Ch6 Test Bank + Answers + Further Inference In The Multiple - Principles of Econometrics 5e Complete Test Bank by R. Carter Hill. DOCX document preview.
File: Chapter 6 – Further Inference in the Multiple Regression Model
Multiple Choice
1. The following model has been estimated using a dataset with 4854 observations.
SS | df | MS | |||||||
Regression | 919587.543 | 4 | 229896.9 | ||||||
Error | 2590390.62 | 121 | 534.2113 | ||||||
Variable |
| |
| Std. Error |
| t |
| P>|t| | |
x2 | -0.0126355 | 0.005519 | -2.28937 | 0.022 | |||||
x3 | 0.5957923 | 0.014482 | 41.13934 | 0.000 | |||||
x4 | 1.124589 | 0.877192 | 1.282032 | 0.200 | |||||
x5 | 0.3237421 | 0.060709 | 5.332661 | 0.000 | |||||
Constant | 8.86016 | 1.766116 | 5.016749 | 0.000 | |||||
| |||||||||
Calculate the F-statistic to test H0: 2 = 3 =- 4 = 5 = 0
a. 430.3500
b. 0.2620
c. 76.8000
d. 2.8169
2. The critical value for a given p-value in the F-distribution depends on the degrees of freedom in the numerator and denominator. How do you find the degrees of freedom in the numerator?
a. It is the number of observations minus the number of coefficients estimated (N-K).
b. It is the number of hypotheses being tested simultaneously (J).
c. It is the number of coefficients being estimated (K).
d. It is the number of observations minus the number of hypotheses tested (N-J).
3. The critical value for a given p-value in the F-distribution depends on the degrees of freedom in the numerator and denominator. How do you find the degrees of freedom in the denominator?
a. It is the number of observations minus the number of coefficients estimated (N-K).
b. It is the number of hypotheses being tested simultaneously (J).
c. It is the number of coefficients being estimated (K).
d. It is the number of observations minus the number of hypotheses tested (N-J).
4. When performing an F-test, if the null hypothesis is H0: 2 = 3 = 0, what is the alternative hypothesis?
a. 2 ≠0 and 3≠0
b. 2 ≠0 or 3≠0
c. (2 ≠0 and 3=0) or (2 =0 and 3≠0)
d. (2 <0 and 3>0) or (2 >0 and 3<0)
5. Suppose you are conducting a two-tailed t-test with a single hypothesis in the null hypothesis and your degrees of freedom in 218. This means that the _____ distribution is equivalent to the _____ distribution.
a. 
b. 
c. 
d. 
6. What statistical test allows joint hypotheses to be tested?
a. Breusch-Pagan Test
b. t-test
c. Gauss-Markov
d. F-test
7. If your computer printout includes an F-statistic and p-value for the overall model, how should you interpret the p-value?
a. The probability that all of the coefficients are actually equal to zero
b. The probability that all of the coefficients other than the intercept are actually zero and we would observe the estimated results
c. The probability that the model is completely invalid
d. The probability that the model is incorrectly specified
8. Why should good non-sample information be incorporated into an econometric model via restricted least squares?
a. It reduces the variance of estimated coefficients without introducing bias.
b. It allows more precise hypotheses testing to be done.
c. It reduces the degrees of freedom in the denominator of an F-test.
d. It reduces the probability of rejecting a true null hypothesis.
9. How does omitting a relevant variable from a regression model affect the estimated coefficient of other variables in the model?
a. They are biased downward and have smaller standard errors.
b. They are biased upward and have larger standard errors.
c. They are biased and the bias can be negative or positive.
d. They are unbiased but have larger standard errors.
10. How does including an irrelevant variable in a regression model affect the estimated coefficient of other variables in the model?
a. They are biased downward and have smaller standard errors.
b. They are biased upward and have larger standard errors.
c. They are biased and the bias can be negative or positive.
d. They are unbiased but have larger standard errors.
11. Which of the following measures is NOT used to evaluate model specification?
a. Adj R2.
b. Akiake Information Criterion (AIC).
c. Bayesian Information Criterion (BIC).
d. Jarque-Bera Test.
12. If you reject the null hypothesis when performing a RESET test, what should you conclude?
a. At least one of the original coefficients is not equal to zero.
b. The original model is incorrectly specified and can be improved upon.
c. Relevant variables are omitted and the coefficient estimates of included variables are biased.
d. An incorrect functional form was used.
13. When are R2 and adjusted R2 equal?
a. When the model is correctly specified
b. When K = 1
c. When the error terms are normally distributed
d. When an unrestricted model is estimated
14. You estimate 4 different specifications of an econometric model by adding a variable each time and get the following results
R2 | adj R2 | AIC | ||
Model A | 0.3458 | 0.3285 | 22.56 | |
Model B | 0.3689 | 0.3394 | 22.37 | |
Model C | 0.4256 | 0.3916 | 21.21 | |
Model D | 0.4299 | 0.3911 | 21.79 | |
Which model appears to be correctly specified?
a. A
b. B
c. C
d. D
15. When collinear variables are included in an econometric model coefficient estimates are _____.
a. biased downward and have smaller standard errors
b. biased upward and have larger standard errors
c. biased and the bias can be negative or positive
d. unbiased but have larger standard errors
16. When a set of variables with exact collinearity is included in an econometric model coefficient estimates are _____.
a. undefined
b. unbiased
c. biased upward
d. biased, but the direction is unclear
17. If your regression results show a high R2, adj R2, and a significant F-test, but low t values for the coefficients, what is the most likely cause?
a. Omitted relevant variables
b. Irrelevant variables included
c. Collinearity
d. Heteroskedasiticity
18. Running auxiliary regressions where each explanatory variable is estimated as a function of the remaining explanatory variables can help detect _____.
a. omitted relevant variables
b. irrelevant variables included
c. collinearity
d. heteroskedasiticity
19. Why is the variance of the forecast y larger than the variance of the expected value of y?
a. The estimated forecast variance includes an estimate of ̂2.
b. The estimated forecast variance includes weighted covariance terms of all paired variables.
c. The Gauss-Markov theorem does not apply to forecast of a single observation.
d. The expected value of confidence intervals relies on the standard normal distribution while forecast use a t distribution.
1. Suppose you have two independent random variables, x1 and x2, that have a chi-squared distribution with degrees of freedom m1 and m2, respectively. Given this information, how would you construct a random variable, W, that has an F-distribution?
2. Briefly explain the relationship between the t- and F-tests.
3. For what does RESET test?
4. When two or more variables move together in systematic ways, they are said to be _____?