Q4. In regards to multiple regression analysis, which of the following statements is most accurate?

A)   Adjusted R² is less than R².

B)   Adjusted R² always decreases as independent variables increase.

C)   R² is less than adjusted R².

Q5. Which of the following tests is used to detect autocorrelation?

A)   Residual Plot.

B)   Breusch-Pagan.

C)   Durbin-Watson.

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Q6. One of the most popular ways to correct heteroskedasticity is to:

A)   adjust the standard errors.

B)   use robust standard errors.

C)   improve the specification of the model.

Q7. Which of the following statements regarding the Durbin-Watson statistic is most accurate? The Durbin-Watson statistic:

A)   can only be used to detect positive serial correlation.

B)   only uses error terms in its computations.

C)   is approximately equal to 1 if the error terms are not serially correlated.

Q8. If a regression equation shows that no individual t-tests are significant, but the F-statistic is significant, the regression probably exhibits:

A)   heteroskedasticity.

B)   multicollinearity.

C)   serial correlation.

Q9. Which of the following is a potential remedy for multicollinearity?

A)     Take first differences of the dependent variable.

B)     Omit one or more of the collinear variables.

C)     Add dummy variables to the regression.

答案和详解如下：

Q4. In regards to multiple regression analysis, which of the following statements is most accurate?

A)   Adjusted R² is less than R².

B)   Adjusted R² always decreases as independent variables increase.

C)   R² is less than adjusted R².

Correct answer is A)

Whenever there is more than one independent variable, adjusted R² is less than R². Adding a new independent variable will increase R², but may either increase or decrease adjusted R².

R² adjusted = 1 − [((n − 1) / (n − k − 1)) × (1 − R²)]

Where:
n = number of observations
K = number of independent variables
R² = unadjusted R²

Q5. Which of the following tests is used to detect autocorrelation?

A)   Residual Plot.

B)   Breusch-Pagan.

C)   Durbin-Watson.

Correct answer is C)

Durbin-Watson is used to detect autocorrelation. Breusch-Pagan and the residual plot are methods to detect heteroskedasticity.

Q6. One of the most popular ways to correct heteroskedasticity is to:

A)   adjust the standard errors.

B)   use robust standard errors.

C)   improve the specification of the model.

Correct answer is B)         

Using generalized least squares and calculating robust standard errors are possible remedies for heteroskedasticity. Improving specifications remedies serial correlation. The standard error cannot be adjusted, only the coefficient of the standard errors.

Q7. Which of the following statements regarding the Durbin-Watson statistic is most accurate? The Durbin-Watson statistic:

A)   can only be used to detect positive serial correlation.

B)   only uses error terms in its computations.

C)   is approximately equal to 1 if the error terms are not serially correlated.

Correct answer is B)         

The formula for the Durbin-Watson statistic uses error terms in its calculation. The Durbin-Watson statistic is approximately equal to 2 if there is no serial correlation. A Durbin-Watson statistic less than 2 indicates positive serial correlation, while a Durbin-Watson statistic greater then 2 indicates negative serial correlation.

Q8. If a regression equation shows that no individual t-tests are significant, but the F-statistic is significant, the regression probably exhibits:

A)   heteroskedasticity.

B)   multicollinearity.

C)   serial correlation.

Correct answer is B)         

Common indicators of multicollinearity include: high correlation (>0.7) between independent variables, no individual t-tests are significant but the F-statistic is, and signs on the coefficients that are opposite of what is expected.

Q9. Which of the following is a potential remedy for multicollinearity?

A)     Take first differences of the dependent variable.

B)     Omit one or more of the collinear variables.

C)     Add dummy variables to the regression.

Correct answer is B)         

The first differencing is not a remedy for the collinearity, nor is the inclusion of dummy variables. The best potential remedy is to attempt to eliminate highly correlated variables.

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