# CHAPTER 6

# TRANSFORMATION OF VARIABLES

## 6.1 INTRODUCTION

Data do not always come in a form that is immediately suitable for analysis. We often have to transform the variables before carrying out the analysis. Transformations are applied to accomplish certain objectives such as to ensure linearity, to achieve normality, or to stabilize the variance. It often becomes necessary to fit a linear regression model to the transformed rather than the original variables. This is common practice. In this chapter, we discuss the situations where it is necessary to transform the data, the possible choices of transformation, and the analysis of transformed data.

We illustrate transformation mainly using simple regression. In multiple regression where there are several predictors, some may require transformation and others may not. Although the same technique can be applied to multiple regression, transformation in multiple regression requires more effort and care.

The necessity for transforming the data arises because the original variables, or the model in terms of the original variables, violates one or more of the standard regression assumptions. The most commonly violated assumptions are those concerning the linearity of the model and the constancy of the error variance. As mentioned in Chapters 2 and 3, a regression model is linear when the parameters present in the model occur linearly even if the predictor variables occur nonlinearly. For example, each of the four following models is linear: ...

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