A Clearer View of the Data: Smoothing Scatterplots

摘要

Plots of data are everywhere: stock market closings, production yields, waveform measurements. Usually we plot data to summarize the information contained therein; sheer volume of numbers can be overwhelming. Besides, a graphical display of the data often can provide more information than numerical methods. But sometimes the message can get lost in the medium, or, worse, can be misleading. Consider Example 1. A glance of a few moments or even more at the points on this graph will more often than not suggest a linear association between the two variables. But smoothing this scatterplot (solid trace) reveals otherwise: the trend really consists of two distinct linear trends (dashed lines), the second half with twice the variability and half the slope of the first half. The solid curve is a smoothed version of the response (ordinate); it illustrates the value of smoothing scatterplots to convey the message in the data by reducing the distracting &ail and enhancing our visual interpretation.