The Monotone Smoothing of Scatterplots

We consider the problem of summarizing a scatterplot with a smooth, monotone curve. A solution that combines local averaging and isotonic regression is proposed, and we demonstrate its use with two examples. In the second example, the procedure is applied, in a regression setting, to some data from Box and Cox (1964), and it is shown how this new procedure generalizes Box and Cox's well-known family of transformations. In the same example, the bootstrap is applied to obtain a measure of the variability of the procedure.