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254 Chapter 6 Linear Regression with Multiple Regressors

have information on the class size to include in the regression. What effect
would the omission of the class size variable have on her estimated coef-
ficient on the private school indicator variable? Will the effect of this omis-
sion disappear if she uses a larger sample of students?

6.2 A multiple regression includes two regressors: Yi = b0 + b1X1i +
b2X2i + ui. What is the expected change in Y if X1 increases by 8 units
and X2 is unchanged? What is the expected change in Y if X2 decreases
by 3 units and X1 is unchanged? What is the expected change in Y if X1
increases by 4 units and X2 decreases by 7 units?

6.3 What are the measures of fit that are commonly used for multiple regres-
sions? How can an adjusted R 2 take on negative values?

6.4 What is a dummy variable trap and how is it related to multicollinearity of
regressors? What is the solution for this form of multicollinearity?

6.5 How is imperfect collinearity of regressors different from perfect collinear-
ity? Compare the solutions for these two concerns with multiple regression
estimation.

Exercises

The first four exercises refer to the table of estimated regressions on page 255,
computed using data for 2012 from the CPS. The data set consists of information on
7440 full-time, full-year workers. The highest educational achievement for each
worker was either a high school diploma or a bachelor’s degree. The workers’
ages ranged from 25 to 34 years. The data set also contains information on the
region of the country where the person lived, marital status, and number of chil-
dren. For the purposes of these exercises, let

AHE = average hourly earnings (in 2012 dollars)
College = binary variable (1 if college, 0 if high school)
Female = binary variable (1 if female, 0 if male)
Age = age (in years)
Ntheast = binary variable (1 if Region = Northeast, 0 otherwise)
Midwest = binary variable (1 if Region = Midwest, 0 otherwise)
South = binary variable (1 if Region = South, 0 otherwise)
West = binary variable (1 if Region = West, 0 otherwise)

6.1 Compute R 2 for each of the regressions.