E1C04 09/14/2010
14:7:44 Page 146
KNOWN N ¼ 5
ASSUMPTIONS Data related by E ¼ a þ bU
m
FIND a and b
SOLUTION The suggested functional equation can be transformed into
log E À a
ð
Þ¼log b þ mlogU
which has the linear form
Y ¼ B þ mX
Because at U ¼ 0 m/s, E ¼ 3.19 V, the value of a must be 3.19 V. The values for Y and X are
computed below with the corresponding deviations from the resulting fit of 4 values:
U
Y¼ log(E-a)
X ¼ log U
E i À E ci
0.0
—
—
0.0
10.0
À0.097
1.000
À0.01
20.0
0.045
1.301
0.02
30.0
0.111
1.477
0.0
40.0
0.164
1.602
À0.01
Substituting the values for Y and X into Equation 4.40 gives a 0 ¼ B ¼ À0.525 and a 1 ¼ m ¼ 0.43.
The standard error of the fit is found using Equation 4.35 to be s yx ¼ 0.007. From Table 4.4, t 2,95 ¼
4.30 so that t 2;95 s yx =
ffiffiffiffi
N
p ¼ 0.015. This gives the curve fit with confidence interval as
Y ¼ À0:525 þ 0:43X Æ 0:015 95%
ð
Þ
0
1 0
2 0
3 0
95%
confidence
interval
of fit
40
50
U, (ft/s)
E (V)
3.0
3.5
4.0
4.5
5.0
E = 3.19 + 0.3U
0.43
Figure 4.11 Curve fit for Example 4.10.
146 Chapter 4 Probability and Statistics