June 24, 2010, by Bruce Ratner, Ph.D.
Assessing the relationship between predictor and dependent variables is an essential task in the model building process. If the relationship is identified and tractable, then the variables are subject to re-expression to reflect the uncovered relationship, and consequently tested for inclusion into the model. The purpose of this article is two-fold:
1) to review the standard smooth scatterplot for unmasking a presuming existent underlying relationship as depicted in a raw-data scatterplot; and
2) to introduce a new method of obtaining a smoother scatterplot, which exposes a more reliable depiction of the unmasked relationship. The former scatterplot uses averages of raw data, and the latter uses the averages of fitted values of CHAID end-nodes. I illustrate both the smooth and smoother scatterplots using a real study.