Computes a constructed variable for the Box-Cox transformation of the response variable in a linear model.
The constructed variable is defined as y[log(y/y') -1], where
y' is the geometric mean of
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
a numeric vector of the same length as
John Fox [email protected]
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.
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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
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