CFA Level II ExamQuantitative MethodsMedium
A researcher is using a simple linear regression to model stock returns (dependent variable) based on the market's daily volume (independent variable). The researcher plots the residuals against the predicted values and observes a distinct fan-shaped pattern, with the spread of the residuals increasing as the predicted returns increase. What is the primary consequence of this observation for the OLS regression results?
- AThe model will suffer from multicollinearity.
- BThe standard errors of the coefficients will be unreliable.
- CThe R-squared value will be artificially inflated.
- DThe coefficient estimates will be biased.
Show answer & explanationAnswer & explanation
Correct answer: B. The standard errors of the coefficients will be unreliable.
A fan-shaped pattern in residuals indicates heteroskedasticity, where the variance of the error terms is not constant. While OLS coefficient estimates remain unbiased and consistent under heteroskedasticity, their standard errors become incorrect, leading to unreliable hypothesis tests and confidence intervals.
Why the other options are wrong
- A. Multicollinearity is a problem of high correlation between independent variables, not related to the pattern of residuals against predicted values in a simple linear regression.
- C. Heteroskedasticity does not directly or systematically inflate the R-squared value; it primarily affects the reliability of inference.
- D. Heteroskedasticity does not cause OLS coefficient estimates to be biased; they remain unbiased and consistent.
Consequences of Heteroskedasticity
Heteroskedasticity is when the variance of the error term in a regression model is not constant across observations. Its main consequence is unreliable standard errors.
- OLS coefficient estimates remain unbiased and consistent.
- Standard errors of coefficients are incorrect (usually underestimated).
- Hypothesis tests (t-tests, F-tests) are invalid.
- Confidence intervals are unreliable.
Memory trick: Uneven errors make our 'errors' in judgment.