Graphics Programs Reference
In-Depth Information
10. The table displays thermalefficiencies of someearly steamengines. 6 Determine
thepolynomialthatprovides thebestfit to thedataanduse ittopredict the thermal
efficiencyinthe year 2000.
Year
Efficiency (%)
Type
1718
0
.
5
Newcomen
1767
0
.
8
Smeaton
1774
1
.
4
Smeaton
1775
2
.
7
Watt
1792
4
.
5
Watt
.
1816
7
5
Woolf compound
.
1828
12
0
ImprovedCornish
1834
17
.
0
ImprovedCornish
1878
17
.
2
Corliss compound
1906
23
.
0
Triple expansion
11.
The table shows the variation of the relative thermalconductivity k of sodium
with temperature T . Find the quadraticthat fits the datainthe least-squares
sense.
T ( C)
79
190
357
524
690
k
1
.
00
0
.
932
0
.
839
0
.
759
0
.
693
ax b be the least-squares fitofthedata ( x i ,
12. Let f ( x )
=
y i ), i
=
1
,
2
,...,
n , and let
F ( x )
=
ln a
+
b ln x be the least-squares fitof(ln x i ,
ln y i )—see Table 3.3. Prove
that R i r i /
y i , where the residuals are r i =
y i
f ( x i ) and R i =
ln y i
F ( x i ).As-
y i .
13. Determine a and b forwhich f ( x )
sumethat r i <<
=
a sin(
π
x
/
2)
+
b cos(
π
x
/
2) fits the following
datainthe least-squares sense.
x
0
.
5
0
.
19
0
.
02
0
.
20
0
.
35
0
.
50
y
3
.
558
2
.
874
1
.
995
1
.
040
0
.
068
0
.
677
6
Source: Singer, C.,Holmyard, E.J.,Hall, A.R., and Williams, T.H., AHistory of Technology ,Oxford
University Press, 1958.
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