# Chapter 4 Logistic regression

As we saw in Chapters 2 and 3, linear regression assumes that the response variable \(Y\) is *continuous*. In this chapter we will see how *logistic regression* can deal with a *discrete* response \(Y\). The simplest case is with \(Y\) being a *binary* response, that is, a variable encoding two categories. In general, we assume that we have \(X_1,\ldots,X_k\) predictors for explaining \(Y\) (*multiple* logistic regression) and cover the peculiarities for \(k=1\) as particular cases.