Biomedical Engineering Reference
In-Depth Information
can then be used to “build” a model or fine-tune the model parameters to predict yield at
a given temperature level. This model can also be used for process optimization, such as
finding the level of temperature that maximizes yield, or for process control purposes.
As an illustration, consider the data in
Table 7.1
generated in our lab. In this table,
y
is the
flow rate of water through a tube, and
x
is the percentage reading from a rotameter mounted
on the tube.
Figure 7.1
presents a scatter diagram of the data in
Table 7.1
. This is just a graph
on which each (
x
i
,
y
i
) pair is represented as a point plotted in a two-dimensional coordinate
system. We know for the fact that the rotameters are scaled linearly to reflect the flow rate for
a given fluid passing through it. Inspection of this scatter diagram confirms our knowledge
that, although no simple curve will pass exactly through all the points, there is a strong indi-
cation that the points lie scattered randomly around a straight line. Therefore, it is reasonable
to assume that the mean of the random variable
Y
is related to
x
by the following straight-line
relationship:
EðYjxÞ¼y ¼ a
0
þ a
1
x
(7.1)
TABLE 7.1
Water Flow Rates and Rotameter Readings
Observation number
Rotameter reading, %
Flow rates, g/s
1
5
0.3261
2
10
0.5912
3
15
0.8908
4
20
1.206
5
25
1.544
6
30
1.844
7
35
2.148
8
40
2.434
9
45
2.753
10
50
3.032
11
55
3.326
12
60
3.573
13
65
3.908
14
70
4.143
15
75
4.471
16
80
4.704
17
85
5.015
18
90
5.263
19
95
5.582
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