**Logistic regression**, also known as **logit regression**, or **logit model** is a probabilistic linear model for dichotomous data. The response variable is a binary variable (nominal variable), which means the variable has two categories or two values; True vs. False, or \(1\) vs. \(0\), or success vs. failure, with the probabilities of \(\pi\) and \(1-\pi\), respectively. Thus, the response variable follows a binomial distribution written as

\[y \sim B(\eta,\pi)\text{,}\]

where \(\eta\) is the binomial denominator, which is for a binary variable \(0\) or \(1\) and \(\pi\) is the probability of success.