4.6 Logistic regression

The logistic regression model is a generalization of the linear regression model, which we can use when the response variable is binary. This model uses the logistic function as an inverse link function. Let’s get familiar with this function before we move on to the model:

For our purpose, the key property of the logistic function is that irrespective of the values of its argument z, the result will always be a number in the [0-1] interval. Thus, we can see this function as a convenient way to compress the values computed from a linear model into values that we can feed into a Bernoulli distribution. This logistic function is also known as the sigmoid function because of its characteristic S-shaped aspect, as we can see from Figure 4.10.

Figure 4.10: Logistic function

4.6.1 The logistic model

We have almost all the elements to turn a simple linear regression into a simple logistic regression. Let’s begin with the case of only two classes...