Box-Cox Transformation.

The Box-Cox transformation is a generalized “power transformation” that transforms data to make the distribution more normal.

For example, when its lambda parameter is 0, it’s equivalent to the log-transformation.

It’s used to stabilize the variance (eliminate heteroskedasticity) and normalize the distribution.

It is used to transform the data in order to fit better in a model.

There are many way to transform some numbers, the Box-Cox transformation finds the best one.

For example we can transform the numbers (4, 3, 5, 8, 9) in many ways:

raising to the power of 2 → (4^2, 3^2, 5^2, 8^2, 9^2) → (16, 9, 25, 64, 81)

putting them under square roots → (2, sqrt(3), sqrt(5), sqrt(8), 3)

dividing by 10 → (0.4, 0.3, 0.5, 0.8, 0.9)

taking the log and so many other ways