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Reading 12: Multiple Regression and Issues in Regression A

Q9. Suppose there is evidence that the variance of the error term is correlated with the values of the independent variables. The most likely effect on the statistical inferences Smith can make from the regressions results is to commit a:

A)   Type II error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.

B)   Type I error by incorrectly rejecting the null hypotheses that the regression parameters are equal to zero.

C)   Type I error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.

Q10. Which of the following is most likely to indicate that two or more of the independent variables, or linear combinations of independent variables, may be highly correlated with each other? Unless otherwise noted, significant and insignificant mean significantly different from zero and not significantly different from zero, respectively.

A)   The R2 is low, the F-statistic is insignificant and the Durbin-Watson statistic is significant.

B)   The R2 is high, the F-statistic is significant and the t-statistics on the individual slope coefficients are insignificant.

C)   The R2 is high, the F-statistic is significant and the t-statistics on the individual slope coefficients are significant.

Q11. Suppose there is evidence that two or more of the independent variables, or linear combinations of independent variables, may be highly correlated with each other. The most likely effect on the statistical inferences Smith can make from the regression results is to commit a:

A)   Type I error by incorrectly rejecting the null hypothesis that the regression parameters are equal to zero.

B)   Type I error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.

C)   Type II error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero.

Q12. Using the Durban-Watson test statistic, Smith rejects the null hypothesis suggested by the test. This is evidence that:

A)   two or more of the independent variables are highly correlated with each other.

B)   the error terms are correlated with each other.

C)   the error term is normally distributed.

Q13. An analyst is estimating whether a fund’s excess return for a quarter is related to interest rates and last quarter’s excess return. The regression equation is found to have unconditional heteroskedasticity and serial correlation. Which of the following is most accurate? Parameter estimates will be:

A)   inaccurate and statistical inference about the parameters will not be valid.

B)   accurate but statistical inference about the parameters will not be valid.

C)   inaccurate but statistical inference about the parameters will be valid.

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