Problem:
The following table gives the total 2004 payroll (on opening day of the season, rounded to the nearest million dollars) & the % of games won during the 2004 season by each of the National League baseball teams.
| Team |
Total Payroll (million of dollars) |
% of games won |
| Diamonbacks |
70 |
31.5 |
| Braves |
90 |
59.3 |
| Cubs |
91 |
54.9 |
| Reds |
47 |
46.9 |
| Rockies |
65 |
42 |
| Marlins |
42 |
51.2 |
| Astros |
75 |
56.8 |
| Dodgers |
93 |
57.4 |
| Brewers |
28 |
41.6 |
| Expos |
41 |
41.4 |
| Mets |
97 |
43.8 |
| Philies |
93 |
53.1 |
| Pirates |
32 |
44.7 |
| Cardinals |
83 |
64.8 |
| Padres |
55 |
53.7 |
| Giants |
82 |
56.2 |
a) Find the least squares regression line with total payroll as an independent variable & % of games won as a dependent variable.
b) Is the regression line obtained in part of the population regression line? Why or why not? Do the values of the y-intercept & the slope of the regression line give β0 and β1 or b0 and b1?
c) Give a brief interception of the values of the y-intercept and the slope.
d) How good is the regression equation in explaining the change in % of games won based on payroll?
e) Conduct the test for the population slope.
f) Predict the % of games won for a team with the total payroll of $60 million.