IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
In a simple linear regression fitted to 12 observations, the total sum of squares is 480 and the regression (explained) sum of squares is 360. What is the coefficient of determination R²?
R² equals the regression sum of squares divided by the total sum of squares, 360/480 = 0.75. So 75% of the variation in the response is explained by the fitted line; 0.25 would be the unexplained proportion.
- A0.25
- B0.50
- C0.67
- D0.75Correct
- 1.33
Explanation
R² = SSR/SST = 360/480 = 0.75. The value 0.25 is the residual share (SSE/SST = 120/480), which uses the wrong numerator. A ratio above 1 such as 1.33 comes from inverting the fraction.
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