Use the football data in Exercise 12-21 to build regression models using the following techniques:

(a) All possible regressions. Find the equations that minimize MS_E and that minimize C_p.

(b) Stepwise regression.

(c) Forward selection.

(d) Backward elimination.

(e) Comment on the various models obtained. Which model seems €œbest,€™€™ and why?

Exercise 12-21

Table E12-11 presents quarterback ratings for the 2008 National Football League season (The Sports Network).

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Yds per Rating Pet Pet Pet Comp Comp Team Player Philip Att Yds Att TD Lng Int Int Pts Rivers SD 478 312 65.3 4,009 8.39 34 7.1 67 11 2.3 105.5 Chad Pennington MIA 476 321 67.4 3,653 7.67 19 4.0 80 1.5 97.4 Kurt 598 5.0 Warner ARI 401 67.1 4,583 7.66 30 79 14 2.3 96.9 Drew Brees NO 635 413 65 5,069 7.98 34 5.4 84 17 2.7 96.2 66.8 7.21 Peyton Manning IND 555 371 4,002 27 4.9 75 12 2.2 95 4,038 Aaron Rodgers GB 536 341 63.6 7.53 28 5.2 71 13 2.4 93.8 HOU 3,043 8.01 Matt Schaub 380 251 66.1 15 3.9 65 10 2.6 92.7 Tony DAL 276 61.3 Romo 450 3,448 7.66 26 5.8 75 14 3.1 91.4 2,712 Jeff Garcia TB 376 244 64.9 7.21 12 3.2 71 1.6 90.2 Cassel NE 3,693 Matt 516 327 63.4 7.16 21 4.1 76 11 2.1 89.4 Matt Ryan ATL 434 265 61.1 3,440 7.93 16 3.7 70 11 2.5 87.7 2,046 87.5 Shaun Hill SF 288 181 62.8 7.10 13 4.5 48 2.8 Wallace Seneca SEA 242 141 58.3 1,532 6.33 11 4.5 90 1.2 87 Manning Eli NYG 479 289 60.3 3,238 6.76 21 4.4 48 10 2.1 86.4 Donovan MeNabb PHI 571 345 60.4 3,916 6.86 23 4.0 90 11 1.9 86.4 DEN 7.35 Jay Cutler 616 384 62.3 4,526 25 4.1 93 18 2.9 86 BUF Trent Edwards 374 245 65.5 2,699 7.22 11 2.9 65 10 2.7 85.4 Jake Delhomme CAR 414 246 59.4 3,288 7.94 15 3.6 65 12 2.9 84.7 Jason Campbell WAS 506 315 62.3 3,245 6.41 13 2.6 67 1.2 84.3 David 2.8 Garrard JAC 535 335 62.6 3,620 6.77 15 41 13 2.4 81.7 522 3,472 6.65 Brett Favre NYJ 343 65.7 22 4.2 56 22 4.2 81 Joe Flacco BAL 428 257 60 2,971 6.94 14 3.3 70 12 2.8 80.3 Kerry Collins TEN 415 242 58.3 2,676 6.45 12 2.9 56 1.7 80.2 Roethlisberger PIT Ben 469 281 59.9 3,301 7.04 17 3.6 65 15 3.2 80.1 Kyle Orton CHI 465 272 58.5 2,972 6.39 18 3.9 65 12 2.6 79.6 6.58 JaMarcus Russell OAK 368 198 53.8 2,423 13 3.5 84 2.2 77.1 Tyler Thigpen KC 420 230 54.8 2,608 6.21 18 4.3 75 12 2.9 76 Gus Frerotte MIN 301 178 59.1 2,157 7.17 12 4.0 99 15 5.0 73.7 Dan Orlovsky DET 255 143 56.1 1,616 6.34 3.1 96 8. 3.1 72.6 251 Marc Bulger STL 440 57 2,720 6.18 11 2.5 80 13 3.0 71.4 Ryan Fitzpatrick 1,905 5.12 CIN 372 221 59.4 8. 2.2 79 9. 2.4 70 Derek CLE Anderson 283 142 50.2 1,615 5.71 3.2 70 2.8 66.5