Exercises Unit B - Conceptual

Bachelor’s Degree Programme in Philosophy, International and Economic Studies, Ca’ Foscari University of Venice.

Author

Affiliation

Aldo Solari

Department of Economics, Ca’ Foscari University of Venice

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Chapter 3 Exercise 3.

Suppose we have a data set with five predictors:

• X_1 = \text{GPA}
• X_2 = \text{IQ}
• X_3 = \text{Level} (1 for College and 0 for High School)
• X_4 = \text{GPA} \times \text{IQ}
• X_5 = \text{GPA} \times \text{Level}

The response is starting salary after graduation (in thousands of dollars).
Suppose we use least squares to fit the model, and obtain:

\hat{\beta}_0 = 50,\quad \hat{\beta}_1 = 20,\quad \hat{\beta}_2 = 0.07,\quad \hat{\beta}_3 = 35,\quad \hat{\beta}_4 = 0.01,\quad \hat{\beta}_5 = -10

1. Which answer is correct, and why?

   1. For a fixed value of IQ and GPA, high school graduates earn more, on average, than college graduates.

   2. For a fixed value of IQ and GPA, college graduates earn more, on average, than high school graduates.

   3. For a fixed value of IQ and GPA, high school graduates earn more, on average, than college graduates provided that the GPA is high enough.

   4. For a fixed value of IQ and GPA, college graduates earn more, on average, than high school graduates provided that the GPA is high enough.

2. Predict the salary of a college graduate with IQ of 110 and a GPA of 4.0.

3. 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.