Graphics Programs Reference
In-Depth Information
PROBLEM SET 3.2
Instructions
Plot the datapoints and the fitting functionwhenever appropriate.
1. Show that the straight lineobtainedbyleast-squares fitofunweighteddataalways
passes through the point(
x
,
y
).
2.
Use linear regression to find the linethat fits the data
x
−
1
.
0
−
0
.
5
0
0
.
5
1
.
0
y
−
1
.
00
−
0
.
55
0
.
00
0
.
45
1
.
00
and determine the standard deviation.
3.
Three tensile tests werecarried outonanaluminum bar. In each test the strain
was measuredat the same values of stress. The results were
Stress (MPa)
34
.
5
69
.
0
103
.
5
138
.
0
Strain (Test 1)
0
.
46
0
.
95
1
.
48
1
.
93
Strain (Test 2)
0
.
34
1
.
02
1
.
51
2
.
09
Strain (Test 3)
0
.
73
1
.
10
1
.
62
2
.
12
where the units of strainaremm/m. Use linear regression to estimate themodulus
of elasticity of the bar (modulusofelasticity =stress/strain).
4.SolveProb. 3 assuming that the third test was performed onaninferiormachine,
so that its results carry only half the weight of the other two tests.
5.
Fit a straight line to the following data and compute the standard deviation.
x
0
0
.
5
1
1
.
5
2
2
.
5
y
3
.
076
2
.
810
2
.
588
2
.
297
1
.
981
1
.
912
x
3
3
.
5
4
4
.
5
5
.
.
.
.
.
y
1
653
1
478
1
399
1
018
0
794
6.
The table displays themass
M
andaveragefuel consumption
φ
ofmotorvehicles
φ
=
+
manufacturedbyFord and Honda in 1999. Fit a straight line
a
bM
to the
data and compute the standard deviation.
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