7.1 Dependent Variable

The output of a logistic regression is a binary or dummy variable:

\[ Y = \begin{cases} 1 & \text{if success} ,\\ 0 & \text{if failure} \end{cases} \] Then,

\[ Y \sim \text{Bernoulli}(\pi) \]

where \(\pi\) is the probability if \(Y=1\), \(\mathbb{P}(Y=1)\). Thus:

\[ \mathbb{P}(Y|\pi) = \begin{cases} \pi & \text{if } \, \, Y=1,\\ 1-\pi & \text{if } \, \, Y=0. \end{cases} \]