# Logistic Regression
- Instead of modeling $Y$ directly, we may model $\Pr(Y = 1 \mid X)$
- _Logit function_
$
\mathrm{logit}(p_X) =
\ln\frac{p_X}{1 - p_X} = \beta_0 + \beta_1X \Rightarrow
p_X = \frac1{1 + e^{-(\beta_0+\beta_1X)}}
$
- Terms
- _Probability_: $\Pr(Y = 1 \mid X)$
- _Odds_: $\Pr(Y = 1 \mid X)/\Pr(Y = 0 \mid X)$
- _Log-odds_: $\beta_0 + \beta_1X$
- e