 Since formula_15 (a fixed but unknown parameter that can be estimated), the variance of the predicted response is given by

The formula_17 confidence intervals are computed as formula_18.Thus, the confidence interval for predicted response is wider than the interval for mean response.This is expected intuitively – the variance of the population of formula_19 values does not shrink when one samples from it, because the random variable "εi" does not decrease, but the variance of the mean of the formula_19 does shrink with increased sampling, because the variance in formula_21 and formula_22 decrease, so the mean response (predicted response value) becomes closer to formula_23.