119 Baseball batting averages versus wins. Is the number of games won by a major league baseball team in a season related to the team’s batting average? Consider data from the Baseball Almanac on the number of games won and the batting averages for the 14 teams in the American League for the 2010 Major League Baseball season. The data are listed in the next table and saved in the ALWINS file.

a. If you were to model the relationship between the mean (or expected) number of games won by a major league team and the team’s batting average x , using a straight line, would you expect the slope of the line to be positive or negative? Explain.

b. Construct a scatterplot of the data. Does the pattern revealed by the scatterplot agree with your answer to part a ?

c. An SAS printout of the simple linear regression is shown below. Find the estimates of the b>s on the printout and write the equation of the least squares line.

d. Graph the least squares line on your scatterplot. Does your least squares line seem to fit the points on your scatterplot?

e. Interpret the estimates of b0 and b1 in the words of the problem.

f. Conduct a test (at a = .05 ) to determine whether the mean (or expected) number of games won by a major

league baseball team is positively linearly related to the team’s batting average.
g. Find the coefficient of determination, r2, and interpret its value.
h. Do you recommend using the model to predict the number of games won by a team during the 2010 season?

Transcribed Image Text:

Games Team Won Batting Avg. (average number of hits per 1,000 at bats) New York 95 .267 Toronto 85 .248 Baltimore 66 .259 Boston 89 .268 Tampa Bay 96 .247 Cleveland 69 .248 Detroit 81 .268 Chicago 88 .268 Kansas City 67 .274 Minnesota 94 .273 Los Angeles 80 .248 Texas 90 .276 Seattle 61 .236 Oakland 81 .256 Based on data from Baseball Almanac, 2010; www.mlb.com.