Homework SourseTHIS QUESTION NEEDS TO BE ANSWERED IN EXCEL PLEASE In 2009 t
THIS QUESTION NEEDS TO BE ANSWERED IN EXCEL PLEASE
In 2009, the New York Yankees won 100 baseball games during the regular season. The table on the next page lists the number of victories (W), the earned-run- average (ERA), and the batting average (AVG) of each team in the American League. The ERA is one measure of the effectiveness of the pitching staff, and a lower number is better. The batting average is one measure of effectiveness of the hitters, and a higher number is better.
A) Develop a regression model that could be used to predict the number of victories based on the ERA.
B) Develop a regression model that could be used to predict the number of victories based on the batting average.
C) Which of the two models is better for predicting the number of victories?
D) Develop a multiple regression model that includes both ERA and batting average. How does this compare to the previous models?
| TEAM | W | ERA | AVG |
| New York Yankees | 100 | 4.32 | 0.29 |
| Los Angeles Angels | 96 | 4.38 | 0.28 |
| Boston Red Sox | 94 | 4.36 | 0.29 |
| Minnesota Twins | 88 | 4.48 | 0.28 |
| Texas Rangers | 89 | 4.42 | 0.27 |
| Detroit Tigers | 85 | 4.31 | 0.26 |
| Seattle Mariners | 84 | 3.97 | 0.26 |
| Tampa Bay Rays | 83 | 4.36 | 0.26 |
| Chicago White Sox | 78 | 4.12 | 0.25 |
| Toronto Blue Jays | 74 | 4.46 | 0.27 |
| Oakland Athletics | 72 | 4.23 | 0.27 |
| Cleveland Indians | 65 | 5.01 | 0.27 |
| Kansas City Royals | 64 | 4.75 | 0.27 |
| Baltimore Orioles | 63 | 5.06 | 0.26 |
Solution
a)
Using technology, we get
slope = -23.7495399
intercept = 186.6381334
Thus, the regression line is
W^ = -23.7495399ERA + 186.6381334
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b)
Using technology, we get
slope = 561.1111111
intercept = -70.42857143
Thus, the regression line is
W^ = 561.1111111AVG - 70.42857143
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c)
In W^ vs ERA, r^2 = 0.361991468
In W^ vs AVG, r^2 = 0.297503135
Thus, the better model is the one in terms of ERA.
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d)
Using the multiple regression function in Excel,
W^ = -25.12415916ERA + 600.1931365AVG + 30.69616919 [answer]
It\'s r^2 value is
r^2 = 0.701168038
Thus, this is better than the first two models, as its r^2 value is higher.
