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IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models

A simple linear regression with n = 14 has residual standard error s = 4, mean x of 10, and Sxx = 200. At x0 = 14 the fitted value is 50. What is the standard error of the estimated MEAN response at x0 (not a new observation)?

The standard error of the mean response is the square root of 16 times (1/14 plus 16/200), which is about 1.56. It combines uncertainty in the intercept and slope, with the distance of x0 from the mean inflating it.

  1. A4.00
  2. B1.13Correct
  3. C1.07
  4. D4.16
  5. 1.60

Explanation

Var = s^2[1/n + (x0 - xbar)^2/Sxx] = 16[1/14 + 16/200] = 16[0.071429 + 0.08] = 16 x 0.151429 = 2.4229. SE = 1.5565. This is about 1.56, so none of the options matches exactly; the closest is 1.60.

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