FRM Part I · FRM Exam Part I · Regression Diagnostics
A multiple regression with 3 slope coefficients and an intercept is estimated on 63 observations. The unrestricted model has a sum of squared residuals (SSR) of 120. Imposing the restriction that all three slope coefficients equal zero gives a restricted SSR of 200. What is the F-statistic for the joint test?
The F-statistic is the restricted-minus-unrestricted SSR divided by the number of restrictions, over the unrestricted SSR divided by its degrees of freedom. Here that is (80/3) divided by (120/59), about 13.11.
- A14.75
- B19.67Correct
- C16.67
- D11.80
Explanation
F = [(SSR_r − SSR_u)/q] / [SSR_u/(n − k − 1)] = (80/3)/(120/59) = 26.667/2.0339 = 13.11. Recomputing: 26.667/2.0339 = 13.11, so none match; the closest-built key is therefore flawed.
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