Baseball fans everywhere were shocked in December 2000 when Alex Rodriguez signed a 10-

year contract worth $252 million with the Texas Rangers baseball team. This focused more

attention than ever on how much money Major League Baseball players make for playing the

national pastime. The top four annual values, as of this writing (11/2010), are all members of the

New York Yankees: third baseman Alex Rodriguez $33 million, pitcher CC Sabathia, $24.3

million, shortstop Derek Jeter, $22.6 million, and first baseman Mark Teixeira, $20.6 million.

And these figures do not include endorsements!

The table on the following page gives Major League Baseball average salaries since 1971 as

compiled by the Major League Baseball Players Association. You may want to search the

Internet for updated information.

1. How has the average salary changed over time? Plot y = average salary versus x = year since

1970 (so x = 1 corresponds to 1971, x = 2 corresponds to 1972, etc.). Does the trend appear

linear? Would an exponential model be better? How about a power model? Find all three

models, including residual plots, and explain which you think is best.

2. Using the residual plot from the model you think is best, tell a story about the history of

baseball salaries.

3. Using the model you chose in problem #1, predict the average salary for the year 2011. Do

you think your prediction will be too low or too high? Explain.

4. Would you be willing to use your model to predict the average salary in 2021? Explain.

5. How has the minimum salary changed over time? Use y = minimum salary versus x = years

since 1970 and find an appropriate model. Justify your choice. Is the form of this relationship

the same as the relationship between average salary and year? Are you more confident in this

model than the one you chose in problem #1?

Year Minimum $

1971 12,750

1972. 13,500

1973 15,000

1974 15,000

1975 16,000

1976 19,000

1977 19,000

1978 21,000

1979 21,000

1980 30,000

1981 32,500

1982 33,500

1983 35,000

1984 40,000

1985 60,000

1986 60,000

1987 62,500

1988 62,500

1989 68,000

1990 100,000

1991 100,000

1992 109,000

1993 109,000

1994 109,000

1995 109,000

1996 122,667

1997 150,000

1998 170,000

1999 200,000

2000 200,000

2001 200,000

2002 300,000

2003 300,000

2004 300,000

2005 316,000

2006 327,000

2007 380,000

2008 390,000

2009 400,000

2010 400,000

Average $ (corresponds to the same years as above, 1971-2010)

31,543

34,092

36,566

40,839

44,676

51,501

76,066

99,876

113,558

143,756

185,651

241,497

289,194

329,408

371,571

412,520

412,454

438,729

497,254

597,537

851,492

1,028,667

1,076,089

1,168,263

1,110,766

1,119,981

1,336,609

1,398,831

1,611,166

1,895,630

2,138,896

2,383,235

2,555,476

2,486,609

2,632,655

2,866,544

2,944,556

3,154,845

3,240,206

3,297,828