IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
In a simple linear regression fitted to 12 observations, the total sum of squares is 500 and the residual sum of squares is 125. What is the coefficient of determination R²?
R² equals one minus RSS over TSS, which is 1 - 125/500 = 0.75. The regression explains 75 percent of the total variation. The figure 0.25 is the unexplained proportion, not R².
- A0.25
- B0.50
- C0.75Correct
- D0.80
- 0.90
Explanation
Regression SS = 500 - 125 = 375. R² = 375/500 = 0.75. The value 0.25 is RSS/TSS, which is the proportion unexplained, so it is the wrong ratio.
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