Logistic Regression

A member of the generalized linear model (GLM) family and similar to linear regression in many ways, logistic regression (despite the confusing name) is used for classification problems with two possible outcomes. Logistic regression is handy for classification problems since it fits an S shaped logistic (or Sigmoid) function to the data, squishing the linear equation to an output range of 0–1. This convenient range allows logistic regression to model the probabilities of a data point belonging to a particular class, typically with the decision point at the probability of .5. So, what does that look like in math? How does the sigmoid function squish the linear equation?