Team League Wins X1 X2 ERA X3 BA X4 HR X5 SB X6 Errors X7 X8 Built Size Attendance Payroll X9 X10 X11 X12 Arizona Diamondbacks NL 65 4.250 180 86 102...

Question 30: Refer to the Baseball 2010 data, which report information on the 30 Major League Base- ball teams for the 2010 season. Let the number of games won be the dependent variable and the following variables be independent variables: team batting average, number of stolen bases, number of errors committed, team ERA, number of home runs, and whether the team plays in the American or the National League. Add a league code variable using 0 for the National League and 1 for the American League.

a. Use a statistical software package to determine the multiple regression equation. Dis- cuss each of the variables. For example, are you surprised that the regression coefficient for ERA is negative? Is the number of wins affected by whether the team plays in the National or the American League?

b. Find the coefficient of determination for this set of independent variables.

c. Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable? Do you see any problems with multicollinearity?

d. Conduct a global test on the set of independent variables. Interpret.

e. Conduct a test of hypothesis on each of the independent variables. Would you consider deleting any of the variables? If so, which ones?

f. Rerun the analysis until only significant net regression coefficients remain in the analysis. Identify these variables.

g. Develop a histogram of the residuals from the final regression equation developed in part (f). Is it reasonable to conclude that the normality assumption has been met?

h. Plot the residuals against the fitted values from the final regression equation developed in part (f). Plot the residuals on the vertical axis and the fitted values on the horizontal axis.