Biochemical Reactions - A First Look
87
R has the rank 2; the last two rows are multiples of the second row. The reduced redundancy matrix is
thus found to be
Rr
1
0
1
1
1
0
-0.286
-0.286
0.143
0.014
(3)
At
D -
0.3 h"1
we have the following measured rates from Example 3.5
4 „
'-0.279^
-0.047
0.102
0.055
v 0.078 ;
The vector of residuals is then
* = Rr4 m
-0.0440
-0.0067
(4)
(5)
For the variance-covariance matrix we use the same measurement errors as in Example 3.10, i.e, 10% in
the gas measurements and 5% in the medium-based measurements. Consequently
and
(0.05 0.279)2
0
0
0
0
'
0
(0.1-0.047)2
0
0
0
0
0
(0.1 0.102)2
0
0
0
0
0
(0.05-0.055)2
0
,
0
0
0
0
(Ü.05 0.078)2,
P = RrF R /
0.321
-0.028'
1 -0.028
0.010
P_l
=105
0.041
0.111
0.111
1.260
Now we calculate the test function
h = e TF~le =
20.27
(6)
(7)
(
8
)
Comparison of the calculated
h
with the values of the X2 distribution for rank(R)= 2 shows that there is
an overwhelming probability that the data set contains significant deficiencies.
Since rank(R)= 2, it is possible to drop one of the measurements and still have an over-determined
system. We can therefore carry out the error diagnosis described above, i.e. delete one of the measured
rates at a time and calculate the test function. The results of this analysis give the test function for each
case, i.e., with each of the measured rates deleted from the analysis:
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