Q1. 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)   Positive serial correlation.

B)   Multicollinearity.

C)   Homoskedasticity.

Q2. Alex Wade, CFA, is analyzing the result of a regression analysis comparing the performance of gold stocks versus a broad equity market index. Wade believes that serial correlation may be present, and in order to prove his theory, should use which of the following methods to detect its presence?

A)   The Breusch-Pagan test.

B)   The Hansen method.

C)   The Durbin-Watson statistic.

Q3. Which of the following statements regarding serial correlation that might be encountered in regression analysis is least accurate?

A)   Serial correlation occurs least often with time series data.

B)   Negative serial correlation causes a failure to reject the null hypothesis when it is actually false.

C)   Positive serial correlation typically has the same effect as heteroskedasticity.

Q4. An analyst is estimating whether company sales is related to three economic variables. The regression exhibits conditional heteroskedasticity, serial correlation, and multicollinearity. The analyst uses Hansen’s procedure to adjust for the standard errors. Which of the following is most accurate? The:

A)   regression will still exhibit multicollinearity, but the heteroskedasticity and serial correlation problems will be solved.

B)   regression will still exhibit heteroskedasticity and multicollinearity, but the serial correlation problem will be solved.

C)   regression will still exhibit serial correlation and multicollinearity, but the heteroskedasticity problem will be solved.

Q5. 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.

Q6. Which of the following is least accurate regarding the Durbin-Watson (DW) test statistic?

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

B)     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.

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

答案和详解如下：

Q1. 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)   Positive serial correlation.

B)   Multicollinearity.

C)   Homoskedasticity.

Correct answer is A)

Positive serial correlation is the condition where a positive regression error in one time period increases the likelihood of having a positive regression error in the next time period. The residual terms are correlated with one another, leading to coefficient error terms that are too small.

Q2. Alex Wade, CFA, is analyzing the result of a regression analysis comparing the performance of gold stocks versus a broad equity market index. Wade believes that serial correlation may be present, and in order to prove his theory, should use which of the following methods to detect its presence?

A)   The Breusch-Pagan test.

B)   The Hansen method.

C)   The Durbin-Watson statistic.

Correct answer is C)

The Durbin-Watson statistic is the most commonly used method for the detection of serial correlation, although residual plots can also be utilized. For a large sample size, DW ≈ 2(1-r), where r is the correlation coefficient between residuals from one period and those from a previous period. The DW statistic is then compared to a table of DW statistics that gives upper and lower critical values for various sample sizes, levels of significance and numbers of degrees of freedom to detect the presence or absence of serial correlation.

Q3. Which of the following statements regarding serial correlation that might be encountered in regression analysis is least accurate?

A)   Serial correlation occurs least often with time series data.

B)   Negative serial correlation causes a failure to reject the null hypothesis when it is actually false.

C)   Positive serial correlation typically has the same effect as heteroskedasticity.

Correct answer is A)

Serial correlation, which is sometimes referred to as autocorrelation, occurs when the residual terms are correlated with one another, and is most frequently encountered with time series data.

Q4. An analyst is estimating whether company sales is related to three economic variables. The regression exhibits conditional heteroskedasticity, serial correlation, and multicollinearity. The analyst uses Hansen’s procedure to adjust for the standard errors. Which of the following is most accurate? The:

A)   regression will still exhibit multicollinearity, but the heteroskedasticity and serial correlation problems will be solved.

B)   regression will still exhibit heteroskedasticity and multicollinearity, but the serial correlation problem will be solved.

C)   regression will still exhibit serial correlation and multicollinearity, but the heteroskedasticity problem will be solved.

Correct answer is A)

The Hansen procedure simultaneously solves for heteroskedasticity and serial correlation.

Q5. 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.

Correct answer is B)         

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

Q6. Which of the following is least accurate regarding the Durbin-Watson (DW) test statistic?

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

B)     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.

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

Correct answer is C)

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.

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