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Refer to the Prostate cancer data set in Appendix C.5 and Case-Study 9.30. Select a random sample of 65 observations to use as the model-building data set.
a. Develop a regression tree for predicting PSA. Justify your choice of number of regions (tree size), and interpret your regression tree.
b. Assess your model's ability to predict and discuss its usefulness to the oncologists.
c. Compare the performance of your regression tree model with that of the best regression model obtained in Case Study 9.30. Which model is more easily interpreted and why?
Case-Study 9.30
Refer to the Prostate cancer data set in Appendix C5. Serum prostate-specific antigen (PSA) was determined in 97 men with advanced prostate cancer. PSA is a well-established screening test for prostate cancer and the oncologists wanted to examine the correlation between level of PSA and a number of clinical measures for men who were about to undergo radical prostatectomy. The measures are cancer volume, prostate weight. patient age, the amount of benign prostatic hyperplasia. seminal vesicle invasion, capsular penetration, and Gleason score. Select a random sample of 65 observations to use as the model-building data set. Develop a best subset model for predicting PSA. Justify your choice of model. Assess your model's ability to predict and discuss its usefulness to the oncologists.
Appendix C5
A university medical center urology group was interested in the association between prostate-specific antigen (PSA) and a number of prognostic clinical measurements in men with advanced prostate cancer. Data were collected on 97 men who were about to undergo radical prostectomies. Each line of the data set has an identification number and provides information on 8 other variables for each person. The 9 variables are:
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This task provides a clear working example of constructing a regression tree, Regression tree, also known as classification tree, normally used in many data mining situations. Classification tree analysis is one of the main techniques used in Data Mining. The goal of classification trees is to predict or explain responses
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31 6.821 1.3364 59.740 65 7.0993 0 0.4493 6 32 7.463 1.1972 450.339 65 5.4739 0 0.0000 6 33 7.463 3.5966 20.905 71 3.5609 0 0.0000 6 34 7.538 1.0101 26.311 54 0.0000 0 0.0000 6 35 7.768 0.9900 25.028 63 0.0000 0 0.4493 6 36 8.085 3.7062 61.559 64 8.7583 0 0.0000 7 37 8.671 4.1371 38.861 73 0.5599 0 5.2593 8 38 8.935 1.5841 10.697 64 0.0000 0 0.0000 7 39 9.116 14.2963 59.740 68 3.9354 1 6.2339 7 40 9.777 2.2255 20.287 56 2.5600 0 0.8521 7 41 9.974 1.8589 23.104 60 0.0000 0 0.0000 8 42 10.074 4.2207 39.646 68 0.0000 0 0.0000 7 43 10.278 1.7860 47.942 62 5.5290 0 0.6505 6 44 10.697 5.8709 49.402 61 0.0000 0 2.2479 7 45 12.429 4.4371 30.265 66 5.7546 0 0.6505 7
16 4.263 4.6646 21.328 66 0.0000 0 0.0000 6 17 4.349 0.6570 33.784 70 3.4556 0 0.5488 7 18 4.437 9.8749 38.475 66 0.0000 0 1.4477 6 19 4.759 0.5712 26.311 41 0.0000 0 0.0000 6 20 4.953 1.1972 46.063 70 5.2593 0 0.0000 7 21 5.155 3.1582 30.569 59 0.0000 0 0.0000 6 22 5.259 7.8460 33.115 60 4.3492 0 3.8574 7 23 5.474 0.5827 29.371 59 0.4493 0 0.0000 6 24 5.529 5.9299 31.500 63 1.5527 0 3.2544 7 25 5.641 1.4770 39.252 69 4.9530 0 0.0000 6 26 5.871 4.2631 22.646 68 1.3499 0 0.0000 6 27 6.050 1.6653 41.264 65 0.0000 0 0.4493 7 28 6.172 0.6703 47.942 67 6.1719 0 0.0000 7 29 6.360 2.8292 22.874 67 1.2461 0 1.0513 7 30 6.619 11.1340 29.371 65 0.0000 0 5.0531 6
1 0.651 0.5599 15.959 50 0.0000 0 0.0000 6 2 0.852 0.3716 27.660 58 0.0000 0 0.0000 7 3 0.852 0.6005 14.732 74 0.0000 0 0.0000 7 4 0.852 0.3012 26.576 58 0.0000 0 0.0000 6 5 1.448 2.1170 30.877 62 0.0000 0 0.0000 6 6 2.160 0.3499 25.280 50 0.0000 0 0.0000 6 7 2.160 2.0959 32.137 64 1.8589 0 0.0000 6 8 2.340 1.9937 34.467 58 4.6646 0 0.0000 6 9 2.858 0.4584 34.467 47 0.0000 0 0.0000 7 10 2.858 1.2461 25.534 63 0.0000 0 0.0000 6 11 3.561 1.2840 36.598 65 0.0000 0 0.0000 6 12 3.561 0.2592 36.598 63 3.5609 0 0.0000 6 13 3.561 5.0028 20.491 63 0.0000 0 0.5488 7 14 3.857 4.3929 20.086 67 0.0000 0 0.0000 7 15 4.055 3.3535 31.187 57 0.0000 0 0.6505 7
Basing ?ndings on 60 successful pregnancies involving natural birth, an experimenter found that the mean pregnancy term was 274 days, with a standard deviation of 14 days. Construct a 99% con?dence interval for the true mean pregnancy term μ.
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