Q7. An analyst is estimating whether a fund’s excess return for a month is dependent on interest rates and whether the S& 500 has increased or decreased during the month. The analyst collects 90 monthly return premia (the return on the fund minus the return on the S& 500 benchmark), 90 monthly interest rates, and 90 monthly S& 500 index returns from July 1999 to December 2006. After estimating the regression equation, the analyst finds that the correlation between the regressions residuals from one period and the residuals from the previous period is 0.199. Which of the following is most accurate at a 0.05 level of significance, based solely on the information provided? The analyst:

A)   cannot conclude that the regression exhibits either serial correlation or multicollinearity.

B)   can conclude that the regression exhibits multicollinearity, but cannot conclude that the regression exhibits serial correlation.

C)   can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits multicollinearity.

Q8. An analyst is estimating whether a fund’s excess return for a month is dependent on interest rates and whether the S& 500 has increased or decreased during the month. The analyst collects 90 monthly return premia (the return on the fund minus the return on the S& 500 benchmark), 90 monthly interest rates, and 90 monthly S& 500 index returns from July 1999 to December 2006. After estimating the regression equation, the analyst finds that the correlation between the regressions residuals from one period and the residuals from the previous period is 0.145. Which of the following is most accurate at a 0.05 level of significance, based solely on the information provided? The analyst:

A)   cannot conclude that the regression exhibits either serial correlation or heteroskedasticity.

B)   can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits heteroskedasticity.

C)   can conclude that the regression exhibits heteroskedasticity, but cannot conclude that the regression exhibits serial correlation.

答案和详解如下：

Q7. An analyst is estimating whether a fund’s excess return for a month is dependent on interest rates and whether the S& 500 has increased or decreased during the month. The analyst collects 90 monthly return premia (the return on the fund minus the return on the S& 500 benchmark), 90 monthly interest rates, and 90 monthly S& 500 index returns from July 1999 to December 2006. After estimating the regression equation, the analyst finds that the correlation between the regressions residuals from one period and the residuals from the previous period is 0.199. Which of the following is most accurate at a 0.05 level of significance, based solely on the information provided? The analyst:

A)   cannot conclude that the regression exhibits either serial correlation or multicollinearity.

B)   can conclude that the regression exhibits multicollinearity, but cannot conclude that the regression exhibits serial correlation.

C)   can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits multicollinearity.

Correct answer is C)         

The Durbin-Watson statistic tests for serial correlation. For large samples, the Durbin-Watson statistic is approximately equal to two multiplied by the difference between one and the sample correlation between the regressions residuals from one period and the residuals from the previous period, which is 2 × (1 − 0.199) = 1.602, which is less than the lower Durbin-Watson value (with 2 variables and 90 observations) of 1.61. That means the hypothesis of no serial correlation is rejected. There is no information on whether the regression exhibits multicollinearity.

Q8. An analyst is estimating whether a fund’s excess return for a month is dependent on interest rates and whether the S& 500 has increased or decreased during the month. The analyst collects 90 monthly return premia (the return on the fund minus the return on the S& 500 benchmark), 90 monthly interest rates, and 90 monthly S& 500 index returns from July 1999 to December 2006. After estimating the regression equation, the analyst finds that the correlation between the regressions residuals from one period and the residuals from the previous period is 0.145. Which of the following is most accurate at a 0.05 level of significance, based solely on the information provided? The analyst:

A)   cannot conclude that the regression exhibits either serial correlation or heteroskedasticity.

B)   can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits heteroskedasticity.

C)   can conclude that the regression exhibits heteroskedasticity, but cannot conclude that the regression exhibits serial correlation.

Correct answer is A)

The Durbin-Watson statistic tests for serial correlation. For large samples, the Durbin-Watson statistic is equal to two multiplied by the difference between one and the sample correlation between the regressions residuals from one period and the residuals from the previous period, which is 2 × (1 − 0.145) = 1.71, which is higher than the upper Durbin-Watson value (with 2 variables and 90 observations) of 1.70. That means the hypothesis of no serial correlation cannot be rejected. There is no information on whether the regression exhibits heteroskedasticity.

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