# Box-Cox Transformation for ANOVA Model

## Toxic Agents Example

Minitab homepage offers a macro that execute Box-Cox transformation
in regression. It finds the MLE of λ on maximizing the
log-likelihood of the joint distribution of the responses under
such regression model. It's equivalent to minimizing the residual
sum of squares as does the classnotes' procedure. The
code can be found in
http://support.minitab.com/en-us/minitab/17/macro-library/macro-files/quality-control-and-doe-macros/box-cox-transformation-for-regression-and-response-surface-models
(with download instruction on the link). You can go on the
MINITAB Homepage
and click on **Support** and pull down to select
**Macro Library** to go to the abovementioned page.

Now click **ANOVA & Regression** and select item 3
(Box-Cox ...). Then click **code** for download and
click **Documentation** for a brief documentation.

## Setup

The macro can be used for ANOVA context. We only need to create
indicator variables for each factor involved.

### Make Indicator Variables

Do *Calc* → *Make Indicator Variables*.
For factor **poison**:

Note that, for a factor of **k** levels, MINITAB requires
**k** output columns. However, only **k−1** indicator
variables will be used. Here we will use C4 and C5 (named
**poison1** and **poison2**, respectively) and allow
C6 be recycled for the indicator variables of factor **treat**:
Since factor **treat** has four levels, only indicator
variables C6, C7, and C8 (named **treatA**, **treatB**,
and **treatC**, respectively) will be used in regression.
These indicator variables (C4 to C8) constitute the 5 = 2 + 3
degrees of freedom of the main effects. The following gives
a (portion of) screeshot of the the worksheet:
### Submit Macro Call

Do *Edit* → *Command Line Editor* (or use
Ctrl-L keyboard shortcut):
#### Session Output

Macro is running ... please wait
**Box-Cox Power Transformation Analysis**
Model Information
------------------------------
Response: time
Predictor(s): poison1 , poison2 , treatA , treatB , treatC
------------------------------
Estimated Lambda: -0.75
Approximate 95% CI for Lambda: (-1.13 , -0.36)

#### Box-Cox Power Transformation Analysis

It yielded the same λ as in the classnotes with
comparable 95% confidence interval.