New Approach in Fitting Linear Regression Models with the Aim of Improving Accuracy and Power

The main contribution of this work lies in challenging the common practice of inferential statistics in the realm of simple linear regression for attaining a higher degree of accuracy when multiple observations are available, at least, at one level of the regressor variable. We derive sufficient conditions under which one can improve the accuracy of the interval estimations at quite affordable extra computational cost. Two algorithms and a numerical example will be presented to fully explain how our approach works and to compare the results of our approach versus the results obtained from three of the well known statistical software systems.