Statistics Ii Week 6 Homework

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 E(y)= β_0+ β_1 x   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


Calculate the regression residuals.
Plot the residuals against x.   Do you detect a trend?
Propose an alternative model based on the plot part b.
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

E(y)= β_0+ β_1 x+ β_2 x^2

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...