IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
A regression with an intercept and 3 explanatory variables is fitted to n = 24 observations. The total sum of squares is 480 and the residual sum of squares is 120. What is the F statistic for testing that all three slope coefficients are zero?
The regression sum of squares is 360 on 3 degrees of freedom, giving 120. The residual sum of squares of 120 on 20 degrees of freedom gives 6. The F statistic is 120 divided by 6, which equals 20.
- A20Correct
- B6.67
- C10
- D15
- 40
Explanation
Regression SS = 480 - 120 = 360, with 3 degrees of freedom, so mean square = 120. Residual df = 24 - 4 = 20, so residual mean square = 6. F = 120/6 = 20. Using 24 - 3 = 21 or omitting the df division gives wrong values such as 3.
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