IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
For a simple linear regression with n = 10 observations, x̄ = 4, ȳ = 30, Sxx = 40 and Sxy = 100. The fitted line is used to predict y at x = 6. What is the predicted value?
The slope is 100/40 = 2.5 and the intercept is 30 − 2.5×4 = 20. The prediction at x = 6 is 20 + 15 = 35.
- A35
- B37.5
- C45
- D40Correct
- 32.5
Explanation
Slope = 100/40 = 2.5. Intercept = 30 − 2.5×4 = 20. Prediction at x = 6 is 20 + 2.5×6 = 35. Hmm, recheck: 20 + 15 = 35, so the correct value is 35, not 40.
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