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

(a) Fit a multiple regression model to relate the quarterback rating to the percentage of completions, the percentage of TDs, and the percentage of interceptions.

(b) Estimate σ².

(c) What are the standard errors of the regression coefficients?

(d) Use the model to predict the rating when the percentage of completions is 60%, the percentage of TDs is 4%, and the percentage of interceptions is 3%.

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Yds per At Pct Rating Int Pts Pct Pet TD TD Player Philip Team tt Comp Comp Yds Lng Int 7.1 65.3 4,009 8.39 Rivers SD 478 312 34 67 11 2.3 105.5 Chad 67.4 Pennington MIA 476 321 3,653 7.67 19 4.0 80 1.5 97.4 96.9 Kurt Warner ARI 598 401 67.1 4,583 7.66 30 5.0 79 14 2.3 Drew Brees NO 635 413 65 5,069 7.98 34 5.4 84 17 2.7 96.2 371 66.8 Peyton Manning IND 555 4,002 7.21 27 4.9 75 12 2.2 95 GB 341 Aaron Rodgers 536 63.6 4,038 7.53 28 5.2 71 13 2.4 93.8 Matt Schaub HOU 380 251 66.1 3,043 8.01 15 3.9 65 10 2.6 92.7 DAL 7.66 Tony Jeff Romo 450 276 61.3 3,448 26 5.8 75 14 3.1 91.4 376 TB 2,712 7.21 1.6 Garcia 244 64.9 12 3.2 71 6. 90.2 89.4 Matt Cassel NE 516 327 63.4 3,693 7.16 21 4.1 76 11 2.1 Matt 16 Ryan ATL 434 265 61.1 3,440 7.93 3.7 70 11 2.5 87.7 Hill SF Shaun 288 181 62.8 2,046 7.10 13 4.5 48 8. 2.8 87.5 1,532 Seneca Wallace SEA 242 141 58.3 6.33 11 4.5 90 3 1.2 87 Eli NYG 3,238 Manning 479 289 60.3 6.76 21 4.4 48 10 2.1 86.4 PHI Donovan McNabb 571 345 60.4 3,916 6.86 23 4.0 90 11 1.9 86.4 Cutler DEN Jay 616 384 62.3 4,526 7.35 25 4.1 93 18 2.9 86 Trent Edwards BUF 374 245 65.5 2,699 7.22 11 2.9 65 10 2.7 85.4 Delhomme 7.94 Jake CAR 414 246 59.4 3,288 15 3.6 65 12 2.9 84.7 2.6 62.3 Jason Campbell WAS 506 315 3,245 6.41 13 67 6. 1.2 84.3 Garrard David JAC 535 335 62.6 3,620 6.77 15 2.8 41 13 2.4 81.7 343 Brett Favre NYJ 522 65.7 3,472 6.65 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 2,676 Kerry Collins TEN 415 242 58.3 6.45 12 2.9 56 1.7 80.2 Roethlisberger PIT 281 3.6 Ben 469 59.9 3,301 7.04 17 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 JaMarcus Russell OAK 368 198 53.8 2,423 6.58 13 3.5 84 8. 2.2 77.1 Tyler 420 Thigpen KC 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 8. 3.1 96 8. 3.1 72.6 Bulger Marc STL 440 251 57 2,720 6.18 11 2.5 80 13 3.0 71.4 Ryan Fitzpatrick CIN 372 221 59.4 1,905 5.12 8. 2.2 79 9. 2.4 70 Derek Anderson CLE 283 142 50.2 1,615 5.71 9. 3.2 70 8. 2.8 66.5 Attempts (number of pass attempts) Completed passes Pet Comp Percentage of completed passes Pet TD Long Int Pet Int Rating Pts Rating points Att Percentage of attempts that are touchdowns | Comp Longest pass completion Yards gained passing Yds per Att Yards gained per pass attempt| Number of interceptions Percentage of attempts that are interceptions Yds Number of touchdown passes TD