FRM Part I · FRM Exam Part I · Regression Diagnostics
A risk manager adds several irrelevant explanatory variables to a correctly specified regression that already includes all relevant variables. Which outcome is most consistent with the effect of including these extraneous variables?
Estimates on relevant variables stay unbiased, but their variances tend to increase. Extraneous regressors consume degrees of freedom and may be correlated with relevant variables, reducing precision. They do not create omitted variable bias, and R-squared cannot decrease when variables are added.
- ACoefficient estimates on relevant variables remain unbiased but their variances tend to riseCorrect
- BCoefficient estimates on relevant variables become biased upward
- CCoefficient estimates become inconsistent because of omitted variable bias
- DThe R-squared decreases mechanically
Explanation
Including irrelevant variables does not cause bias in the relevant coefficients, but it uses up degrees of freedom and, if the extras are correlated with relevant regressors, raises estimator variance. R-squared never falls when variables are added.
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