Statistics in a Nutshell, 2nd Edition

Chapter 11. Logistic, Multinomial, and Polynomial Regression

Multiple linear regression is a powerful and flexible technique that can handle many types of data. However, there are many other of types of regression that are more appropriate for particular types of data or to express particular relationships among the data. We discuss a few of these regression techniques in this chapter. Logistic regression is appropriate when the dependent variable is dichotomous rather than continuous, multinomial regression when the outcome variable is categorical (with more than two categories), and polynomial regression is appropriate when the relationship between the predictors and the outcome variable is best expressed through an equation including polynomial terms (such as x² or x³). If you are unfamiliar with odds ratios, it would be good to read the section of Chapter 15 covering them before reading this chapter because the odds ratio plays a key role in interpreting the output of logistic regression.

Logistic Regression

Multiple linear regression may be used to find the relationship between a single, continuous outcome variable and a set of predictor variables that might be continuous, dichotomous, or categorical; if categorical, the predictors must be recoded into a set of dichotomous dummy variables.

Logistic regression is in many ways similar to multiple linear regression, but it’s used when the outcome variable is dichotomous (when it can take only two values). The outcome might be dichotomous ...