FRM Part I · FRM Exam Part I · Regression Diagnostics
After fitting a multiple regression, an analyst finds that a plot of residuals against a regressor shows a systematic U-shaped pattern. Which action best addresses this diagnostic finding?
The best action is to add a nonlinear term, such as the squared regressor, because a U-shaped residual pattern shows functional form misspecification. Robust standard errors, dropping collinear variables, or collecting more data do not correct a missing curvature in the relationship.
- AAdd a nonlinear term such as the square of the regressor to capture the curvatureCorrect
- BReplace the standard errors with Newey-West standard errors only
- CDrop the regressor with the highest variance inflation factor
- DIncrease the sample size without changing the specification
Explanation
A U-shaped pattern in residuals versus a regressor indicates a misspecified functional form: the relationship is nonlinear. Adding a quadratic term or transforming the variable addresses this. Newey-West fixes standard errors for autocorrelation and heteroskedasticity but not curvature. Dropping a collinear variable addresses multicollinearity, and more data does not remove misspecification bias.
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