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

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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.

土豆妮

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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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.

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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 Durbin-Watson statistic.

C) The Hansen method.

土豆妮

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 Durbin-Watson statistic.

C) The Hansen method.

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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.

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

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

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

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

土豆妮

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

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

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

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

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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.

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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 heteroskedasticity and multicollinearity, but the serial correlation problem will be solved.

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

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

土豆妮

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 heteroskedasticity and multicollinearity, but the serial correlation problem will be solved.

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

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

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The Hansen procedure simultaneously solves for heteroskedasticity and serial correlation.

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.