# boxCoxVariable

0th

Percentile

##### Constructed Variable for Box-Cox Transformation

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

Keywords
manip, regression
##### 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.

##### 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. (2008) Applied Regression Analysis and Generalized Linear Models, Second Edition. Sage. Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage.

boxcox, powerTransform, bcPower

##### Aliases
• boxCoxVariable
##### Examples
mod <- lm(interlocks + 1 ~ assets, data=Ornstein)
mod.aux <- update(mod, . ~ . + boxCoxVariable(interlocks + 1))
summary(mod.aux)
# avPlots(mod.aux, "boxCoxVariable(interlocks + 1)")
Documentation reproduced from package car, version 2.0-11, License: GPL (>= 2)

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