STAT 2509 C Assignment #4 DUE DATE: Wednesday, March 23, 2016 (to be submitted in class) 1. Suppose we are interested in predicting of surgery survival rate as a function of x1 = blood clotting score, x2 = prognostic index, x3 = enzyme function test score, x4 = liver function test score and y= log(surgery survival rate). The TSS for the full model y = 0 + 1 x1 + 2 x2 + 3 x3 + 4 x4 + is : TSS = 21.07733. We decided to screen the independent variables to determine the best set for predicting the surgery rates. The sums of squares for all possible regression models were found to be as follows: MSE Independent variables SSR SSE d.f. SSE in the model ________________________________________________________________ X1 X2 X3 X4 X1, X2 X1, X3 X1, X4 X2, X3 X2, X4 X3, X4 X1, X2, X3 X1, X2, X4 X1, X3, X4 X2, X3, X4 X1, X2, X3 ,X4 2.52720 7.39311 9.33966 11.10557 12.76391 13.62588 11.11514 17.13462 13.67307 14.47288 20.49376 13.68169 15.16439 18.60417 20.49413 18.55013 13.68422 11.73767 9.97176 8.31342 7.45145 9.96219 3.94271 7.40426 6.60445 0.58357 7.39564 5.91294 2.47316 0.5832 52 52 52 52 51 51 51 51 51 51 50 50 50 50 49 0.3567332 0.263158 0.2257244 0.1917646 0.1630082 0.1461068 0.195337 0.077308 0.1451815 0.129499 0.0116714 0.1479128 0.1182588 0.0494632 0.011902 (a) Determine the subset of variables that is selected as best by the Forward Selection Procedure using F0* = 4.2 (to-add-variable). Show your steps. (b) Determine the subset of variables that is selected as best by the Backward Elimination Procedure using F0** = 4.1 (to-delete-variable). Show your steps. NOTE: ( t0** ) 2 = F0** (c) Determine the subset of variables that is selected as best by the Stepwise Regression Procedure using F0* = 4.2 (to-add) and F0** = 4.1 (to-delete). Show your steps. 1 2. A large company buys thousands of lightbulbs every year. The company is currently considering four brands of lightbulbs to choose from. Before the company decides which lightbulb to buy, it wants to investigate if the mean lifetimes of the four types of lightbulbs are the same. The company's research department randomly selected a few bulbs of each type and tested them. The following table lists the number of hours (in thousands) that each of the bulbs in each brand lasted before being burned out: Brand I 23 24 19 26 22 23 25 Brand II Brand III 19 23 18 24 20 22 19 23 27 25 26 23 21 27 Brand IV 26 24 21 29 28 24 28 Establish whether the mean lifetimes are the same for the four brands of lightbulbs; if not, do a follow-up analysis to determine which are the same and which differ. (Use =0.10). List all necessary assumptions and indicate which might be suspect. Also perform a non-parametric analysis. Verify your results using SAS. 3. An experiment is conducted to compare four different mixtures of the components oxidizer, binder and fuel used in the manufacturing of rocket propellant. To compare the four mixtures, five samples of propellant are prepared from each mixture and readied for testing. Each of five investigators is randomly assigned one sample of each of the four mixtures and asked to measure the propellant thrust. These data are summarized bellow: _ Investigator_________________________ Mixture 1 2 3 4 5 1 2 3 4 2 340 2 658 2 449 2 403 2 355 2 650 2 458 2 410 2 362 2 665 2 432 2 418 2 350 2 640 2 437 2 397 2 348 2 653 2 445 2 405 Is it possible to be 99% certain that the propellant samples from four different mixtures are not equal? Conduct the appropriate follow-up analysis (use =0.01) to establish which means are significantly different. List all necessary assumptions and indicate which might be suspect. Also perform a non-parametric analysis. Verify your results using SAS. Note: Remember to put a FOOTNOTE statement with your name and student number in the first line of your program. Submit both your program and your output, with the appropriate measures highlighted. Submit only the required output when possible. 2