Prediction Interval

Generally, predictive models for regression problems (i.e. predicting a numerical value) make a point prediction.

This means they predict a single value but do not give any indication of the uncertainty about the prediction.

By definition, a prediction is an estimate or an approximation and contains some uncertainty. The uncertainty comes from the errors in the model itself and noise in the input data. The model is an approximation of the relationship between the input variables and the output variables.

A prediction interval is a quantification of the uncertainty on a prediction.

It provides a probabilistic upper and lower bounds on the estimate of an outcome variable.

A prediction interval for a single future observation is an interval that will, with a specified degree of confidence, contain a future randomly selected observation from a distribution.

— Page 27, Statistical Intervals: A Guide for Practitioners and Researchers, 2017.

Prediction intervals are most commonly used when making predictions or forecasts with a regression model, where a quantity is being predicted.

The prediction interval surrounds the prediction made by the model and hopefully covers the range of the true outcome.