Logistic Regression

Definition

Logistic regression is a Generalized Linear Model with Logit link function. Logistic regression models the log-odds of an event as a linear combination of independent variables. $\mathrm{logit}(\pi )=\ln \left(\frac{\pi }{1-\pi }\right)={\mathbf{x}}^{⊺}\mathbf{\beta }$ The probability is calculated as $\pi (\mathbf{x})=P(Y=1|X=\mathbf{x})=\frac{\exp ({\mathbf{x}}^{⊺}\mathbf{\beta })}{1+\exp ({\mathbf{x}}^{⊺}\mathbf{\beta })}=\frac{1}{1+\exp (-{\mathbf{x}}^{⊺}\mathbf{\beta })}$