IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
A regression through five points gives residual sum of squares 18 for the model y = α + βx + ε with errors N(0, σ²). What is the unbiased estimate of σ²?
The unbiased variance estimate is the residual sum of squares divided by n − 2, since two parameters are fitted. That is 18 divided by 3, which equals 6.0.
- A3.6
- B6.0Correct
- C4.5
- D9.0
- 18.0
Explanation
Two parameters are estimated, so the degrees of freedom are n − 2 = 3. The unbiased estimate is 18/3 = 6.0. Dividing by n gives 3.6, and dividing by n − 1 gives 4.5, both biased.
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