Boxcox Plot. Computes and optionally plots profile log likelihoods for the parameter of the box cox power transformation. The box cox linearity plot is a plot of the correlation between y and the transformed x for given values of lambda.
That is lambda is the coordinate for the horizontal axis variable and the value of the correlation between y and the transformed x is the coordinate for the vertical axis of the plot. If plotit true plots log likelihood vs lambda and indicates a 95. So logically speaking the horse which came first and the fast horses along with it will have the same difference of completion time whereas the slowest ones will have a larger difference in their completion time.
A transformation is appropriate.
Boxcox object lambda seq 2 2 1 10 plotit true interp eps 1 50 xlab expression lambda ylab log likelihood. Usage boxcox object default s3 method. The function plot boxcox is a method for the generic function plot for the class boxcox see boxcox object. For the box cox transformation a λ value of 1 is equivalent to using the original data.