Prediction intervals [PI]

A prediction interval is a range of values that is likely to contain the value of a single new observation given specified settings of the predictors. For example, for a 95% prediction interval of [5 10], you can be 95% confident that the next new observation will fall within this range.

After you fit a regression model that provides an adequate fit to the data, you can use the model to generate predictions based on specific predictor values. However, predictions are not as simple as a single predicted value. The predicted value is actually the mean response value. Like any mean, there is variability around that mean.

Prediction intervals account for the variability around the mean response inherent in any prediction. Like confidence intervals, predictions intervals have a confidence level and can be a two-sided range, or an upper or lower bound. Unlike confidence intervals, prediction intervals predict the spread for individual observations rather than the mean.

Note that a prediction interval is different than a confidence interval of the prediction. The prediction interval is always wider than the confidence interval of the prediction because of the added uncertainty involved in predicting a single response versus the mean response.