For a given confidence level,the prediction interval is always wider than the confidence interval because
A)The confidence interval is for a particular value of y rather than for the expected value E(y).
B)The prediction interval is for a particular value of y rather than for the expected value E(y).
C)The confidence interval is for a particular value of x rather than for the expected value E(x).
D)The prediction interval is for a particular value of x rather than for the expected value E(x).

Question

Quizplus · Accepted Answer

A confidence interval provides a range within which we can expect the true mean response (E(y)) to fall with a given level of confidence. A prediction interval, on the other hand, provides a range within which we can expect an individual response (a particular value of y) to fall with a given level of confidence. Since the prediction interval accounts for the natural variation in individual responses, it will always be wider than the confidence interval, which only accounts for the variation in the mean response. Hence, option B is the correct choice.

For a Given Confidence Level,the Prediction Interval Is Always Wider