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In statistics, a prediction interval bears the same relationship to a future observation that a confidence interval bears to an unobservable population parameter.

[edit] Example

Suppose one has drawn a sample from a normally distributed population. The mean and standard deviation of the population are unknown except insofar as they can be estimated based on the sample. It is desired to predict the next observation. Let n be the sample size; let μ and σ be respectively the unobservable mean and standard deviation of the population. Let X₁, ..., X_n, be the sample; let X_n+1 be the future observation to be predicted. Let

and

Then it is fairly routine to show that

has a Student's t-distribution with n − 1 degrees of freedom. Consequently we have

where A is the 100(1 − (p/2))^th percentile of Student's t-distribution with n − 1 degrees of freedom. Therefore the numbers

are the endpoints of a 100p% prediction interval for X_n+1.

[edit] See also

• Confidence interval
• Extrapolation
• Prediction
• Regression analysis
• Seymour Geisser
• Trend estimation

[edit] References

• Chatfield, C. (1993) "Calculating Interval Forecasts," Journal of Business and Economic Statistics, 11 121-135.
• Meade, N. and T. Islam (1995) "Prediction Intervals for Growth Curve Forecasts," Journal of Forecasting, 14 413-430.

This page uses content from the English-language version of Wikipedia. The original article was at Prediction_interval. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License.