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==Classification of Regression models==
†'Multivariable' can be rephrased as 'Multiple'; Multivariable is <font color="red">'''NOT equal to 'Multivariate'!!'''</font>
==Binary logistic regression=====Conversion of binary logistic regression equation logit of outcome odds to outcome probability <math>p</math>===
Equation of binary logistic regression can be converted to outcome probablity <math>p</math> as,
:<math>
\begin{alignarray}{lrll}\log Y = & \log \left ( \fracdfrac{p}{1-p} \right ) & = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots \\\Leftrightarrow & \dfrac{p}{1-p} & = \exp (a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots) & = e^{(a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots)} \\\Leftrightarrow & p & = \dfrac { \exp (a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots) }{ 1 + \exp (a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots) } & = \dfrac { e^{(a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots)} }{ 1 + e^{(a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots)} } \\\end{alignarray}
</math>
===How to convert Conversion of coefficient of binary logistic regressoin to odds ratio===
When thinking about outcome probability <math>p</math> and the changed outcome probability <math>p\prime</math> by adding <math>1</math> to explanatory variable <math>X_1</math>, the following two equations are obtained,
:<math>
\log \left ( \frac{p\prime}{1-p\prime} \right ) - \log \left ( \frac{p}{1-p} \right ) & = b_1({\color{red}X_1 + 1}) - b_1X_1 \\
& = b_1 \\
\Leftrightarrow \frac {\left ( \dfrac{p\prime}{1-p\prime} \right )}{ \left ( \dfrac{p}{1-p} \right ) } & = \exp (b_1) = e^{b_1}
\end{align}
</math>
Thus, converted <math>b_1</math> to <math>\color{red}{e^{b_1}}</math> or <math>\color{red}{\exp (b_1)}</math> gives the '''odds ratio of outocome probabilities''' before and after variable <math>X_1</math> gains <math>1</math>. ::<math>\begin{align}\exp (\text{coefficient}) = e^{\text{coefficient}} & = \text{odds ratio} \\\log (\text{odds ratio}) & = \text{coefficient}\end{align}</math>
==Generalized linear model==
