STAT 501
Final Exam Solutions and Comments
Spring 2001
1. a. (3 points)
(1.49/7) x 100%
=
21.3%
b.
(3 points)
0
c.
(3 points)
0.89
=
3.82
(0.453)
d.
(3 points)
3.82
=
1
^
λ
e.
(5 points)
The formula for the scores use the standardized values of the measured traits,
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
77
7
7j
66
6
6j
55
5
5j
44
4
4j
33
3
3j
22
2
2j
11
1
1j
j
1
s
X
X
0.434
s
X
X
0.453
s
X
X
0.453
s
X
X
0.435
s
X
X
0.294
s
X
X
0.211
s
X
X
0.285
Y
ˆ
This is an overall size component with more emphasis on body length and height
measurements than on head size measurements.
This component accounts for about 54.6%
of the total variance of the standardized measurements.
f.
(5 points)
The second principal component compares head size with length of body
measurements.
It assumes large positive values for tall criminals with relatively small
heads, and it assumes extreme negative values for short criminals with relatively large
heads.
This component accounts for about 21.3% of the total variance of the standardized
measurements.
The third principal component is a head shape component that compares head length with
head width.
It assumes large positive values for criminals with relatively long and narrow
heads, and it assumes extreme negative values for criminals with relatively short and wide
heads.
This component accounts for about 9.3% of the total variance of the standardized
measurements.
g.
(3 points)
The first principal component corresponds to the positive correlations between all of
the measurements.
The higher loadings of the body length measurements on the first
component reflects that correlations among the body length measurements are stronger than
1
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The second principal component
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 Fall '09
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 Normal Distribution, Covariance matrix, Estimation of covariance matrices

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