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

An analyst fits a model with 4 explanatory variables and an intercept on 50 observations. The sum of squared residuals is 90 for the full model. She imposes 2 linear restrictions on the coefficients, and the restricted model's sum of squared residuals is 120. What is the F-statistic for the joint test of the restrictions?

The F-statistic is 7.50. The increase in squared residuals from the restrictions is 30, which is 15 per restriction across 2 restrictions. The unrestricted error variance estimate is 90 divided by 45 degrees of freedom, which is 2. Dividing 15 by 2 gives 7.50.

  1. A7.50Correct
  2. B8.33
  3. C15.00
  4. D3.75

Explanation

The unrestricted model has 5 parameters, so the residual df is 50−5=45. F = ((120−90)/2) / (90/45) = 15/2 = 7.50. Using 50 as the denominator df gives 8.33, which is wrong. Omitting the division by q gives a numerator of 15 over 2 only if the denominator is mishandled, and 3.75 divides by q twice.

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