Information Technology Reference
In-Depth Information
Chapter 9
Univariate Regression
Are the data adequate? Does your data set cover the entire range
of interest? Will your model depend on one or two isolated data
points?
T HE SIMPLEST EXAMPLE OF A MODEL, THE RELATIONSHIP between exactly two
variables, illustrates at least five of the many complications that can inter-
fere with the task of model building:
1. Limited scope—the model we develop may be applicable for only a
portion of the range of each variable.
2. Ambiguous form of the relationship—a variable may give rise to
a statistically significant linear regression without the underlying
relationship being a straight line.
3. Confounding—undefined confounding variables may create the
illusion of a relationship or may mask an existing one.
4. Assumptions—the assumptions underlying the statistical proce-
dures we use may not be satisfied.
5. Inadequacy—goodness of fit is not the same as prediction.
We consider each of these error sources in turn along with a series of pre-
ventive measures. Our discussion is divided into problems connected with
model selection and difficulties that arise during the estimation of model
coefficients.
MODEL SELECTION
Limited Scope
Almost every relationship has both a linear and a nonlinear portion where
the nonlinear portion is increasingly evident for both extremely large and
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