In 2009, the New York Yankees won 103 baseball
games during the regular season. The table on the next
page lists the number of victories (W), the earnedrun-
average (ERA), and the batting average (AVG)
of each team in the American League. The ERA is
one measure of the effectiveness of the pitching staff,
and a lower number is better. The batting average
is one measure of effectiveness of the hitters, and a
higher number is better.
(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 batting
(c) Which of the two models is better for predicting
the number of victories?
(d) Develop a multiple regression model that includes
both ERA and batting average. How does
this compare to the previous models?
TEAM W ERA AVG
New York Yankees 103 4.26 0.283
Los Angeles Angels 97 4.45 0.285
Boston Red Sox 95 4.35 0.270
Minnesota Twins 87 4.50 0.274
Texas Rangers 87 4.38 0.260
Detroit Tigers 86 4.29 0.260
Seattle Mariners 85 3.87 0.258
Tampa Bay Rays 84 4.33 0.263
Chicago White Sox 79 4.14 0.258
Toronto Blue Jays 75 4.47 0.266
Oakland Athletics 75 4.26 0.262
Cleveland Indians 65 5.06 0.264
Kansas City Royals 65 4.83 0.259
Baltimore Orioles 64 5.15 0.268
This solution is comprised of a detailed explanation of regression analysis. In this solution, step-by-step explanation of this complicated topic provides students with a clear perspective of standard normal distribution to find the probability.