Refer to the Baseball 2016 data, which report information on the 30 Major League Baseball teams for the 2016 season. Let the number of games won be the dependent variable and the following variables be independent variables: team batting average, team earned run average (ERA), number of home runs, and whether the team plays in the American or the National League.

a. Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable? Do you see any problems with multicollinearity? Are you surprised that the correlation coefficient for ERA is negative?

b. Use a statistical software package to determine the multiple regression equation. How did you select the variables to include in the equation? How did you use the information from the correlation analysis? Show that your regression equation shows

a significant relationship. Write out the regression equation and interpret its practical application. Report and interpret the R-square. Is the number of wins affected by whether the team plays in the National or the American League?

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

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

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

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