FRM Part I · FRM Exam Part I · Regression Diagnostics
An analyst regresses a stock's return on three factors. Auxiliary regressions of each factor on the other two give R-squared values of 0.50 for Factor 1, 0.80 for Factor 2, and 0.20 for Factor 3. Which factor has the largest variance inflation factor, and what is its value?
Factor 2 has the largest VIF, equal to 5.0. The VIF is 1 divided by (1 minus the auxiliary R-squared), so 1/(1-0.80) = 5. Factors 1 and 3 have VIFs of 2.0 and 1.25, reflecting lower collinearity with the other regressors.
- AFactor 1, VIF = 2.0
- BFactor 2, VIF = 5.0Correct
- CFactor 2, VIF = 4.0
- DFactor 3, VIF = 1.25
Explanation
VIF = 1/(1 - R²). Factor 1: 1/0.5 = 2.0. Factor 2: 1/0.2 = 5.0. Factor 3: 1/0.8 = 1.25. The largest is Factor 2 at 5.0. The value 4.0 would come from wrongly using 1/(1-0.75) or similar, and 1.25 is Factor 3's VIF.
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