boxCoxVariable {car} | R Documentation |

## Constructed Variable for Box-Cox Transformation

### Description

Computes a constructed variable for the Box-Cox transformation of the
response variable in a linear model.

### Usage

```
boxCoxVariable(y)
```

### Arguments

### Details

The constructed variable is defined as `y[\log(y/\widetilde{y}) - 1]`

, where
`\widetilde{y}`

is the geometric mean of `y`

.

The constructed variable is meant to be
added to the right-hand-side of the linear model. The t-test for the
coefficient of the constructed variable is an approximate score test for whether a
transformation is required.

If `b`

is the coefficient of the constructed variable,
then an estimate of the normalizing power transformation based on the score statistic
is `1 - b`

. An added-variable plot for the constructed
variable shows leverage and influence on the decision to transform `y`

.

### Value

a numeric vector of the same length as `y`

.

### Author(s)

John Fox jfox@mcmaster.ca

### References

Atkinson, A. C. (1985)
*Plots, Transformations, and Regression*. Oxford.

Box, G. E. P. and Cox, D. R. (1964)
An analysis of transformations.
*JRSS B* **26** 211–246.

Fox, J. (2016)
*Applied Regression Analysis and Generalized Linear Models*,
Third Edition. Sage.

Fox, J. and Weisberg, S. (2019)
*An R Companion to Applied Regression*, Third Edition, Sage.

### See Also

`boxcox`

, `powerTransform`

, `bcPower`

### Examples

```
mod <- lm(interlocks + 1 ~ assets, data=Ornstein)
mod.aux <- update(mod, . ~ . + boxCoxVariable(interlocks + 1))
summary(mod.aux)
# avPlots(mod.aux, "boxCoxVariable(interlocks + 1)")
```

[Package

*car* version 3.1-0

Index]