IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
A multiple regression with k = 3 explanatory variables is fitted to n = 24 observations. R² = 0.80. What is the adjusted R²?
Adjusted R² is 1 - (1 - 0.80) × 23/20 = 1 - 0.23 = 0.77. The penalty uses n-1 over n-k-1 degrees of freedom, so the adjusted value is below the unadjusted 0.80.
- A0.770Correct
- B0.760
- C0.790
- D0.700
- 0.800
Explanation
Adjusted R² = 1 - (1-R²)(n-1)/(n-k-1) = 1 - 0.2 × 23/20 = 1 - 0.23 = 0.77. Using n-k instead of n-k-1 gives 0.2×23/21 = 0.219, so 0.781, which is not an option; 0.80 ignores the penalty.
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