#1) Write the meaning of each of the following terms without referring to the book (or your notes), and compare your definition with the version in the text for each:

1. dummy variable (p. 79)
2. omitted condition (p. 80)
3. six steps in applied regression analysis (p. 66)
4. specification (p. 67)
5. specification error (p. 68)

#3) Do liberal arts colleges pay economists more than they pay other professors? To find out, we looked at a sample of 2,929 small-college faculty members and built a model of their salaries that included a number of variables, four of which were:

where:

Si = the salary of the ith college professor

Mi = a dummy variable equal to 1 if the ith professor is a male and 0 otherwise

Ai = a dummy variable equal to 1 if the ith professor is African American and 0 otherwise

Ri = the years in rank of the ith professor

Ti = a dummy variable equal to 1 if the ith professor teaches economics and 0 otherwise

1. Carefully explain the meaning of the estimated coefficient of M.
2. The equation indicates that African Americans earn $426 more than members of other ethnic groups, holding constant the other variables in the equation. Does this coefficient have the sign you expected? Why or why not?
3. Is R a dummy variable? If not, what is it? Carefully explain the meaning of the coefficient of R. (Hint: A professor's salary typically increases each year based on rank.)
4. What's your conclusion? Do economists earn more than other professors at liberal arts colleges? Explain.
5. The fact that the equation ends with the notation "+..." indicates that there were more than four independent variables in the equation. If you could add a variable to the equation, what would it be? Explain.

#5) The Graduate Record Examination (GRE) subject test in economics was a multiple-choice measure of knowledge and analytical ability in economics that was used mainly as an entrance criterion for students applying to Ph.D. programs in the "dismal science." For years, critics claimed that the GRE, like the Scholastic Aptitude Test (SAT), was biased against women and some ethnic groups. To test the possibility that the GRE subject test in economics was biased against women, Mary Hirschfeld, Robert Moore, and Eleanor Brown estimated the following equation (standard errors in parentheses):

where

GREi = the score of the ith student in the Graduate Record Examination subject test in economics

Gi = a dummy variable equal to 1 if the ith student was a male, 0 otherwise

GPAi = the GPA in economics classes of the ith student (4 = A, 3 = B, etc.)

SATMi = the score of the ith student on the mathematics portion of the Scholastic Aptitude Test

SATV1 = the score of the ith student on the verbal portion of the Scholastic Aptitude Test

1. Carefully explain the meaning of the coefficient of G in this equation. (Hint: Be sure to specify what 39.7 stands for.)
2. Does this result prove that the GRE is biased against women? Why or why not?
3. If you were going to add one variable to Equation 3.9, what would it be? Explain your reasoning.
4. Suppose that the authors had defined their gender variables as Gi = a dummy variable equal to 1 if the ith student was a female, 0 otherwise. What would the estimated Equation 3.9 have been in that case? (Hint: Only the intercept and the coefficient of the dummy variable change.)

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