Baseball batting averages versus wins. Is the number of games won by a major league baseba...

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 β’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?

Team	Games 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 Ba	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.

---

e. Interpret the estimates of β0 and β1 in the words of the problem.

---

f. Conduct a test (at α =.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?