IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
In a simple linear regression with n = 27 observations, the total sum of squares is 500 and the regression sum of squares is 300. What is the F statistic for testing that the slope is zero?
The F statistic is 37.5. The residual sum of squares is 200 on 25 degrees of freedom, giving a mean square of 8, while the regression mean square is 300 on one degree of freedom. Their ratio, 300 over 8, is 37.5.
- A1.50
- B37.5Correct
- C0.60
- D25.0
- 7.50
Explanation
Residual SS = 500 - 300 = 200 with 25 degrees of freedom, so residual mean square = 8. Regression mean square = 300/1 = 300. F = 300/8 = 37.5. Using 200 in the denominator without dividing by 25 would give 1.5.
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