# boxCoxVariable: Constructed Variable for Box-Cox Transformation In car: Companion to Applied Regression

 boxCoxVariable 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

 `y` response variable.

### 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.

`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)")
``````

car documentation built on March 31, 2023, 6:51 p.m.