# CHAPTER 5

# TRANSFORMATIONS AND WEIGHTING TO CORRECT MODEL INADEQUACIES

## 5.1 INTRODUCTION

Chapter 4 presented several techniques for checking the adequacy of the linear regression model. Recall that regression model fitting has several implicit assumptions, including the following:

- The model errors have mean zero and constant variance and are uncorrelated.
- The model errors have a normal distribution—this assumption is made in order to conduct hypothesis tests and construct CIs—under this assumption, the errors are independent.
- The form of the model, including the specification of the regressors, is correct.

Plots of residuals are very powerful methods for detecting violations of these basic regression assumptions. This form of model adequacy checking should be conducted for every regression model that is under serious consideration for use in practice.

In this chapter, we focus on methods and procedures for building regression models when some of the above assumptions are violated. We place considerable emphasis on **data transformation**. It is not unusual to find that when the response and/or the regressor variables are expressed in the correct scale of measurement or metric, certain violations of assumptions, such as inequality of variance, are no longer present. Ideally, the choice of metric should be made by the engineer or scientist with **subject-matter knowledge**, but there are many situations where this information is not available. In these cases, a data transformation may be ...