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

An analyst regresses a fund's excess return on four factors using 64 monthly observations. The unrestricted model has R-squared of 0.40. She tests the joint null that two of the slope coefficients are zero. The restricted model, with those two variables removed, has R-squared of 0.34. What is the F-statistic for this joint test?

The F-statistic is about 2.95. It is the gain in R-squared per restriction, 0.06 divided by 2, over the unexplained share per residual degree of freedom, 0.60 divided by 59. Dividing by the two restrictions and using 59 residual degrees of freedom are both essential.

  1. A2.95Correct
  2. B5.90
  3. C3.00
  4. D1.48

Explanation

Unrestricted model: k = 4, so residual df = 64 - 4 - 1 = 59. F = [(0.40 - 0.34)/2] / [(1 - 0.40)/59] = 0.03 / 0.010169 = 2.95. Omitting the division by q gives 5.90. Using n - k = 60 as the denominator df gives 3.00, which is wrong because the intercept uses a degree of freedom.

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