FRM Part I · FRM Exam Part I · Linear Regression
A risk analyst estimates a linear regression by OLS and later finds that the error variance changes with the level of an explanatory variable (heteroskedasticity). Which statement best describes the consequence for the OLS results?
Under heteroskedasticity OLS coefficients stay unbiased and consistent, but the conventional standard errors are wrong. Hypothesis tests and confidence intervals therefore become unreliable. Robust standard errors can correct inference, while the coefficient estimates themselves do not need to change.
- AThe slope estimates become biased and inconsistent
- BThe slope estimates remain unbiased, but the conventional standard errors are unreliable, so t-tests may misleadCorrect
- CThe R-squared becomes negative and the model cannot be interpreted
- DThe mean of the residuals is no longer zero
Explanation
Heteroskedasticity does not violate the conditions needed for unbiasedness or consistency of OLS coefficients. It does invalidate the usual formula for standard errors, so t-statistics and confidence intervals are unreliable. Robust (White) standard errors are a common fix. Residuals still average zero when an intercept is included.
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