FRM Part I · FRM Exam Part I · Regression Diagnostics
A risk analyst adds three irrelevant variables, uncorrelated with the dependent variable in the population, to a correct regression model that already includes all relevant regressors. Which is the most accurate consequence?
Coefficient estimates stay unbiased, but their variances tend to rise and adjusted R² may fall. Irrelevant variables use degrees of freedom and may be correlated with relevant regressors, which reduces precision without introducing bias. Plain R² never decreases when variables are added.
- ACoefficient estimates become biased, and the standard errors fall
- BCoefficient estimates remain unbiased, but their variances tend to increase and adjusted R² may fallCorrect
- CCoefficient estimates remain unbiased and R² is guaranteed to fall
- DThe residuals become autocorrelated, invalidating the t-tests
Explanation
Including irrelevant variables does not cause bias, since the true coefficients on them are zero. It does use up degrees of freedom and, if they are correlated with the relevant regressors, inflates variances. R² never falls when variables are added, while adjusted R² can fall.
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.
More Regression Diagnostics questions
- In a cross-sectional regression of household food spending on household income, the dispersion of the residuals grows steadily as income ris…
- A risk manager estimates a time-series regression by OLS and finds the residuals are positively autocorrelated, while the regressors are not…
- After fitting a multiple regression, an analyst finds that a plot of residuals against a regressor shows a systematic U-shaped pattern. Whic…
- In a multiple regression of a fund's excess return on several factor returns, an analyst finds that the R-squared is high and the F-test is …
- A risk analyst is concerned about severe multicollinearity between two regressors, X1 and X2, in a model used to forecast portfolio losses. …
- A regression of y on x gives a slope of 2.00 with a conventional standard error of 0.50. After applying heteroskedasticity-robust (White) st…