Contrary to their name, dummy variables are not easy to understand without a little bit of practice:

a. Specify a dummy variable that would allow you to distinguish between undergraduate students and graduate students in your econometrics class.

b. Specify a regression equation to explain the grade (measured on a scale of 4.0) each student in your class received on his or her first econometrics test (Y) as a function of the student’s grade in a previous course in statistics (G), the number of hours the student studied for the test (H), and the dummy variable you created above (D). Are there other variables you would want to add? Explain.

c. What is the hypothesized sign of the coefficient of D? Does the sign depend on the exact way in which you defined D?

d. Suppose that you collected the data and ran the regression and found an estimated coefficient for D that had the expected sign and an absolute value of 0.5. What would this mean in real-world terms?

e. Suppose three of the students in your class are high school seniors who are taking econometrics as part of an accelerated study program for especially talented youngsters. What’s the best way to use dummy variables to distinguish between the three types of students in your class? Be specific as to the definition of the dummy variable(s) you’d use.