Skip to content

FRM Part I · FRM Exam Part I · Regression Diagnostics

An analyst fits a linear regression of monthly fund returns on a market factor and plots the residuals against the fitted values. The plot shows a clear funnel shape, with residuals becoming more widely dispersed as fitted values increase. Which conclusion is most appropriate?

A funnel-shaped residual plot signals heteroskedasticity, meaning residual variance changes with the fitted values. OLS coefficients stay unbiased, but conventional standard errors are wrong, making t-tests unreliable. Robust standard errors are the usual remedy. Multicollinearity and serial correlation are diagnosed differently.

  1. AThe residuals suggest heteroskedasticity, so the usual OLS standard errors are unreliableCorrect
  2. BThe residuals suggest multicollinearity, so the coefficient estimates are biased
  3. CThe residuals suggest serial correlation, so the R-squared is overstated
  4. DThe residuals suggest the model is well specified because the mean of the residuals is zero

Explanation

A funnel-shaped residual plot indicates that the residual variance changes with the fitted values, which is heteroskedasticity. OLS coefficients remain unbiased, but the conventional standard errors are incorrect, so t-tests are unreliable. Multicollinearity is detected from correlations among regressors, not from a funnel in residuals, and OLS residuals always average zero when an intercept is included.

Did you get it right without looking?

One question tells you little. A timed set on Regression Diagnostics shows your real accuracy, how long you take and where you lose marks.

Practise Regression DiagnosticsFree diagnostic mock

More Regression Diagnostics questions