# box.cox.var

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
box.cox.var(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. (1997) Applied Regression, Linear Models, and Related Methods. Sage.

##### See Also

boxcox, box.cox, box.cox.powers, box.cox.axis, av.plots

• box.cox.var
##### Examples
data(Ornstein)
mod<-lm(interlocks+1~assets, data=Ornstein)
mod.aux<-update(mod, .~.+box.cox.var(interlocks+1))
summary(mod.aux)
## Call:
## lm(formula = interlocks + 1 ~ assets + box.cox.var(interlocks +
##     1), data = Ornstein)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -23.189  -6.701   0.541   6.773  12.051
##
## 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
## box.cox.var(interlocks + 1)  7.427e-01  4.136e-02  17.956   <2e-16
##
## 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 degrees of freedom,     p-value:     0
av.plots(mod.aux, "box.cox.var(interlocks + 1)")
Documentation reproduced from package car, version 0.8-3, License: GPL version 2 or newer

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