Stat 462 April 5 1. Use the dataset prostatecancer.txt at www.stat.psu.edu/~rho/462data/. Dataset consists of n = 97 prostate cancer patients y = PSA_level, prostate specific antigen, a blood chemistry measurement affected by x1 x1 = CancerVol, cancer volume x2 = Capsular, a measure of the invasiveness of the cancer A. Fit the model E(y) = 0 + 1 x1 + 2 x2 Use the Storage button, Store Deleted t residuals, Hi (leverages), and DFITS, and FITS What is the estimated regression equation? What is the value of MSE? B. Do a dotplot of the Cook’s D values. Use Editor>Brush to help you identify any extreme values. What observation(s) have extreme Cook’s D values? C. Explain what (in general) is measured by a Cook’s D value. D. Do a dotplot of the DFITS. Identify any “extreme” points. (The book’s criterion for extreme is that absolute DFIT>1.) E Explain what (in general) is measured by a DFFIT value. F. Do a dotplot of the hi values. Identify any “extreme” points. The Minitab criterion for a large leverage is 3p/n. Use this as the definition of “extreme.” G. Do a dotplot of the deleted residuals. Identify any “extreme” data points. H. Graph PSA_level versus CancerVol. Identify any unusual points. I. Graph PSA_level versus Capsular. Identify any unusual points. J. What is the predicted value for observation 97? K. Delete observation 97 by replacing the y-value with an asterisk (by replacing the value of y with an asterisk). Recompute the regression equation. What is the predicted value for observation 97? What is the difference between this predicted value and the value found in the previous part? Note: This is the “unstandardized” version of a DFIT for observation 97. L. In addition to observation 97, delete observations 95 and 96. Re-run the regression, and then repeat part A based on this new regression. Describe differences between the two sets of results. 3. Use the dataset party200.txt. We’ll use logistic regression to predict the probability that a student would say they have ever driven under the influence of alcohol based on X= how many days per month they say they drink at least two beers. The underlying model of logistic regression for one X-variable is e 01X where p = probability of falling into a category of interest (saying yes to having driven p 1 e 01X under the influence. Use Stat>Regression>Binary Logistic Regression. Enter “DrvDrnk” as “Response” enter “DaysBeer” in the Model box, click Storage and click to Store “Event Probabilities” (item is on right side of dialog box). Then, use Graph>Plot to plot the stored event probabilities versus DaysBeer. A. Based on this plot, estimate the probability of ever having driven under the influence for DaysBeer = 0, DaysBeer=10, and DaysBeer = 20 B. What are the estimated values of 0 and 1? (See output in session window.) C. Use the equation given for the model to calculate predicted probabilities for DaysBeer = 0 and for DaysBeer=10.