FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
An analyst regresses a stock's return on two factors, X1 and X2. An auxiliary regression of X1 on X2 (with an intercept) gives an R-squared of 0.80. What is the variance inflation factor (VIF) for X1?
The VIF is 5.00. It is computed as one divided by one minus the auxiliary regression R-squared, so 1/(1 − 0.80) = 5. This means the variance of the X1 coefficient estimate is five times larger than it would be if X1 were uncorrelated with X2.
- A1.25
- B4.00
- C5.00Correct
- D10.00
Explanation
VIF = 1/(1 - R²) where R² comes from regressing X1 on the other regressors. VIF = 1/(1 - 0.80) = 1/0.20 = 5.00. The value 1.25 results from using 1/0.80, the wrong base, and 4.00 from using 0.80/0.20.
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