FRM Part I · FRM Exam Part I · Linear Regression
A regression with 5 explanatory variables and an intercept is estimated on 64 observations, giving a sum of squared residuals (SSR) of 120. Imposing 3 linear restrictions raises the SSR to 150. What is the F-statistic for the joint test of the restrictions?
The F-statistic is about 4.83. It is the increase in SSR of 30 divided by the 3 restrictions, giving 10, over the unrestricted SSR divided by 58 degrees of freedom, which is 2.069. The denominator uses the unrestricted model.
- A4.83Correct
- B14.50
- C3.87
- D4.92
Explanation
Unrestricted degrees of freedom = 64 − 5 − 1 = 58. F = [(150 − 120)/3] / (120/58) = 10/2.069 = 4.83. Omitting the division by 3 gives 14.50. Using the restricted SSR in the denominator gives 3.87.
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