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

The prediction interval gives a range within which a future observation is expected to fall with a certain degree of confidence. This range includes both variability in the response variable and variability in the predictor variable(s). In contrast, the confidence interval only gives a range within which the population mean of the response variable is expected to fall with a certain degree of confidence. Therefore, the prediction interval must be wider than the confidence interval. Choice A is incorrect because the confidence interval is actually for the expected value E(y), not a particular value of y. Choices C and D are also incorrect because they refer to x rather than y.

For a Given Confidence Level, the Prediction Interval Is Always