06.05.1
Chapter 06.05
Adequacy of Models for Regression
Quality of Fitted Model
In the application of regression models, one objective is to obtain an equation
)
(
x
f
y
=
that best describes the
n
response data points
)
,
(
),
.......
,
,
(
),
,
(
2
2
1
1
n
n
y
x
y
x
y
x
.
Consequently, we are faced with answering two basic questions.
1.
Does the model
)
(
x
f
y
=
describe the data adequately, that is, is there an adequate
fit?
2.
How well does the model predict the response variable (predictability)?
To answer these questions, let us limit our discussion to straight line models as
nonlinear models require a different approach.
Some authors [1] claim that nonlinear model
parameters are not unbiased.
To exemplify our discussion, we will take example data to go through the process of
model evaluation.
Given below is the data for the coefficient of thermal expansion vs.
temperature for steel.
We assume a linear relationship between the data as
T
a
a
T
1
0
)
(
+
=
α
Table 1
Values of coefficient of thermal expansion vs. temperature.
F)
(
T
F)
μin/in/
(
α
-340
-260
-180
-100
-20
60
2.45
3.58
4.52
5.28
5.86
6.36
Following the procedure for conducting linear regression as given in Chapter 06.03, we get
T
T
0096964
.
0
0325
.
6
)
(
+
=
α
Let us now look at how we can evaluate the adequacy of a linear regression model.
1. Plot the data and the regression model.
Figure 1 shows the data and the regression model.
From a visual check, it looks like the
model explains the data adequately.

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