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underlying politic, market, or environment, for example). We take
up this problem again in our chapter on prediction error.
And lest we forget: Association does not “prove” causation, it can only
contribute to the evidence.
Indicator Variables
The use of an indicator (yes/no) or a nonmetric ordinal variable
(improved, much improved, no change) as the sole independent (
X
) vari-
able is inappropriate. The two-sample and
k
-sample procedures described
in Chapter 5 should be employed.
Transformations
It is often the case that the magnitude of the residual error is proportional
to the size of the observations; that is,
y
=
E
(
Y
|
x
)e. A preliminary log
transformation will restore the problem to linear form log(
y
) = log
E
(
Y
|
x
)
+ e ¢. Unfortunately, even if e is normal, e ¢ is not, and the resulting confi-
dence intervals need to be adjusted (Zhou and Gao, 1997).
Curve-Fitting and Magic Beans
Until recently, what distinguished statistics from the other branches of
mathematics was that at least one aspect of each analysis was firmly
grounded in reality. Samples were drawn from real populations and, in
theory, one could assess and validate findings by examining larger and
larger samples taken from that same population.
In this reality-based context, modeling has one or possibly both of the
following objectives:
1. To better understand the mechanisms leading to particular
responses.
2. To predict future outcomes.
Failure to achieve these objectives has measurable losses. While these losses
cannot be eliminated because of the variation inherent in the underlying
processes, it is hoped that by use of the appropriate statistical procedure,
they can be minimized.
By contrast, the goals of curve fitting (nonparametric or local regres-
sion)
3
are aesthetic in nature; the resultant graphs, though pleasing to the
eye, may bear little relation to the processes under investigation. To quote
Green and Silverman [1994, p. 50], “there are two aims in curve estima-
tion, which to some extent conflict with one another, to maximize
goodness-of-fit and to minimize roughness.”
3
See, for example Green and Silverman [1994] and Loader [1999].
