Beyond the Sigmoid: The Mathematical Soul of Logistic Regression

In the world of Machine Learning, most beginners treat model.fit as a magic wand. You feed in data, and out comes a prediction. But if you are building algorithms from scratch - with nothing but Numpy and Math - you quickly realize that a classifier is not just a "binary switcher." It is a probability engine. Linear Regression fails at classification because lines are infinite, but probabilities are not.