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Spring 2007  STA 4702/5701  Practice Final Exam
Name:
Directions
: Please read all problems carefully. The exam is worth a total of 300 points. The
points for each problem are shown to the left. Good luck!
1.
Principal Components.
(a)
(20)
Write out the system of equations for the principal components for a two variable
(
X
1
,X
2
) problem.
(b)
(30)
List the three constraints that are used to solve for the coeﬃcients.
(c)
(20)
Draw a twodimensional graphical illustration of principal components for a two variable
problem.
1
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PCR and PLSR.
The results from a PCR on the
penta
data set are shown below.
Percent Variation Accounted for by Principal Components
Number of
Extracted
Model Effects
Dependent Variables
Factors
Current
Total
Current
Total
1
26.6287
26.6287
27.5658
27.5658
2
16.6775
43.3061
12.9949
40.5606
3
14.6891
57.9953
6.2947
46.8553
4
11.9836
69.9788
21.6112
68.4665
5
7.7781
77.7569
3.7982
72.2647
6
4.6176
82.3746
7.6959
79.9606
7
4.1984
86.5730
1.7188
81.6794
8
3.4299
90.0029
2.6699
84.3493
9
3.0657
93.0687
0.1702
84.5195
10
2.3696
95.4382
0.8501
85.3696
11
2.1619
97.6002
0.5082
85.8779
12
1.3956
98.9958
1.3728
87.2507
13
0.8081
99.8039
4.2639
91.5145
14
0.1951
99.9990
0.6533
92.1678
15
0.0010
100.0000
0.7637
92.9316
Cross Validation for the Number of Extracted Factors
Number of
Root
Extracted
Mean
Prob >
Factors
PRESS
T**2
T**2
0
1.034483
7.218584
0.0010
1
0.90721
5.279472
0.0060
2
0.858513
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 Spring '08
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