Simple Regression in Light of Future Data

Abstract

Simple regression using maximization of log likelihood in light of future data is attempted. Conventional maximum likelihood method is regarded as maximization of log likelihood in light of data at hand. Simple regression using maximization of log likelihood in light of future data gives a bias to the gradient. Extent of bias is yielded by the gradient given by least squares and the variance of the gradient. Use of this bias provides better regression equations than the conventional maximum likelihood method in terms of log likelihood in light of future data.