Deck 8: Further Inference in the Multiple Regression Model

Question 1

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

Answer 1

B

Question 2

The following model has been estimated using a dataset with 4854 observations. Calculate the F-statistic to test H₀: $\beta$ ₂ = $\beta$ ₃ =- $\beta$ ₄ = $\beta$ ₅ = 0

A)430.35
B).2620
C)76.80
D)2.8169

Answer 2

430.35

Question 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)

Answer 3

A

Question 4

When performing an F-test,if the null hypothesis is H₀: $\beta$ ₂ = $\beta$ ₃ = 0 what is the alternative hypothesis?

A) $\beta$ ₂ ≠0 and $\beta$ ₃≠0
B) $\beta$ ₂ ≠0 or $\beta$ ₃≠0
C)( $\beta$ ₂ ≠0 and $\beta$ ₃=0)or ( $\beta$ ₂ =0 and $\beta$ ₃≠0)
D)( $\beta$ ₂ <0 and $\beta$ ₃>0)or ( $\beta$ ₂ >0 and $\beta$ ₃<0)

Question 5

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

Question 6

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

Question 7

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

Question 8

The F_(1,218) distribution is equivalent to what distribution?

A)N (1,218)
B)F_(2,114)
C)t₍₂₁₈₎
D) $\chi$ ²(_2,114)

Question 9

What statistical test allows joint hypotheses to be tested?

A)Breusch-Pagan Test
B)t-test
C)Gauss-Markov
D)F-test

Question 10

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 variable are omitted and the coefficient estimates of included variables are biased
D)an incorrect functional form was used

Question 11

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

Question 12

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

Question 13

You estimate 4 different specifications of an econometric model by adding a variable each time and get the following results Which model appears to be correctly specified?

A)A
B)B
C)C
D)D

Question 14

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 $\sigma$ 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 rely on the standard normal distribution while forecast use a t distribution.

Question 15

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)

Question 16

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

Question 17

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

Question 18

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

Question 19

For what does RESET test?

Question 20

Running auxillary regressions where each explanatory variable is estimated as a function of eth remaining explanatory variables can help detect

A)omitted relevant variables
B)irrelevant variables included
C)collinearity
D)heteroskedasiticity

Question 21

When two or more variables move together in systematic ways they are said to be ________________?