IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
A simple linear regression with an intercept is fitted to n = 12 observations. The residual sum of squares is 90 and the leverage of one observation is h = 0.19. Its raw residual is 2.7. What is its internally studentised residual?
The internally studentised residual is 1.00. The estimated variance is 90/10 = 9, so sigma-hat is 3, and dividing the residual 2.7 by 3 times the square root of (1 - 0.19) = 0.9 gives 2.7/2.7 = 1.
- A0.30
- B0.90
- C1.00
- D1.11Correct
- 1.23
Explanation
Sigma-hat^2 = 90/(12-2) = 9, so sigma-hat = 3. The standardised residual is 2.7/(3*sqrt(1-0.19)) = 2.7/(3*0.9) = 1.0. Check: sqrt(0.81)=0.9, so the result is 1.0. Ignoring leverage gives 0.9, which is a distractor.
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