Logistic Regression (Classification)

The Problem with Linear Regression for Categories

Linear regression outputs continuous numbers. But what if we want to predict if an email is Spam (1) or Not Spam (0)? We need an output between 0 and 1 representing a probability.

The Sigmoid Function

We pass the linear equation through a "squishing" function:

σ(z) = 1 / (1 + e^(-z))

• If z is very large → σ(z) approaches 1.
• If z is very small → σ(z) approaches 0.

Decision Boundary

• Probability >= 0.5 → Class 1
• Probability < 0.5 → Class 0