# Latex equations

January 4, 2017

1 minute

\(\displaystyle p=\frac{\mbox{e}^{(\beta_o+\beta_1x)}}{\mbox{e}^{(\beta_o+\beta_1x)}+1}\)

\(\implies \displaystyle p(\mbox{e}^{(\beta_o+\beta_1x)}+1)=\mbox{e}^{(\beta_o+\beta_1x)}\)

\(\implies\displaystyle p.\mbox{e}^{(\beta_o+\beta_1x)}+p=\mbox{e}^{(\beta_o+\beta_1x)}\)

\(\implies\displaystyle p=\mbox{e}^{(\beta_o+\beta_1x)}-p.\mbox{e}^{(\beta_o+\beta_1x)}\)

\(\implies\displaystyle p=\mbox{e}^{(\beta_o+\beta_1x)}(1-p)\)

\(\implies\displaystyle\frac{p}{1-p}=\mbox{e}^{(\beta_o+\beta_1x)}\)

\(\implies\displaystyle \mbox{ln}\left(\frac{p}{1-p}\right)=\beta_0+\beta_1x\)