Refer to Prostate cancer Case Study 9.30. The regression model identified in Case Study 9.30 is to be validated by means of the validation d'1ta set consisting of those cases not selected for the model-building data set.
a. Fit the regression model identified in Case Study 9.30 to the validation data set. Compare the estimated regression coefficients and their estimated standard errors with those obtained in Case Study 9.30. Also compare the error mean square and coefficients of multiple de· termination. Does the model fitted to the validation data set yield similar estimates as the model fitted to the model-building data set?
b. Calculate the mean squared prediction error (9.20) and compare it to MSE obtained from the model-building data set. Is there evidence 01',1 substantial bias problem in MSE here?
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.
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: