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FRM Part I · FRM Exam Part I · Regression Diagnostics

A researcher adds an irrelevant variable, which has a true coefficient of zero and is correlated with an existing regressor, to a correct regression model. Which outcome is most likely?

The estimates remain unbiased, but their standard errors tend to rise. An irrelevant variable correlated with existing regressors adds multicollinearity and so lowers precision. It does not introduce bias, and R-squared cannot decrease when a regressor is added.

  1. AThe OLS estimates become biased and inconsistent
  2. BThe estimates remain unbiased but their standard errors tend to increaseCorrect
  3. CThe R-squared decreases mechanically
  4. DThe adjusted R-squared must always increase

Explanation

Including an irrelevant variable does not bias the OLS coefficients, but correlation with other regressors inflates the variance of the estimates, reducing efficiency. Unadjusted R-squared never falls when a variable is added. Adjusted R-squared typically falls for a useless variable.

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