IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
For 10 observations, Sxx = 40, Sxy = 90 and Syy = 250, where S denotes sums of squares about the means. The mean of x is 5 and the mean of y is 30. What is the fitted value of y at x = 7?
The fitted value is 34.5. The slope is 90/40 = 2.25, and the line passes through the means (5, 30), so at x = 7 the prediction is 30 + 2.25 times 2, which equals 34.5.
- A34.5
- B39.0Correct
- C43.5
- D47.0
- 30.0
Explanation
The slope is b = Sxy/Sxx = 90/40 = 2.25. The intercept is a = 30 - 2.25*5 = 18.75. The fitted value at x = 7 is 18.75 + 15.75 = 34.5. Check using the mean: 30 + 2.25*(7-5) = 34.5. So the key is 34.5, option A, not B.
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