Digital Signal Processing Reference
In-Depth Information
6
4
4
2
2
0
0
−
2
−
2
−
4
−
4
−
6
50
100
150
20
40
60
80
100
120
Observed eye height (mV)
Observed eye width (ps)
(a)
Standardized Eye Height Residuals
Standardized Eye Width Residuals
10
10
8
6
5
4
2
0
0
0
2
4
4
2
0
2
4
−
4
−
2
−
−
No. of standard deviations from mean
No. of standard deviations from mean
(b)
Figure 14-3
Residuals for the response surface model: (a) scatterplots of residuals (
e
H
,
e
W
) versus actuals (
y
H
,
y
W
); (b) standardized residual histograms (
d
H
,
d
W
).
Case Study Application
The residuals for our model are summarized in
columns 11 and 12 of Table 14-3 and are plotted against the observed responses
in Figure 14-3a, while the histograms of standardized residuals are shown in
Figure 14-3b. The residual scatterplot shows no apparent correlation to the
responses observed, and the histogram meets our expectation that it be normally
distributed with zero mean and residuals that lie within 3 standard deviations
of the mean. So the residuals give us our first indication that we have a good
model.
14.4.2 Fit Coefficients
A common metric for the quality of model fit is the coefficient of multiple
determination,
R
2
. It describes the amount of variability of the response that is
explained by the model, and is equal to the ratio of the model sum of squares to
the total sum of squares:
SS
model
SS
total
SS
error
SS
total
R
2
=
=
1
−
(14-16)
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