Mean and Single Prediction Bands for a Nonlinear Model

For linear and nonlinear regression models, prediction bands provide a measure of confidence concerning where the true function lives. Here the model is a function of the form where is the predictor variable and , , and are parameters. A higher level of confidence requires wider bands. Single prediction bands incorporate both the variation in parameter estimates and the overall variation in response values, while the mean confidence bands incorporate only the variation in parameter estimates. As a result, single prediction bands are wider than mean prediction bands for the same confidence level. Mean prediction bands also exhibit more variation in width.