Chapter 4
1. The normality assumption implies that:
a. the population error u is dependent on the explanatory variables and is normally distributed with
mean equal to one and variance σ2.
b. the population error u is independent of the explanatory variables and is normally distributed with
mean equal to one and variance σ.
c. the population error u is dependent on the explanatory variables and is normally distributed with
mean zero and variance σ.
d. the population error u is independent of the explanatory variables and is normally distributed with
mean zero and variance σ2.
2. Which of the following statements is true?
a. Taking a log of a nonnormal distribution yields a distribution that is closer to normal.
b. The mean of a nonnormal distribution is 0 and the variance is σ2.
c. The CLT assumes that the dependent variable is unaffected by unobserved factors.
d. OLS estimators have the highest variance among unbiased estimators.
3. A normal variable is standardized by:
a. subtracting off its mean from it and multiplying by its standard deviation.
b. adding its mean to it and multiplying by its standard deviation.
c. subtracting off its mean from it and dividing by its standard deviation.
d. adding its mean to it and dividing by its standard deviation.
4. Which of the following is a statistic that can be used to test hypotheses about a single population
parameter?
a. F statistic
b. t statistic
c. χ2 statistic
d. Durbin Watson statistic
5. Consider the equation, Y = β1 + β2X2 + u. A null hypothesis, H0: β2 = 0 states that:
a. X2 has no effect on the expected value of β2.
b. X2 has no effect on the expected value of Y.
c. β2 has no effect on the expected value of Y.
d. Y has no effect on the expected value of X2.
6. The significance level of a test is:
a. the probability of rejecting the null hypothesis when it is false.
b. one minus the probability of rejecting the null hypothesis when it is false.
c. the probability of rejecting the null hypothesis when it is true.
d. one minus the probability of rejecting the null hypothesis when it is true.
7. The general t statistic can be written as:
a. t = 𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑧𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟
b. t = (𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒 – ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑧𝑒𝑑 𝑣𝑎𝑙𝑢𝑒)
c. t = (𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒 – ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑧𝑒𝑑 𝑣𝑎𝑙𝑢𝑒)
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒
d. t = (𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒 – ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑧𝑒𝑑 𝑣𝑎𝑙𝑢𝑒)
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟
8. Which of the following statements is true of confidence intervals?
a. Confidence intervals in a CLM are also referred to as point estimates.
b. Confidence intervals in a CLM provide a range of likely values for the population parameter.
c. Confidence intervals in a CLM do not depend on the degrees of freedom of a distribution.
d. Confidence intervals in a CLM can be truly estimated when heteroskedasticity is present.
9. Which of the following statements is true?
a. When the standard error of an estimate increases, the confidence interval for the estimate narrows
down.
b. Standard error of an estimate does not affect the confidence interval for the estimate.
c. The lower bound of the confidence interval for a regression coefficient, say βj, is given by 𝛽
̂J –
[standard error × (𝛽
̂J)]
d. The upper bound of the confidence interval for a regression coefficient, say βj, is given by 𝛽
̂J + [Critical
value × standard error (𝛽
̂J)]
10. Which of the following tools is used to test multiple linear restrictions?
a. t test
b. z test
c. F test
d. Unit root test
11. Which of the following statements is true of hypothesis testing?
a. The t test can be used to test multiple linear restrictions.
b. A test of single restriction is also referred to as a joint hypotheses test.
c. A restricted model will always have fewer parameters than its unrestricted model.
d. OLS estimates maximize the sum of squared residuals.
12. Which of the following correctly defines F statistic if SSRr represents sum of squared residuals from
the restricted model of hypothesis testing, SSRur represents sum of squared residuals of the unrestricted
model, and q is the number of restrictions placed?
a. F = (SSRur − SSRr)/q
SSRur/(n−k−1)
b. F = (SSRr − SSRur)/q
SSRur/(n−k−1)
c. F = (SSRur − SSRr)/q
SSRr/(n−k−1)
d. F = (SSRur − SSRr)/(n−k−1)
SSRur/q
13. Which of the following statements is true?
a. If the calculated value of F statistic is higher than the critical value, we reject the alternative
hypothesis in favor of the null hypothesis.
b. The F statistic is always nonnegative as SSRr is never smaller than SSRur.
c. Degrees of freedom of a restricted model is always less than the degrees of freedom of an
unrestricted model.
d. The F statistic is more flexible than the t statistic to test a hypothesis with a single restriction.
14. If R2ur = 0.6873, R2r = 0.5377, number of restrictions = 3, and n – k – 1 = 229, F statistic equals:
a. 21.2
b. 28.6
c. 36.5
d. 42.1
15. Which of the following correctly identifies a reason why some authors prefer to report the standard
errors rather than the t statistic?
a. Having standard errors makes it easier to compute confidence intervals.
b. Standard errors are always positive.
c. The F statistic can be reported just by looking at the standard errors.
d. Standard errors can be used directly to test multiple linear regressions.
16. Whenever the dependent variable takes on just a few values it is close to a normal distribution.
17. If the calculated value of the t statistic is greater than the critical value, the null hypothesis, H0 is
rejected in favor of the alternative hypothesis, H1.
18. H1: βj ≠ 0, where βj is a regression coefficient associated with an explanatory variable, represents a
one-sided alternative hypothesis.
19. If 𝛽
̂1 and 𝛽
̂2 are estimated values of regression coefficients associated with two explanatory variables
in a regression equation, then the standard error (𝛽
̂1 – 𝛽
̂2) = standard error (𝛽
̂1) – standard error (𝛽
̂2).
20. Standard errors must always be positive.