Regression Analysis by Example, 4th Edition

CHAPTER 12

LOGISTIC REGRESSION

12.1 INTRODUCTION

In our discussion of regression analysis so far the response variable Y has been regarded as a continuous quantitative variable. The predictor variables, however, have been both quantitative, as well as qualitative. Indicator variables, which we have described earlier, fall into the second category. There are situations, however, where the response variable is qualitative. In this chapter we present methods for dealing with this situation. The methods presented in this chapter are very different from the method of least squares considered in earlier chapters.

Consider a procedure in which individuals are selected on the basis of their scores in a battery of tests. After five years the candidates are classified as “good” or “poor”. We are interested in examining the ability of the tests to predict the job performance of the candidates. Here the response variable, performance, is dichotomous. We can code “good” as 1 and “poor” as 0, for example. The predictor variables are the scores in the tests.

In a study to determine the risk factors for cancer, health records of several people were studied. Data were collected on several variables, such as age, sex, smoking, diet, and the family's medical history. The response variable was, the person had cancer (Y = 1), or did not have cancer (Y = 0).

In the financial community the “health” of a business is of primary concern. The response variable is solvency of the firm (bankrupt = 0, solvent ...