Note that the average number of earned runs per inning pitched is multiplied by nine, the number of innings in a regulation game. thus, era represents the average number of runs the pitcher gives up per nine innings. for instance, in 2008, roy halladay, a pitcher for the toronto blue jays, pitched 246 innings and gave up 76 earned runs; his era was (76/246)9 = 2.78. to investigate the relationship between era and other measures of pitching performance, data for 50 major league baseball pitchers for the 2008 season appear in the data set named mlbpitching (mlb website, february 2009). descriptions for variables which appear on the data set follow:
w no. of games wonl no. of games lostwpct % of games wonh/9 average no. of hits given up/minhr/9 average no. of home runs given up/nine inningsbb/9 average no. of bases on balls given up/min
enter negative values as negative, if necessary. a. develop an estimated regression equation that can be used to predict the earned run average given the average number hits given up per nine innings (to 2 decimals).era = + h/9b. develop an estimated regression equation that can be used to predict the earned run average given the average number hits given up per nine innings, the average number of home runs given up per nine innings, and the average number of bases on balls given up per nine innings (to 3 decimals).era = + h/9 + hr/9 + bb/9c. at the .05 level of significance, test whether the two independent variables added in part (b), the average number of home runs given up per nine innings and the average number of bases on ball given up per nine innings, contribute significantly to the estimated regression equation developed in part (a) (to 2 decimals).player team w l wpct era h/9 hr/9 bb/9r halladay tor 20 11 0.645 2.78 8.05 0.66 1.43j santana nym 16 7 0.696 2.53 7.92 0.88 2.42c hamels phi 14 10 0.583 3.09 7.65 1.11 2.10t lincecum sf 18 5 0.783 2.62 7.22 0.44 3.33b webb ari 22 7 0.759 3.3 8.20 0.52 2.59c lee cle 22 3 0.88 2.54 8.63 0.48 1.37a burnett tor 18 10 0.643 4.07 8.59 0.77 3.50e santana laa 16 7 0.696 3.49 8.14 0.95 1.93m buehrle cws 15 12 0.556 3.79 9.90 0.91 2.14m cain sf 8 14 0.364 3.76 8.54 0.79 3.77d haren ari 16 8 0.667 3.33 8.50 0.79 1.67j shields tb 14 8 0.636 3.56 8.71 1.00 1.67r nolasco fla 15 8 0.652 3.52 8.15 1.19 1.78a cook col 16 9 0.64 3.96 10.06 0.55 2.05d lowe lad 14 11 0.56 3.24 8.27 0.60 1.92j lester bos 16 6 0.727 3.21 8.65 0.60 2.83g meche kc 14 11 0.56 3.98 8.74 0.81 3.13r oswalt hou 17 10 0.63 3.54 8.60 0.99 2.03j vazquez cws 12 16 0.429 4.67 9.26 1.08 2.64r dempster chc 17 6 0.739 2.96 7.59 0.61 3.32g floyd cws 17 8 0.68 3.84 8.30 1.31 3.06p maholm pit 9 9 0.5 3.71 8.78 0.92 2.75t lilly chc 17 9 0.654 4.09 8.24 1.41 2.82a pettitte nyy 14 14 0.5 4.54 10.28 0.84 2.43z greinke kc 13 10 0.565 3.47 9.00 0.94 2.49s olsen fla 8 11 0.421 4.2 8.72 1.34 3.09j verlander det 11 17 0.393 4.84 8.73 0.81 3.90c billingsley lad 16 10 0.615 3.14 8.45 0.63 3.60f hernandez sea 9 11 0.45 3.45 8.90 0.76 3.60m pelfrey nym 13 11 0.542 3.72 9.40 0.54 2.88m mussina nyy 20 9 0.69 3.37 9.63 0.76 1.39b arroyo cin 15 11 0.577 4.77 9.86 1.31 3.06k lohse stl 15 6 0.714 3.78 9.50 0.81 2.21b looper stl 12 14 0.462 4.16 9.77 1.13 2.04u jimenez col 12 12 0.5 3.99 8.26 0.50 4.68b sheets mil 13 9 0.591 3.09 8.22 0.77 2.14j saunders laa 17 7 0.708 3.41 8.50 0.95 2.41j garland laa 14 8 0.636 4.9 10.87 1.06 2.71j moyer phi 16 7 0.696 3.71 9.13 0.92 2.85e volquez cin 17 6 0.739 3.21 7.67 0.64 4.27j danks cws 12 9 0.571 3.32 8.40 0.69 2.63g maddux lad 8 13 0.381 4.22 9.46 0.97 1.39o perez nym 10 7 0.588 4.22 7.75 1.11 4.87n blackburn min 11 11 0.5 4.05 10.44 1.07 1.82a sonnanstine tb 13 9 0.591 4.38 9.88 0.98 1.72t wellemeyer stl 13 9 0.591 3.71 8.38 1.18 2.92j guthrie bal 10 12 0.455 3.63 8.33 1.14 2.74g smith oak 7 16 0.304 4.16 8.00 0.99 4.12r wolf hou 12 12 0.5 4.3 9.04 0.99 3.36b myers phi 10 13 0.435 4.55 9.33 1.37 3.08