Question

Many baseball sportswriters believe that the key to success in baseball is pitching. One way to measure success in pitching is a team’s Earned Run Average (ERA). The team ERA gives the number of earned runs per game scored by opponents, where the lower the team ERA is, the better a team’s pitching. In the United States, professional baseball is played in a season of 162 games. For the 2013 season, the number of wins (y) and team ERA (x), have been recorded for the 30 teams in major league baseball. To assist you in your calculations, the following have been computed from this data:

n=30   ∑iXi1= 115.90 ∑iXi2=452.4556    ∑iYi1=2,431 ∑iYi2= 201347   ∑iXiYi= 9,284.92

Using the information given, find the least-squares estimators for B0 and B1 and write out the estimated regression line of the number of wins in a season on team ERA.

The data below shows W and ERA

1. 81   3.92

2. 96   3.18

3, 85   4.2

4. 97   3.79

5. 66   4

6. 63 3.98

7. 90   3.38

8. 92   3.82

9. 74   4.44

10. 93   3.61

11. 51   4.79

12. 86   3.45

13. 78   4.23

14, 92   3.25

15. 62   3.71

16. 74   3.84

17. 66   4.55

18. 74   3.77

19. 85   3.94

20. 96   3.56

21. 73   4.32

22. 94   3.26

23. 76   3.98

24. 71   4.31

25. 76   4

26. 97   3.42

27. 92   3.74

28. 91   3.62

29. 74   4.25

30. 86   3.59

Answer 1

predictor (x): team ERA

response (y) = the number of wins (y)

the given data are:-

the slope be:-

the intercept be:-

the regression equation be:-

the number of wins = 168.9454 - 22.7555* team ERA

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