Logistic Regression
Logistic regression is an algorithm for linear and binary classification problems. It is a classification, not regression algorithm.
1. From odds ratio to sigmoidal logistic function If $p$ is the probability of a sample being a positive event, then the odds ratio is defined as: $$\textrm{odds ratio} = \frac{p}{1-p}. \tag{1.1}$$
The logarithm of the odds ratio function is called logit function: $$z = \textrm{logit}(p) = log(\frac{p}{1-p}). \tag{1.2}$$
Logit function maps the probability $\{p|p\in[0, 1]\}$ to the entire real domain $\{z|z\in(-\infty, +\infty)\}$.