FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
In a two-regressor model, the standard error of the slope on X1 is 0.30 when X1 and X2 are correlated with an auxiliary R-squared of 0.75. Holding everything else constant, what would the standard error be if X1 were uncorrelated with X2?
The standard error would be 0.15. The VIF is 1/(1 − 0.75) = 4, which inflates variance fourfold and the standard error by its square root, 2. Dividing 0.30 by 2 gives 0.15. Dividing by 4 would wrongly treat VIF as applying to standard error.
- A0.075
- B0.150Correct
- C0.600
- D1.200
Explanation
Variance is inflated by VIF = 1/(1 - 0.75) = 4. Standard error is inflated by the square root of VIF, which is 2. Removing collinearity gives 0.30/2 = 0.15. Option 0.075 divides by 4, forgetting the square root.
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