FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
In a multiple regression, a risk manager tests a single linear restriction, namely that one slope coefficient equals zero. The t-statistic for that coefficient is −2.40. What is the F-statistic for the same hypothesis test?
The F-statistic is 5.76. When only one restriction is tested, F with 1 numerator degree of freedom equals the square of the t-statistic. Squaring −2.40 gives 5.76, so the sign disappears and the two tests give identical conclusions.
- A5.76Correct
- B2.40
- C1.55
- D11.52
Explanation
With a single restriction, the F-statistic equals the square of the t-statistic: (−2.40)² = 5.76. Option 2.40 forgets to square. Option 1.55 is the square root of 2.40. Option 11.52 doubles the squared value, which has no basis.
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