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FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables

In a multiple regression, the standard error of a slope coefficient would be 0.040 if its regressor were uncorrelated with the other regressors. The regressor's auxiliary regression on the other explanatory variables has an R-squared of 0.84. What is the approximate standard error of the coefficient in the actual regression, holding other factors constant?

The standard error is about 0.100. The VIF is 1/(1 - 0.84) = 6.25, and standard errors rise by the square root of the VIF, which is 2.5. Multiplying 0.040 by 2.5 gives 0.100.

  1. A0.100Correct
  2. B0.250
  3. C0.160
  4. D0.064

Explanation

VIF = 1/(1 - 0.84) = 6.25. Standard error scales with the square root of VIF: sqrt(6.25) = 2.5, so 0.040 x 2.5 = 0.100. Using VIF directly gives 0.250 (the mistake of not taking the square root). 0.160 uses 0.040/0.25 incorrectly, and 0.064 uses 1/(1-0.84) wrongly as 1.6.

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