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

A model has three regressors. Regressing X1 on X2 and X3 gives R-squared 0.90; regressing X2 on X1 and X3 gives 0.50; regressing X3 on X1 and X2 gives 0.75. The estimated slope on X1 is 0.60 with a standard error of 0.45 in the full model. Ignoring other effects, if the collinearity of X1 with the others were eliminated, approximately what would the t-statistic on X1 become (standard error scaled by the relevant VIF)?

The t-statistic would be about 4.22. X1's VIF is 1/(1 − 0.90) = 10, so removing collinearity shrinks its standard error by the square root of 10, from 0.45 to about 0.142. Dividing the 0.60 coefficient by 0.142 gives roughly 4.22.

  1. A1.33
  2. B4.22Correct
  3. C13.3
  4. D0.42

Explanation

VIF for X1 = 1/(1 - 0.90) = 10. The standard error would shrink by sqrt(10) = 3.162, to 0.45/3.162 = 0.1423. The new t = 0.60/0.1423 = 4.22. The current t is 1.33, which is option 1 and ignores the adjustment. 13.3 uses VIF without the square root.

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