Regression Analysis by Example, 4th Edition

CHAPTER 4

REGRESSION DIAGNOSTICS: DETECTION OF MODEL VIOLATIONS

4.1 INTRODUCTION

We have stated the basic results that are used for making inferences about simple and multiple linear regression models in Chapters 2 and 3. The results are based on summary statistics that are computed from the data. In fitting a model to a given body of data, we would like to ensure that the fit is not overly determined by one or few observations. The distribution theory, confidence intervals, and tests of hypotheses outlined in Chapters 2 and 3 are valid and have meaning only if the standard regression assumptions are satisfied. These assumptions are stated in this chapter (Section 4.2). When these assumptions are violated the standard results quoted previously do not hold and an application of them may lead to serious error. We reemphasize that the prime focus of this book is on the detection and correction of violations of the basic linear model assumptions as a means of achieving a thorough and informative analysis of the data. This chapter presents methods for checking these assumptions. We will rely mainly on graphical methods as opposed to applying rigid numerical rules to check for model violations.

4.2 THE STANDARD REGRESSION ASSUMPTIONS

In the previous two chapters we have given the least squares estimates of the regression parameters and stated their properties. The properties of least squares estimators and the statistical analysis presented in Chapters 2 and 3 are based on the following ...