Page 317 - Applied Statistics with R

14.1. RESPONSE TRANSFORMATION 317

-46 95%

-48
log-Likelihood -50 -52

-54

-56

-58
-0.2 0.0 0.2 0.4 0.6

λ

Using the Box-Cox method, we see that = 0.3 is both in the confidence inter-
val, and is extremely close to the maximum, which suggests a transformation of
the form

− 1 0.3 − 1
= .
0.3

We then fit a model with this transformation applied to the response.

gala_model_cox = lm((((Species ^ 0.3) - 1) / 0.3) ~ Area + Elevation + Nearest + Scruz + Adjacent, data = gala)

plot(fitted(gala_model_cox), resid(gala_model_cox), col = "dodgerblue",
pch = 20, cex = 1.5, xlab = "Fitted", ylab = "Residuals")
abline(h = 0, lty = 2, col = "darkorange", lwd = 2)