The number of victories W earned run average ERA runs scored

The number of victories (W), earned run average

(ERA), runs scored (R), batting average (AVG),

and on-base percentage (OBP) for each team in the

American League in the 2012 season are provided

in the following table. The ERA is one measure of

the effectiveness of the pitching staff, and a lower

number is better. The other statistics are measures of

effectiveness of the hitters, and higher numbers are

better for each of these.

Team W ERA R AVG OBP

Baltimore Orioles 93 3.90 712 0.247 0.311

Boston Red Sox 69 4.70 734 0.260 0.315

Chicago White Sox 85 4.02 748 0.255 0.318

Cleveland Indians 68 4.78 667 0.251 0.324

Detroit Tigers 88 3.75 726 0.268 0.335

Kansas City Royals 72 4.30 676 0.265 0.317

Los Angeles Angels 89 4.02 767 0.274 0.332

Minnesota Twins 66 4.77 701 0.260 0.325

New York Yankees 95 3.85 804 0.265 0.337

Oakland Athletics 94 3.48 713 0.238 0.310

Seattle Mariners 75 3.76 619 0.234 0.296

Tampa Bay Rays 90 3.19 697 0.240 0.317

Texas Rangers 93 3.99 808 0.273 0.334

Toronto Blue Jays 73 4.64 716 0.245 0.309

(a) Develop a regression model that could be used to

predict the number of victories based on the ERA.

(b) Develop a regression model that could be used to

predict the number of victories based on the runs

scored.

(c) Develop a regression model that could be used to

predict the number of victories based on the batting

average.

(d) Develop a regression model that could be used to

predict the number of victories based on the onbase

percentage.

(e) Which of the four models is better for predicting

the number of victories?

(f) Find the best multiple regression model to predict

the number of wins. Use any combination of

the variables to find the best model.

Solution

(a) Develop a regression model that could be used to

predict the number of victories based on the ERA.

The regression equation is
W = 155 - 17.9 ERA

(b) Develop a regression model that could be used to

predict the number of victories based on the runs

scored.

The regression equation is
W = - 6.9 + 0.124 R

(c) Develop a regression model that could be used to

predict the number of victories based on the batting

average.

The regression equation is
W = 62.2 + 78 AVG

(d) Develop a regression model that could be used to

predict the number of victories based on the onbase

percentage

The regression equation is
W = - 10.3 + 289 OBP