Box-Cox Transformation Model

Definition

Box-Cox transformation is useful when dealing with heteroskedasticity by stabilizing variance.

Box-Cox Transformation

$w_i=\{\begin{array}{ll}\frac{y_i^{\lambda }-1}{\lambda }& \lambda \ne 0\\ \ln y_i& \lambda =0\end{array}$

Box-Cox Transformation Model

The model using the Box-Cox Transformed variable as a response variable is called a Box-Cox transformation model $\mathbf{w}(\lambda )=\mathbf{X}\mathbf{\beta }+\mathbf{ϵ}$ where $\mathbf{ϵ}\sim N(0,{\sigma }^2\mathbf{I})$