An alternate expression for the slope coefficient of the simple linear regression model is B1= r(Sy/Sx)...
An alternate expression for the slope coefficient of the simple linear regression model is B1= r(Sy/Sx) where r is the Pearson correlation coefficient given by r= Sxy/ (√(SxxSyy) and Sy and Sx are the sample standard deviations of y and x, respectively. Use the data to show that this alternate formulation gives a slope coefficient that is numerically equivalent to what you found using the Least-squares estimations demonstrating that r(Sy/Sx) = Sxy/Sxx. Using the information given, find B0 and B1 and write out the estimated regression line of the number of wins in a season on team ERA.
n=30 ∑iXi1= 115.90 ∑iXi2=452.4556 ∑iYi1=2,431 ∑iYi2= 201347 ∑iXiYi= 9,284.92
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
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An alternate expression for the slope coefficient of the simple
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