# 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