Digital Signal Processing Reference
In-Depth Information
TABLE 14-5. Summary of Model Fit Results
Eye Height
Eye Width
SS
error
71.823
62.62
SS
model
28,435.558
5344.06
SS
total
28,507.381
5406.68
R
2
0.9975
0.9884
R
adj
0.9899
0.9537
RMSE
3.203
2.991
Range
130.97
52.00
Case Study Application
For our example the degrees of freedom are dF
total
=
27
and dF
error
7. The coefficient calculations are shown in Table 14-5, includ-
ing the sum-of-squares terms. We can calculate the RMSE metrics from the
sum-of-squares values in Table 14-5 and extract the ranges of observed responses
from Table 14-3. The RMSE values are 3.203 mV and 2.991 ps for eye height
and width, respectively, while the corresponding ranges from Table 14-3 are
130.97mV and 52.00 ps. The calculated values of
R
2
,
R
adj
, and RMSE for our
example system all meet the fit criteria for both eye height and width.
=
14.5 SIGNIFICANCE TESTING
Thus far we have shown that our response surface model fits the data. A good
fit does not, however, guarantee that the model has a significant impact on the
response of the system, nor does it indicate that all of the model terms are
statistically significant. Drawing conclusions about the significance of the model
is a matter of determining whether or not the model equation is meaningful
compared with the error. Stated in simple terms, the significance of a model
term determines whether or not the term can be removed from the model without
degrading the results. Answering these questions requires the use of tests for
the significance of the model (
F
-test) and of the individual model coefficients
(
t
-test).
14.5.1 Model Significance: The
F
-Test
To test the significance of the regression, we first calculate the
F
-ratio:
SS
model
/
dF
model
SS
error
/
dF
error
=
F
0
(14-23)
The
F
-ratio is used to determine whether or not any of the model inputs contribute
significantly to the model. In other words, the test for significance of regression
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