Statistics_II_Week_6_Homework
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8.4 Elasticity of moissanite. Moissaniteis
popular abrasive material because of its extreme hardness. Another important property of moissanite is
elasticity. The elastic properties of
the material were investigated in the Journal of Applied Physics (September
1993). A diamond anvil cell was used to
compress a mixture of moissanite, sodium chloride, and gold in a ratio of
33.99:1 by volume. The compressed
volume, y, of the mixture (relative to the zero-pressure volume) was measured
at each of 11 different pressures (GPa).
The results are displayed in the table (p.397). A MINITAB printout for the straight-line
regression model
and a MINITAB residual plot are displayed at
left.
MOISSANITE
|
COMPRESSED
VOLUME y, %
|
PRESSURE x,
GPa
|
|
100
|
0
|
|
96
|
9.4
|
|
93.8
|
15.8
|
|
90.2
|
30.4
|
|
87.7
|
41.6
|
|
86.2
|
46.9
|
|
85.2
|
51.6
|
|
83.3
|
60.1
|
|
82.9
|
62.6
|
|
82.9
|
62.6
|
|
81.7
|
68.4
|
a.
Calculate
the regression residuals.
b.
Plot
the residuals against x. Do you detect a
trend?
c.
Propose
an alternative model based on the plot part b.
d.
Fit
and analyze the model you proposed in part c.
8.12 Fair market value of Hawaiian
properties. Prior to 1980, private
homeowners in Hawaii had to lease the land their homes were built on because
the law (dating back to the islands’ feudal period) required that land be owned
only by the big estates. After 1980,
however, a new law instituted condemnation proceedings so that citizens could
buy their own land. To comply with the
1980 law, one large Hawaiian estate wanted to use regression analysis to
estimate the fair market value of its land.
Its first proposal was the quadratic model
HAWAII
|
PROPERTY
|
LEASED FEE
VALUE
y, thousands
of dollars
|
SIZE
x, thousands
|
|
1
|
70.7
|
13.5
|
|
2
|
52.7
|
9.6
|
|
3
|
87.6
|
17.6
|
|
4
|
43.2
|
7.9
|
|
5
|
103.8
|
11.5
|
|
6
|
45.1
|
8.2
|
|
7
|
86.8
|
15.2
|
|
8
|
73.3
|
12.0
|
|
9
|
144.3
|
13.8
|
|
10
|
61.3
|
10.0
|
|
11
|
148.0
|
14.5
|
|
12
|
85.0
|
10.2
|
|
13
|
171.2
|
18.7
|
|
14
|
97.5
|
13.2
|
|
15
|
158.1
|
16.3
|
|
16
|
74.2
|
12.3
|
|
17
|
47.0
|
7.7
|
|
18
|
54.7
|
9.9
|
|
19
|
68.0
|
11.2
|
|
20
|
75.2
|
12.4
|
Where
Data collected
for 20 property sales in a particular neighborhood, given in the table above,
were used to fit the model. The least
squares prediction equation is
a.
Calculate
the predicted values and corresponding residuals for the model.
b.
Plot
the residuals versus
. Do
you detect any trends? If so what does the pattern suggest about the model?
c.
Conduct
a test for heteroscedasticity. [Hint: Divide the data into two subsamples,
,
and fit the model to both subsamples.]
d.
Based
on your results from parts b and c, how should the estate proceed?
8.20 Cooling method for gas turbines. Refer to the Journal of Egineering for Gas
Turbines and Power (January 2005) study of a high-pressure inlet fogging method
for a gas turbine engine, Exercise 8.11 (p.407). Use a residual graph to check the assumption
of normal errors for the interaction model for heat rate (y). Is the normality assumption reasonably
satisfied? If not suggest how to modify the model.
8.28 Modeling an employee’s work-hours
missed. A large manufacturing firm wants
to determine whether a relationship exists between y, the number of work-hours
an employee misses per year, and x, the employee’s annual wages. A sample of 15 employees produced the data in
the accompanying table.
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