CHAPTER 19 Other Useful Kinds of Regression 287

Several kinds of nonparametric data-smoothing methods have been developed.

A popular one, called LOWESS, stands for Locally Weighted Scatterplot Smoothing.

Many statistical programs can perform a LOWESS regression. In the following

sections, we explain how to run a LOWESS analysis and adjust the amount of

smoothing (stiffness) of the curve.

Running LOWESS

Suppose that you discover a new hormone called XYZ believed to be produced in

women’s ovaries throughout their lifetimes. Research suggests blood levels of

XYZ should vary with age, in that they are low before going through puberty and

after completing menopause, and high during child-bearing years. You want to

characterize and quantify the relationship between XYZ levels and age as accu-

rately as possible.

Suppose that for your analysis, you are allowed to obtain 200 blood samples drawn

from consenting female participants aged 2 to 90 years for another research proj-

ect, and analyze the specimens for XYZ levels. A graph of XYZ level versus age may

look like Figure 19-10.

In Figure 19-10, you can observe a lot of scatter in these points, which makes it

hard to see the more subtle aspects of the XYZ-age relationship. At what age does

the hormone level start to rise? When does it peak? Does it remain fairly constant

throughout child-bearing years? When does it start to decline? Is the rate of

decline after menopause constant, or does it change with advancing age?

FIGURE 19-10:

The relationship

between age and

hormone

concentration

doesn’t conform

to a simple

function.

© John Wiley & Sons, Inc.