Information Technology Reference
In-Depth Information
y
Fitted values
1
.8
.6
.4
.2
0
-.2
0
2
x
FIGURE 9.1
A Straight Line Appears to Fit the Data.
function of the differences between what is observed,
y
i
, and what is pre-
dicted by the model,
Y
[
x
i
].
The coefficients a, b, g for all three models can be estimated by a tech-
nique known (to statisticians) as linear regression. Our knowledge of this
technique should not blind us to the possibility that the true underlying
model may require nonlinear estimation as in
Model IV:
Y
=
++
-
ab g
df
XX
X
2
+
e
.
This latter model may have the advantage over the first three in that it
fits the data over a wider range of values.
Which model should we choose? At least two contradictory rules
apply:
•
The more parameters, the better the fit; thus, Model III and
Model IV are to be preferred.
•
The simpler, more straightforward model is more likely to be
correct when we come to apply it to data other than the observa-
tions in hand; thus, Models I and II are to be preferred.
