Why Is Logistic Regression Considered a Linear Model?

Logistic regression as a linear model

We mentioned previously that logistic regression is considered a linear model, while we were exploring whether the relationship between features and response resembled a linear relationship. Recall that we plotted groupby/mean of the EDUCATION feature in the “Data Exploration” chapter, as well as for the PAY_1 feature in this chapter, to see whether the default rates across values of these features exhibited a linear trend. While this is a good way to get a quick approximation of how “linear or not” these features may be, here we formalize the notion of why logistic regression is a linear model.

What is a linear model?

A model is considered linear if the transformation of features that is used to calculate the prediction is a linear combination of the features. The possibilities for a linear combination are that each feature can be multiplied by a numerical constant, these terms can be added together, and an additional constant can be added. For example, in a simple model with two features, $X_1$ and $X_2$ ...