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Chapter 17

Logistic Regression

Note to current readers: This chapter is slightly less tested than previous
chapters. Please do not hesitate to report any errors, or suggest sections that
need better explanation! Also, as a result, this material is more likely to receive
edits.

After reading this chapter you will be able to:

• Understand how generalized linear models are a generalization of ordinary
linear models.
• Use logistic regression to model a binary response.
• Apply concepts learned for ordinary linear models to logistic regression.
• Use logistic regression to perform classification.

So far we have only considered models for numeric response variables. What
about response variables that only take integer values? What about a response
variable that is categorical? Can we use linear models in these situations? Yes!
The model that we have been using, which we will call ordinary linear regression,
is actually a specific case of the more general, generalized linear model. (Aren’t
statisticians great at naming things?)

17.1 Generalized Linear Models

So far, we’ve had response variables that, conditioned on the predictors, were
modeled using a normal distribution with a mean that is some linear combi-
nation of the predictors. This linear combination is what made a linear model
“linear.”

2

∣ X = x ∼ ( + + … + −1 −1 , )
0
1 1
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