$P(\hat{Y})=e^{(\beta_{0}+\beta_{1}X)}/[1+e^{(\beta_{0}+\beta_{1}X)}]$ $\Rightarrow P(\hat{Y})+P(\hat{Y})\times[e^{(\beta_{0}+\beta_{1}X)}]=e^{(\beta_{0}+\beta_{1}X)}$ $\Rightarrow P(\hat{Y})=[1-P(\hat{Y})]\times [e^{(\beta_{0}+\beta_{1}X)}]$ $\Rightarrow P(\hat{Y})/(1-P(\hat{Y}))=e^{(\beta_{0}+\beta_{1}X)} (1.1)$ The left part is called odds ratio. $\Rightarrow\log{(P(X)/(1-P(X)))}=\beta_{0}+\beta_{1}X$ The left hand side is called log odds ratio. This is classified under linear regressions because the right hand side is the basic formula for Linear Regression. Coefficient $\beta_{1}$ means: one-unit increase in x is associated with an increase in the log odds of 0/1 by $\beta_{1}$ units.