# 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 default
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
interp, eps = 1/50, xlab = expression(lambda),
ylab = "log-Likelihood", …)

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

# S3 method for 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

```
# NOT RUN {
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 7.3-51.4, License: GPL-2 | GPL-3*