This chapter covers
- Describing binary outcomes with probabilities and odds
- Constructing and assessing binary classifiers
- Fitting the logistic curve to binary data
- Assessing simple logistic models
As we know from the last chapter, simple linear regression relates the expected value of a quantitative response to a predictor’s value. While this can be the ideal tool to use when the response has a continuous range of possible values, like measurements, it won’t work when the response is categorical. To see how to handle this kind of data, we’ll start with the simplest possible categorical response, a binary variable that has only two possible values. These values correspond to two disjoint categories— Yes or No, Agree or Disagree, True or False— and are usually coded numerically as either 0 or 1, with 0 interpreted generically as failure and 1 interpreted as success. These terms should not be interpreted literally, though; in some medical studies, for example, a response value of 1 denotes death or the presence of a disease, hardly a success from the patient’s point of view!