Information Technology Reference
In-Depth Information
z
Fitted values
1
.8
.6
.4
.2
0
-.2
0
2
x
FIGURE 9.2
Fitting an Inappropriate Model.
Again, the best rule of all is not to let statistics do your thinking for
you, but to inquire into the mechanisms that give rise to the data and that
might account for the relationship between the variables
X
and
Y
. An
example taken from physics is the relationship between volume
V
and
temperature
T
of a gas. All of the preceding four models could be used to
fit the relationship. But only one, the model
V
=
a
+
KT
, is consistent
with Kinetic Molecular Theory.
Inappropriate Models
An example in which the simpler, more straightforward model is
not correct comes when we try to fit a straight line to what is
actually a higher-order polynomial. For example, suppose we tried
to fit a straight line to the relationship
Y
= (
X
- 1)
2
over the range
X
= (0,+2). We'd get a line with slope 0 similar to that depicted in
Figure 9.2. With a correlation of 0, we might even conclude in error
that
X
and
Y
were not related. Figure 9.2 suggests a way we can avoid
falling into a similar trap.
Always plot the data before deciding on a
model.
