I want to predict a factor and also get an upper bound for my prediction. It seems that what I want is prediction interval. but prediction interval only specifies the bound for one next prediction not all. Recently I found tolerance interval definition. Can I use it like prediction interval for future samples?
Prediction intervals can indeed provide a interval for multiple forthcoming observations. The most common usage of the prediction interval is however when the number of forthcoming observations is one. For the normal distribution this is just a special case of the more general version with multiple forthcoming observations. As is seen in the standard ISO standard 16269.
From the standard follows: