ロジスティック回帰

${\displaystyle \operatorname {logit} (p_{i})=\ln \left({\frac {p_{i}}{1-p_{i}}}\right)=\alpha +\beta _{1}x_{1,i}+\cdots +\beta _{k}x_{k,i},}$
${\displaystyle i=1,\dots ,n,\,\!}$

${\displaystyle p_{i}=E(Y|X_{i})=\Pr(Y_{i}=1).\,\!}$

${\displaystyle p_{i}=\Pr(Y_{i}=1|X)={\frac {1}{1+e^{-(\alpha +\beta _{1}x_{1,i}+\cdots +\beta _{k}x_{k,i})}}}}$

${\displaystyle p_{i}=\varsigma _{1}(\alpha +\beta _{1}x_{1,i}+\cdots +\beta _{k}x_{k,i})}$

${\displaystyle p(x)={\frac {e^{B_{0}+B_{1}x}}{1+e^{B_{0}+B_{1}x}}}.}$

${\displaystyle {\frac {p(x)}{1-p(x)}}=e^{B_{0}+B_{1}x},}$

${\displaystyle {\frac {p(50)}{1-p(50)}}={\frac {\frac {2}{3}}{1-{\frac {2}{3}}}}=2.}$