# The Sigmoid

The sigmoid is a function with an s shape that's used in logistic regression (and
elsewhere).

#### The Equation

\begin{aligned} \sigma(z) &= \frac{1}{1+e^{-z}}\\ \sigma(0) &= \frac{1}{2}\\ \lim_{z \to \infty} \sigma(z) &= 1\\ \lim_{z \to -\infty} \sigma(z) &= 0\\ \end{aligned}

#### Applying to a Linear Regression Classifier

1. Apply the Sigmoid to z multiplied by a weight learned by the classifier.
2. Classify using round(Sigmoid(z))