A Note on Shortest Prediction Intervals for Log-Linear Regression

Abstract

In situations where the log transformation is used to make the assumptions of the ordinary linear regression model more reasonable, interval estimates for future observations are often desired in the scale of the original measurements. Common practice is to transfer the usual equal tail interval in the transformed scale back to the original scale. Conditions under which this procedure gives reasonably short intervals as compared with the shortest possible interval having the same content are derived, and a simple procedure that gives a reasonably short interval is suggested when it is not satisfactory. Primarily, a Bayesian point of view is taken.