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Fundamentals of Statistics | 4th Edition | ISBN: 9780321838704 | Authors: Michael Sullivan,III
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Solved: You Explain It! Winning Percentage and On-base

Chapter 3, Problem 15AYU

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QUESTION:

You Explain It! Winning Percentage and On-base Percentage  In his best-selling book Moneyball, author Michael Lewis discusses how statistics can be used to judge both a baseball player’s potential and a team’s ability to win games. One aspect of this analysis is that a team’s on-base percentage is the best predictor of winning percentage. The on-base percentage is the proportion of time a player reaches a base. For example, an on-base percentage of 0.3 would mean the player safely reaches bases 3 times out of 10, on average. For the 2010 baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least-squares regression equation \(\hat {y}= 3.4722 x – 0.6294\).

(a) Interpret the slope.

(b) For 2010, the lowest on-base percentage was 0.298 and the highest on-base percentage was 0.350. Use this information to explain why it does not make sense to interpret the y-intercept.

(c) Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage was 0.250? Why or why not?

(d) The 2010 World Series Champion San Francisco Giants had an on-base percentage of 0.321 and a winning percentage of 0.568. What is the residual for San Francisco? How would you interpret this residual?

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QUESTION:

You Explain It! Winning Percentage and On-base Percentage  In his best-selling book Moneyball, author Michael Lewis discusses how statistics can be used to judge both a baseball player’s potential and a team’s ability to win games. One aspect of this analysis is that a team’s on-base percentage is the best predictor of winning percentage. The on-base percentage is the proportion of time a player reaches a base. For example, an on-base percentage of 0.3 would mean the player safely reaches bases 3 times out of 10, on average. For the 2010 baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least-squares regression equation \(\hat {y}= 3.4722 x – 0.6294\).

(a) Interpret the slope.

(b) For 2010, the lowest on-base percentage was 0.298 and the highest on-base percentage was 0.350. Use this information to explain why it does not make sense to interpret the y-intercept.

(c) Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage was 0.250? Why or why not?

(d) The 2010 World Series Champion San Francisco Giants had an on-base percentage of 0.321 and a winning percentage of 0.568. What is the residual for San Francisco? How would you interpret this residual?

ANSWER:

Step 1 of 4

(a)

The equation of the least-squares regression line for 2010 baseball season, winning percentage, y, and on-base percentage, x is,

The slope of the least-squares regression line is the coefficient of on-base percentage, x:

For each percentage point increase in on-base percentage, the winning percentage will increase by 3.4722 percentage points, on average.

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