In a multiple regression based on 30 observations, the following information is provided:
= 469 - 2x1 + 6x2 - 0.5x3 and se = 16. Also, when x1 = 30, x2 = 10, and x3 = 65 se(
0) = 37.a. Construct a 90% confidence interval for E(y) if x1 = 30, x2 = 10, and x3 = 65.b. Construct a 90% prediction interval for y if x1 = 30, x2 = 10, and x3 = 65.c. Which interval is narrower? Explain.
What will be an ideal response?
a. [373.38, 499.62]
b. [367.73, 505.27]
c. The confidence interval is narrower because it assumes that the expected value of the error term is zero, whereas the prediction interval incorporates the nonzero error term.
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