Financial Risk Manager Part 1
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A financial risk analyst has been investigating a linear regression model that explains the return of a stock based on a set of macroeconomic variables. Upon analyzing the residuals, the analyst suspects the presence of heteroskedasticity in the model. Which of the following consequences of heteroskedasticity should the analyst be most concerned about?
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A
Bias in the regression coefficients.
B
Inaccurate goodness-of-fit measures.
C
Biased standard errors of the coefficients.
D
Violation of the normality assumption.
Explanation:
Explanation
Heteroskedasticity in a regression model refers to a situation where the variability of the error terms is not constant across all levels of the independent variables. This inconsistency in the error variance can lead to biased standard errors of the coefficients. The standard errors are crucial in determining the significance of the regression coefficients. If these are biased, it can lead to incorrect inferences about the significance of the regression coefficients. This can further result in misleading results from t-tests and F-tests that are based on these standard errors. Therefore, the most significant concern with heteroskedasticity is the potential bias it introduces to the standard errors of the coefficients, which can compromise the reliability of the statistical inferences drawn from the model.
Why Other Options Are Incorrect:
Choice A is incorrect: Heteroskedasticity does not cause bias in the regression coefficients. The presence of heteroskedasticity does not affect the unbiasedness property of the OLS estimators, meaning that even if heteroskedasticity is present, on average, we can expect our estimates to be correct.
Choice B is incorrect: While heteroskedasticity may impact certain aspects of a regression model's performance, it does not directly lead to inaccurate goodness-of-fit measures. Goodness-of-fit measures like R-squared are unaffected by heteroskedasticity.
Choice D is incorrect: Heteroskedasticity refers to a situation where the variability of a variable is unequal across different ranges of values of another variable with which it has been paired for analysis. It doesn't necessarily imply violation of normality assumption in regression analysis.
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