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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