Robust Regression

Abstract

As previously indicated, least squares regression suffers from several practical problems. A single unusual point can mask an important and interesting association, and least squares regression can give a distorted view of how the bulk of the observations are related. Even when the outcome measure (Y) has a normal distribution, heteroscedasticity can result in relatively low power when testing the hypothesis that the slope is zero. That is, heteroscedasticity can mask an association because the variance (or squared standard error) of the least squares estimator can be very high compared to other estimators one might use. Nonnormality makes matters worse, and the conventional method for computing a confidence interval for the slope can be highly inaccurate.