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135SE

Expert-verifiedFound in: Page 807

Book edition
13th

Author(s)
James T. McClave, P. George Benson, Terry Sincich

Pages
888 pages

ISBN
9780134506593

When a multiple regression model is used for estimating the mean of the dependent variable and for predicting a new value of y, which will be narrower—the confidence interval for the mean or the prediction interval for the new y-value? Why?

Confidence interval is narrower than the prediction interval because Prediction intervals must account for both the uncertainty in estimating the population mean, plus the random variation of the individual values. So a prediction interval is always wider than a confidence interval. Also, the prediction interval will not converge to a single value as the sample size increases.

The prediction interval predicts in what range a future individual observation will fall, while a confidence interval shows the likely range of values associated with some statistical parameter of the data, such as the population mean.

Confidence interval is narrower than the prediction interval because Prediction intervals must account for both the uncertainty in estimating the population mean, plus the random variation of the individual values. So a prediction interval is always wider than a confidence interval. Also, the prediction interval will not converge to a single value as the sample size increases.

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