The regression dilemma

Abstract

A substantial fraction of the statistical analyses and in particular statistical computing is done under the heading of multiple linear regression. That is the fitting of equations to multivariate data using the least squares technique for estimating parameters The optimality properties of these estimates are described in an ideal setting which is not often realized in practice.

Frequently, we do not have "good" data in the sense that the errors are non-normal or the variance is non-homogeneous. The data may contain outliers or extremes which are not easily detectable but variables in the proper functional, and we. may have the linearity

Prior to the mid-sixties regression programs provided just the basic least squares computations plus possibly a step-wise algorithm for variable selection. The increased interest in regression prompted by dramatic improvements in computers has led to a vast amount of literatur describing alternatives to least squares improved variable selection methods and extensive diagnostic procedures

The purpose of this paper is to summarize and illustrate some of these recent developments. In particular we shall review some of the potential problems with regression data discuss the statistics and techniques used to detect these problems and consider some of the proposed solutions. An example is presented to illustrate the effectiveness of these diagnostic methods in revealing such problems and the potential consequences of employing the proposed methods.

Keywords:

• influential data
• collinearity
• robust regression