IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
A model with an intercept and two explanatory variables is fitted to n = 24 observations by least squares. The residual sum of squares is 90 and the total sum of squares is 400. What is the adjusted R², to 3 decimal places?
Adjusted R² is 0.753. It equals 1 minus (RSS/21)/(TSS/23) = 1 − 4.2857/17.3913, using 21 residual and 23 total degrees of freedom. The unadjusted R² of 0.775 overstates fit because it ignores the number of parameters.
- A0.775
- B0.753Correct
- C0.761
- D0.742
- 0.801
Explanation
R² = 1 − 90/400 = 0.775. Residual degrees of freedom = 24 − 3 = 21 and total df = 23. Adjusted R² = 1 − (90/21)/(400/23) = 1 − 4.2857/17.3913 = 1 − 0.24643 = 0.75357, i.e. 0.753. Option A is the unadjusted R².
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