12: Multiple Regression and Issues in Regression Ana style, center, course, multiple, 2010

土豆妮

Session 3: Quantitative Methods: Quantitative
Methods for Valuation
Reading 12: Multiple Regression and Issues in Regression Analysis

LOS g, (Part 2): Discuss the effects of serial correlation on statistical inference.

 

 

 

During the course of a multiple regression analysis, an analyst has observed several items that she believes may render incorrect conclusions. For example, the coefficient standard errors are too small, although the estimated coefficients are accurate. She believes that these small standard error terms will result in the computed t-statistics being too big, resulting in too many Type I errors. The analyst has most likely observed which of the following assumption violations in her regression analysis?

A) Multicollinearity.

B) Positive serial correlation.

C) Homoskedasticity.

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土豆妮

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.

土豆妮

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.

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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.

土豆妮

Which of the following is least accurate regarding the Durbin-Watson (DW) test statistic?

A) If the residuals have positive serial correlation, the DW statistic will be greater than 2.

B) If the residuals have negative serial correlation, the DW statistic will be greater than 2.

C) In tests of serial correlation using the DW statistic, there is a rejection region, a region over which the test can fail to reject the null, and an inconclusive region.

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A value of 2 indicates no correlation, a value greater than 2 indicates negative correlation, and a value less than 2 indicates a positive correlation. There is a range of values in which the DW test is inconclusive.

土豆妮

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

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

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

土豆妮

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

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

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

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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.

土豆妮

Which of the following is least likely a method of detecting serial correlations?

A) The Durbin-Watson test.

B) The Breusch-Pagan test.

C) A scatter plot of the residuals over time.

土豆妮

Which of the following is least likely a method of detecting serial correlations?

A) The Durbin-Watson test.

B) The Breusch-Pagan test.

C) A scatter plot of the residuals over time.

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The Breusch-Pagan test is a test of the heteroskedasticity and not of serial correlation.