When performing a regression analysis, what is a prediction interval and how is it different from a confidence interval?
Answer
Prediction intervals are used to predict a single future response given a set of predictor values. This is different from confidence intervals, which are used to predict the mean response for a given set of predictor values. Suppose we have built a model that predicts resting blood pressure in women based on their age. You could find a confidence interval for the mean blood pressure of all 50-year-old women, and the prediction interval for the blood pressure of an individual, unobserved 50-year-old woman.
Prediction intervals will always have a larger standard error than confidence intervals for the same data. With both confidence and prediction intervals, there will be uncertainty due to the model fit itself (we do not know the true values for the intercept or parameters in a linear model are unknown). However, with prediction intervals, you also have uncertainty due to the differences between individuals. In other words, different 50-year-old women will have different resting blood pressure measurements.