# boxcox

##### Box-Cox Transformations for Linear Models

Computes and optionally plots profile log-likelihoods for the parameter of the Box-Cox power transformation.

- Keywords
- models, hplot, regression

##### Usage

`boxcox(object, ...)`## S3 method for class 'default':
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
interp, eps = 1/50, xlab = expression(lambda),
ylab = "log-Likelihood", ...)

## S3 method for class 'formula':
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
interp, eps = 1/50, xlab = expression(lambda),
ylab = "log-Likelihood", ...)

## S3 method for class 'lm':
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
interp, eps = 1/50, xlab = expression(lambda),
ylab = "log-Likelihood", ...)

##### Arguments

- object
- a formula or fitted model object. Currently only
`lm`

and`aov`

objects are handled. - lambda
- vector of values of
`lambda`

-- default $(-2, 2)$ in steps of 0.1. - plotit
- logical which controls whether the result should be plotted.
- interp
- logical which controls whether spline interpolation is
used. Default to
`TRUE`

if plotting with`lambda`

of length less than 100. - eps
- Tolerance for
`lambda = 0`

; defaults to 0.02. - xlab
- defaults to
`"lambda"`

. - ylab
- defaults to
`"log-Likelihood"`

. - ...
- additional parameters to be used in the model fitting.

##### Value

- A list of the
`lambda`

vector and the computed profile log-likelihood vector, invisibly if the result is plotted.

##### Side Effects

If `plotit = TRUE`

plots log-likelihood *vs* `lambda`

and
indicates a 95% confidence interval about the maximum observed value
of `lambda`

. If `interp = TRUE`

, spline interpolation is
used to give a smoother plot.

##### References

Box, G. E. P. and Cox, D. R. (1964)
An analysis of transformations (with discussion).
*Journal of the Royal Statistical Society B*, **26**, 211--252.
Venables, W. N. and Ripley, B. D. (2002)
*Modern Applied Statistics with S.* Fourth edition. Springer.

##### Examples

```
boxcox(Volume ~ log(Height) + log(Girth), data = trees,
lambda = seq(-0.25, 0.25, length = 10))
boxcox(Days+1 ~ Eth*Sex*Age*Lrn, data = quine,
lambda = seq(-0.05, 0.45, len = 20))
```

*Documentation reproduced from package MASS, version 7.3-22, License: GPL-2 | GPL-3*