Consider the multiple linear regression model fit to the baseball data in Problem 3.41.

Problem 3.41

Consider the 2016 major league baseball data in Table B.22. While team ERA0 was useful in predicting the number of games that a team wins, there are some other measures of team performance, including the number of strikeouts, the number of errors committed, and the number of runs allowed per game. Fit a multiple linear regression model to wins using team ERA, errors, strikeouts, and runs allowed per game as the regressor variables.

a. Find the value of the PRESS statistic and the $R^{2}$ based on PRESS for this model.

b. What conclusions can you draw about the ability of this model to accurately predict the number of wins?

c. Compare PRESS for this model to PRESS for the simple linear regression model from Problem 4.34. Has adding more regressors to the model improved the potential prediction performance of the model?

Transcribed Image Text:

Batter Pitcher Team Arizona Diamondbacks Atlanta Braves Baltimore Orioles Boston Red Sox Chicago Cubs Chicago White 78 Sox Cincinnati 68 Reds Cleveland 94 Indians Colorado 75 Rockies Detroit Tigers Houston 86 84 Astros Kansas City 81 Royals Los Angeles 74 Angels Los Angeles Dodgers 91 Miami Marlins Milwaukee 73 Yankees Brewers Minnesota Twins New York Mets New York Oakland A's 87 84 69 Philadelphia Phillies 71 Padres Pittsburgh Pirates San Diego Seattle Mariners San Francisco Giants 86 78 87 8 8 69 26.7 752 190 0.432 Wins Age Runs HRS SLG Age ERA SO HRA RA/G Errors 26.4 5.09 1318 202 5.49 101 68 28.9 649 122 0.384 89 28.5 744 253 0.443 26.4 279 4.51 1227 177 4.84 4.22 1248 183 4.41 93 28.5 878 208 0.461 29 4 1362 176 4.28 103 27.4 28.3 808 686 199 0.429 168 0.41 29.9 28.6 3.15 1441 163 3.43 4.1 1270 185 4.41 27.8 716 164 0.408 27.1 4.91 1241 258 5.27 102 29 777 185 0.43 28.1 3.84 1398 186 4.2 27.8 845 204 0.457 27.7 4.91 1223 181 5.31 29.9 750 211 0.438 26.4 724 198 0.417 29 28.9 4.24 1232 182 4.06 1396 181 4.48 4.33 28.5 675 147 0.4 29.9 4.21 1287 206 4.4 28.5 717 156 0.405 28.4 4.28 1136 208 4.49 28.9 725 189 0.409 28.9 3.7 1510 165 3.94 79 28.3 655 128 0.394 27.5 671 194 0.407 28 28.1 4.05 1379 152 4.08 1175 178 4.24 4.52 26.9 722 200 0.421 28.3 5.08 1191 221 5.49 29.5 671 218 0.417 28.4 3.57 1396 152 3.81 30.1 680 183 0.405 279 4.16 1393 214 4.33 28.7 653 169 0.395 26.9 610 161 0.384 279 4.51 1188 185 4.7 26.3 4.63 1299 213 4.91 28.9 729 153 0.402 28.6 4.21 1232 180 4.68 68 28.1 686 177 0.39 28.1 4.43 1222 183 4.75 8 c 8 101 80 75 101 95 89 110 75 77 94 97 80 86 136 126 90 86 97 97 111 109 30.5 768 223 0.43 28.8 4 1318 213 4.36 89 29.2 715 130 0.398 30 3.65 1309 158 3.9 72 St Louis 86 28.5 779 225 0.442 28 4.08 1290 159 4.4 107 Cardinals Tampa Bay 68 27.7 672 216 0.426 26.9 4.2 1357 210 4.4 94 Rays Texas Rangers 95 28.4 Toronto Blue 89 30 765 215 0.433 759 221 0.426 28.8 4.37 1154 201 4.67 97 29.8 3.78 1314 183 4.11 88 Jays Washington 95 28.8 763 203 0.426 29.1 3.51 1476 155 3.78 73 Nationals