Math Problem Solver

A statistical program is recommended.

Major League Baseball (MLB) consists of teams that play in the American League and the National League. MLB collects a wide variety of team and player statistics. Some of the statistics often used to evaluate pitching performance are as follows:

ERA: The average number of earned runs given up by the pitcher per nine innings. An earned run is any run that the opponent scores off a particular pitcher except for runs scored as a result of errors.

SO/IP: The average number of strikeouts per inning pitched.

HR/IP: The average number of home runs per inning pitched.

R/IP: The number of runs given up per inning pitched.

The following data show values for these statistics for a random sample of 20 pitchers from the American League for a full season.

Player Team W L ERA SO/IP HR/IP R/IP

Verlander, J DET 24 5 2.40 1.00 0.10 0.29

Beckett, J BOS 13 7 2.89 0.91 0.11 0.34

Wilson, C TEX 16 7 2.94 0.92 0.07 0.40

Sabathia, C NYY 19 8 3.00 0.97 0.07 0.37

Haren, D LAA 16 10 3.17 0.81 0.08 0.38

McCarthy, B OAK 9 9 3.32 0.72 0.06 0.43

Santana, E LAA 11 12 3.38 0.78 0.11 0.42

Lester, J BOS 15 9 3.47 0.95 0.10 0.40

Hernandez, F SEA 14 14 3.47 0.95 0.08 0.42

Buehrle, M CWS 13 9 3.59 0.53 0.10 0.45

Pineda, M SEA 9 10 3.74 1.01 0.11 0.44

Colon, B NYY 8 10 4.00 0.82 0.13 0.52

Tomlin, J CLE 12 7 4.25 0.54 0.15 0.48

Pavano, C MIN 9 13 4.30 0.46 0.10 0.55

Danks, J CWS 8 12 4.33 0.79 0.11 0.52

Guthrie, J BAL 9 17 4.33 0.63 0.13 0.54

Lewis, C TEX 14 10 4.40 0.84 0.17 0.51

Scherzer, M DET 15 9 4.43 0.89 0.15 0.52

Davis, W TB 11 10 4.45 0.57 0.13 0.52

Porcello, R DET 14 9 4.75 0.57 0.10 0.57

(a)

Develop an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of strikeouts per inning pitched. (Round your numerical values to two decimal places. Let x1 represent the average number of strikeouts per inning pitched and y represent the average number of runs given up per inning.)

ŷ =

(b)

Develop an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of home runs per inning pitched. (Round your numerical values to two decimal places. Let x2 represent the average number of home runs per inning pitched and y represent the average number of runs given up per inning.)

ŷ =

(c)

Develop an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of strikeouts per inning pitched and the average number of home runs per inning pitched. (Round your numerical values to two decimal places. Let x1 represent the average number of strikeouts per inning pitched, x2 represent the average number of home runs per inning pitched, and y represent the average number of runs given up per inning.)

ŷ =

(d)

A certain pitcher had an average number of strikeouts per inning pitched of 0.88 and an average number of home runs per inning of 0.14. Use the estimated regression equation developed in part (c) to predict the average number of runs given up per inning for this pitcher. (Round your answer to two decimal places.)

0.47

runs given up per inning

(e)

Suppose a suggestion was made to also use the earned run average as another independent variable in part (c). What do you think of this suggestion?

This suggestion

does not

Correct: Your answer is correct.

make sense. If a pitcher gives up more runs per inning pitched this pitcher's earned run average has to

increase