Introduction
Every classifier divides the space of possible inputs into regions: "here I predict class A, there I predict class B". The border between the regions is the decision boundary.
Looking at decision boundaries is one of the best ways to understand what a classifier can and can't do. For logistic regression, the answer is simple and important: its boundary is always straight — a line in 2-D, a flat plane in 3-D, a "hyperplane" in more dimensions.
We'll use the classic iris flower dataset: 150 iris flowers of three species, with measurements of their petals and sepals.