A prediction interval is a random interval designed to contain a future observation with prescribed repeated-sampling probability. Unlike a confidence interval for a mean response, it includes both uncertainty in the fitted mean and the new observation's irreducible random variation.
For the full-rank normal linear model and an independent future response , putThen an exact prediction interval isThe additional one inside the square root is the future observation's irreducible error variance; a confidence interval for its mean omits it.
Suppose independent future log responses satisfy , where the errors have variance . Conditional on a fitted normal linear model, the predicted log ratio has estimated mean and estimated varianceA Student t interval on this logarithmic scale can be exponentiated to obtain a prediction interval for the positive ratio.
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A prediction interval is a statistical range that is used to estimate the likely value of a single future observation based on a fitted model. It provides an interval that is expected to contain the actual value of that future observation with a specified level of confidence (e.g., 95% confidence).