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

## Description

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

## Usage

 `1` ```boxCoxVariable(y) ```

## Arguments

 `y` response variable.

## Details

The constructed variable is defined as y[log(y/y') -1], where 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 [email protected]

## 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`

## Examples

 ```1 2 3 4``` ```mod <- lm(interlocks + 1 ~ assets, data=Ornstein) mod.aux <- update(mod, . ~ . + boxCoxVariable(interlocks + 1)) summary(mod.aux) # avPlots(mod.aux, "boxCoxVariable(interlocks + 1)") ```

### Example output

```Call:
lm(formula = interlocks + 1 ~ assets + boxCoxVariable(interlocks +
1), data = Ornstein)

Residuals:
Min       1Q   Median       3Q      Max
-23.1895  -6.7012   0.5411   6.7728  12.0506

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)                     1.461e+01  5.426e-01  26.920   <2e-16 ***
assets                         -7.142e-05  5.119e-05  -1.395    0.164
boxCoxVariable(interlocks + 1)  7.427e-01  4.136e-02  17.956   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 7.247 on 245 degrees of freedom
Multiple R-squared:  0.7986,	Adjusted R-squared:  0.797
F-statistic: 485.7 on 2 and 245 DF,  p-value: < 2.2e-16
```

car documentation built on Dec. 2, 2017, 3 a.m.