PractFinalExam - Spring 2007 - STA 4702/5701 - Practice...

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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 two-dimensional graphical illustration of principal components for a two variable problem. 1
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2. 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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PractFinalExam - Spring 2007 - STA 4702/5701 - Practice...

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