women?

we need to create an interaction term to see if value of econometrics is same for both genders.

Eqn : SAL = A + B* GPA + C* METRICS + D* GENDER* METRICS

D = Coefficient of GENDER* METRICS interaction term

Hence solved

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