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

A risk analyst estimates a model of portfolio returns on market and size factors using 24 monthly observations (intercept plus two slopes). The unrestricted regression has a sum of squared residuals (SSR) of 12.0. Imposing the joint restriction that both slope coefficients equal zero gives a restricted SSR of 30.0. What is the F-statistic for this restriction, and what is the conclusion at a 5% critical value of 3.47?

F = ((30 - 12)/2)/(12/21) = 9/0.5714 = 15.75. This exceeds the 5% critical value of 3.47, so the null that both slopes are zero is rejected.

  1. AF = 15.75; reject the nullCorrect
  2. BF = 31.50; reject the null
  3. CF = 7.88; reject the null
  4. DF = 1.50; fail to reject the null

Explanation

F = [(SSR_r - SSR_u)/q]/[SSR_u/(n-k-1)], with q = 2 and n-k-1 = 24-2-1 = 21. Numerator = 18/2 = 9; denominator = 12/21 = 0.5714. F = 15.75, which exceeds 3.47, so reject. Forgetting to divide by q gives 31.5; omitting the denominator's df division gives other wrong values.

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