Q1. An analyst is trying to estimate the beta for a fund. The analyst estimates a regression equation in which the fund returns are the dependent variable and the Wilshire 5000 is the independent variable, using monthly data over the past five years. The analyst finds that the correlation between the square of the residuals of the regression and the Wilshire 5000 is 0.2. Which of the following is most accurate, assuming a 0.05 level of significance? There is:

A)   no evidence that there is conditional heteroskedasticity or serial correlation in the regression equation.

B)   evidence of serial correlation but not conditional heteroskedasticity in the regression equation.

C)   evidence of conditional heteroskedasticity but not serial correlation in the regression equation.

Q2. Which of the following is least likely a method used to detect heteroskedasticity?

A)     Test of the variances.

B)     Durbin-Watson test.

C)     Breusch-Pagan test.

Q3. Consider the following graph of residuals and the regression line from a time-series regression:

These residuals exhibit the regression problem of:

A)    autocorrelation.

B)    homoskedasticity.

C)    heteroskedasticity.

Q4. Which of the following statements regarding heteroskedasticity is FALSE?

A)     Multicollinearity is a potential problem only in multiple regressions, not simple regressions.

B)     Heteroskedasticity only occurs in cross-sectional regressions.

C)     The presence of heteroskedastic error terms results in a variance of the residuals that is too large.

Q5. Which of the following statements regarding heteroskedasticity is FALSE?

A)     Heteroskedasticity results in an estimated variance that is too large and, therefore, affects statistical inference.

B)     The assumption of linear regression is that the residuals are heteroskedastic.

C)     Heteroskedasticity may occur in cross-section or time-series analyses.

答案和详解如下：

Q1. An analyst is trying to estimate the beta for a fund. The analyst estimates a regression equation in which the fund returns are the dependent variable and the Wilshire 5000 is the independent variable, using monthly data over the past five years. The analyst finds that the correlation between the square of the residuals of the regression and the Wilshire 5000 is 0.2. Which of the following is most accurate, assuming a 0.05 level of significance? There is:

A)   no evidence that there is conditional heteroskedasticity or serial correlation in the regression equation.

B)   evidence of serial correlation but not conditional heteroskedasticity in the regression equation.

C)   evidence of conditional heteroskedasticity but not serial correlation in the regression equation.

Correct answer is A)

The test for conditional heteroskedasticity involves regressing the square of the residuals on the independent variables of the regression and creating a test statistic that is n × R², where n is the number of observations and R² is from the squared-residual regression. The test statistic is distributed with a chi-squared distribution with the number of degrees of freedom equal to the number of independent variables. For a single variable, the R² will be equal to the square of the correlation; so in this case, the test statistic is 60 × 0.2² = 2.4, which is less than the chi-squared value (with one degree of freedom) of 3.84 for a p-value of 0.05. There is no indication about serial correlation.

Q2. Which of the following is least likely a method used to detect heteroskedasticity?

A)     Test of the variances.

B)     Durbin-Watson test.

C)     Breusch-Pagan test.

Correct answer is B)

The Durbin-Watson test is used to detect serial correlation. The Breusch-Pagan test is used to detect heteroskedasticity.

Q3. Consider the following graph of residuals and the regression line from a time-series regression:

These residuals exhibit the regression problem of:

A)    autocorrelation.

B)    homoskedasticity.

C)    heteroskedasticity.

Correct answer is C)

The residuals appear to be from two different distributions over time; in the earlier periods, the model fits rather well compared to the later periods.

Q4. Which of the following statements regarding heteroskedasticity is FALSE?

A)     Multicollinearity is a potential problem only in multiple regressions, not simple regressions.

B)     Heteroskedasticity only occurs in cross-sectional regressions.

C)     The presence of heteroskedastic error terms results in a variance of the residuals that is too large.

Correct answer is B)

If there are shifting regimes in a time-series (e.g., change in regulation, economic environment), it is possible to have heteroskedasticity in a time-series.

Q5. Which of the following statements regarding heteroskedasticity is FALSE?

A)     Heteroskedasticity results in an estimated variance that is too large and, therefore, affects statistical inference.

B)     The assumption of linear regression is that the residuals are heteroskedastic.

C)     Heteroskedasticity may occur in cross-section or time-series analyses.

Correct answer is B)

The assumption of regression is that the residuals are homoskedastic (i.e., the residuals are drawn from the same distribution).

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