Linear regression is used to approximate the relationship between a continuous response variable and a set of predictor variables. However, for many data applications, the response variable is categorical rather than continuous. For such cases, linear regression is not appropriate. Fortunately, the analyst can turn to an analogous method, logistic regression, which is similar to linear regression in many ways.

Logistic regression refers to methods for describing the relationship between a categorical response variable and a set of predictor variables. In this chapter, we explore the use of logistic regression for binary or dichotomous variables; those interested in using logistic regression for response variables with more than two categories may refer to Hosmer and Lemeshow.^{1} To motivate logistic regression, and to illustrate its similarities to linear regression, consider the following example.

13.1 Simple Example of Logistic Regression

Suppose that medical researchers are interested in exploring the relationship between patient age (x) and the presence (1) or absence (0) of a particular disease (y). The data collected from 20 patients is shown in Table 13.1, and a plot of the data is shown in Figure 13.1. The plot shows the least-squares regression line (dotted straight line), and the logistic regression line (solid curved line), along with the estimation error for patient 11 (age = 50, disease = 0) for both lines.

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