Quiz Questions
Chapter 5: Linear Regression with Multiple Regressors
1. Provide a definition for each of the Key Terms at the end of the chapter.
The remaining questions are based on the results in Table 5.2 in the text.
2. In the regression in column (3), the estimated value of β1 is –1.00. What does a value of
–1.00 mean in this regression?
3. Using the results in column (3), construct a 99% confidence interval for β1.
4. Construct the R2 for the regression in column (3).
5. The R 2 in the regression in column (3) is much higher than the regression in column (1).
Does this mean that it has eliminated any potential omitted variable bias? Explain.
6. Let β4 denote the coefficient on the variable “Percent on public income assistance.”.
a. Is β4 statistically significant in the regression in column (4)? Construct a 95% confidence
interval for β4 using the column (4) regression.
b. Is β4 statistically significant in the regression in column (5)? Construct a 95% confidence
interval for β4 using the column (5) regression.
c. Explain why the answers to (a) and (b) are so different.
7. An F-statistic testing the null hypothesis H0 : β2 = β4 = 0 is carried out for the regression
specification in column (5). The value of the statistic is 6.88.
a. Is H0 rejected at the 1% level? Explain.
b. Is the point β2 = β4 = 0 contained in the 99% confidence set for β2 and β4? Explain.
8. In the regression represented in column (1), is the student-teacher ratio uncorrelated with the
regression error? Is the correlation positive or negative?
9. Comparing columns (1) and (2), do you think the student-teacher ratio and the percent of
English learners is positively or negatively correlated? Explain.
10. Suppose that the sample size were doubled, so that n = 840. How would you expect the
standard errors of the ordinary least squares estimators to change? Explain.
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Multiple Choice
1. When you have an omitted variable problem,
a. the assumption that E(ui | Xi) = 0 is violated.
b. the assumption that (Xi, Yi) are i.i.d. is violated.
c. the assumption that (Xi, ui) has finite fourth moments is violated.
d. you have perfect multicollinearity.
2. In a multiple regression regression model with k regressors, the 5% critical value for a
t-statistic is
a. 1.96/k.
b. 1.96×k.
c. 1.96.
d. 1.96/(n–k).
3. The adjusted R2, R 2 , satisfies the relation
a. R 2 ≥ R2.
b. R 2 ≤ R2.
c. R 2 / SER = R2.
d. R 2 = ESS/TSS.
4. When q = 1, the F-statistic
a. is the same as the absolute value of the t-statistic.
b. is the same as the square of the t-statistic.
c. is the same as the square root of the t-statistic.
d. cannot be calculated because 1/(q-1) is not defined.
5. Perfect multicollinearity
a. occurs whenever the correlation of the regressors is greater than 0.8.
b. means that the intercept of the regression line is zero.
c. means that one regressor is an exact linear function of the other regressors.
d. is rare in economics.
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