FRM Part I · FRM Exam Part I · Regression Diagnostics
A multiple regression with 5 slope coefficients and 56 observations is tested for joint significance of all slopes. The explained sum of squares is 300 and the residual sum of squares is 250. What is the F-statistic?
The F-statistic is the explained sum of squares per regressor divided by the residual sum of squares per residual degree of freedom: (300/5)/(250/50) = 60/5 = 12.00. This is a high value, indicating the slopes are jointly significant.
- A6.00
- B12.00Correct
- C1.20
- D10.00
Explanation
F = (ESS/k)/(RSS/(n-k-1)). With k = 5 and n-k-1 = 50: (300/5)/(250/50) = 60/5 = 12.00. Using 6.00 comes from dividing by the wrong degrees of freedom for RSS; 1.20 is the raw ratio ESS/RSS.
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