The following table gives the total 2008 payroll (on the opening day of the season rounded to the nearest million dollars) and the number of runs scored during the 2008 season by each of the National League baseball teams Team Total Payroll (in million $) (x Runs scored Arizona Diamondbacks Atlanta Braves Chicago Cubs Cincinnati Reds Colorado Rockies Florida Marlins Houston Astros Los Angeles Dodgers Milwaukee Brewers New York Mets Philadelphia Phillies Pittsburgh Pirates San Diego Padres San Francisco Giants St. Louis Cardinals Washington Nationals 74 97 135 71 75 37 103 100 80 136 113 49 43 82 89 59 720 753 855 704 747 770 712 700 750 799 799 735 637 640 779 641 y 11 741,Lx 1343 Xyi-8 672 521, = 125 795 2xy-1001 568 Parts (c) to (h) are to be done by hand and then the results verified by SAS in part (i) (a) Plot a scatter diagram (using SAS, see part(i)to get an idea of the form of the relationship between the team's payroll and the scored runs. Does the scatter diagram indicate an approximately straight line? inference Find the least squares estimates of A) and 1. Find the least squares fitted regression line (b) State a SLR model making sure you give all assumptions necessary for statistical (c) For the rest of the question assume that the assumptions hold. (d) Find s, an estimate of 2. (e) Use the t-test to test whether there is a significant linear relationship between the scored runs and the team's payroll. Use a 0.05 (f) Find a 95% confidence interval for A. (g) Set up the ANOVA table and hence test whether there is a significant linear relationship between the scored runs and the team's payroll. Use a 0.05. Find the values of the coefficient of correlation, r, and coefficient of determination, r2, and interpret their meanings in this problem. (h) Verify your above results using SAS (Proc REG in SAS Manual or see the handout, SAS program (a)). (i) 2. Refers to question1 (a) Find a 95% Confidence Interval for the mean value of the response variable (ie. of the when the team's payroll is $84 million (i.e. xp -84). What is your conclusion about the widths of these two intervals? (b) Use SAS to compare your results with part (a) (see handout, SAS program (c) 3. Refers to question 1 Perform a residual analysis using SAS (see handout, SAS program (b)). What can you say about the model