Digital Signal Processing Reference
In-Depth Information
TABLE 14-6.
F
-Test Results for the Model Fit Example
Eye Height
Eye Width
Sum of
Mean
F
-Ratio
Sum of
Mean
F
-Ratio
Source
dF
Squares
Square
Squares
Square
Model
20
28,435.56
1,421.78
138.568
5,344.06
267.203
29.869
Error
7
71.823
10.26
62.62
8.946
Total
27
28,507.381
5,406.679
=
F
0
.
25
,
20
,
7
3
.
445
TABLE 14-7. Summary of Model Fit and Significance Criteria
Metric
Criteria
R
2
≥
0
.
95
R
adj
≥
0
.
90
RMSE
<
Range(
y
)/10
Residuals
Normally distributed
Mean
=
0
Residuals within mean
±
3 standard deviations
F
0
≥
F
α,k,n
−
k
−
1
in the model have a significant effect on the response. To so do, we again use a
hypothesis test. In this case, the hypotheses that we test are
H
0
:
β
i
=
0
(14-26)
H
1
:
β
i
=
0
We can perform the test on any or all of the coefficients in the model. In essence,
failure to reject the null hypothesis for a given model term means that the term
can be deleted without significantly degrading the predictive capability of the
model. The
t
-statistic used to test the hypothesis is
b
i
b
i
SE
i
t
0
i
=
σ
2
C
ii
=
(14-27)
where
t
0
i
is the
t
-statistic for the
i
th term in the model;
b
i
is the estimated fit
coefficient for the
i
th term;
C
ii
is the diagonal element of the covariance matrix
(
X
T
X
)
−
1
, which corresponds to
b
i
; and
σ
2
is the estimated variance of the model
error, which is equal to the ratio of the sum of squares of the error and its
associate degrees of freedom:
SS
error
dF
error
σ
2
ˆ
=
(14-28)
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