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 2013 Major League Baseball season. The data are listed in the next table.

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. A MINITAB printout of the simple linear regression is shown above. 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 2013 season?

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Batting Avg. (average number of Games Won hits per 1,000 at bats) Team New York 85 .242 Toronto 74 .252 Baltimore 85 .260 Boston 97 .277 Tampa Bay 92 .257 Cleveland 92 .255 Detroit 93 .283 Chicago 63 .249 Kansas City 86 .260 Minnesota 66 .242 Los Angeles 78 .264 Texas 91 .262 Seattle 71 .237 Oakland 96 .254