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Statistics: Payroll Example Problem for Baseball

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.

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.

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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.

(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.

Solution (a):

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