Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 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.

Team	League	Year Opened	Team Salary	Attendance	Wins	ERA	BA	HR	Net worth ($billion)
Arizona Diamondbacks	National	1998	89.08	1,043,010	52	5.11	0.236	144	$1.320
Atlanta Braves	National	2017	134.46	2,300,247	88	3.88	0.244	239	$1.875
Baltimore Orioles	American	1992	45.70	793,229	52	5.84	0.239	195	$1.430
Boston Red Sox	American	1912	180.26	1,725,323	92	4.26	0.261	219	$3.465
Chicago Cubs	National	1914	149.67	1,978,934	71	4.87	0.237	210	$3.360
Chicago White Sox	American	1991	125.99	1,596,385	93	3.73	0.256	190	$1.685
Cincinnati Reds	National	2003	118.75	1,505,024	83	4.40	0.249	222	$1.085
Cleveland Indians	American	1994	46.83	1,114,368	80	4.34	0.238	203	$1.160
Colorado Rockies	National	1995	103.99	1,938,645	74	4.82	0.249	182	$1.300
Detroit Tigers	American	2000	80.40	1,102,623	77	4.32	0.242	179	$1.260
Houston Astros	American	2000	171.02	2,068,509	95	3.76	0.267	221	$1.870
Kansas City Royals	American	1973	87.78	1,159,613	74	4.65	0.249	163	$1.060
Los Angeles Angels	American	1966	177.35	1,512,033	77	4.69	0.245	190	$2.025
Los Angeles Dodgers	National	1962	235.41	2,804,693	106	3.01	0.244	237	$3.570
Miami Marlins	National	2012	49.43	642,617	67	3.96	0.233	158	$0.990
Milwaukee Brewers	National	2001	87.57	1,824,282	95	3.50	0.233	194	$1.220
Minnesota Twins	American	2010	121.00	1,310,199	73	4.83	0.241	228	$1.325
New York Mets	National	2009	167.42	1,484,665	77	3.90	0.238	176	$2.450
New York Yankees	American	2009	191.21	1,959,854	92	3.74	0.237	222	$5.250
Oakland Athletics	American	1966	74.62	701,430	86	4.02	0.238	199	$1.125
Philadelphia Phillies	National	2004	174.01	1,515,890	82	4.39	0.24	198	$2.050
Pittsburgh Pirates	National	2001	35.91	859,498	61	5.08	0.236	124	$1.285
San Diego Padres	National	2004	171.69	2,191,950	79	4.10	0.242	180	$1.500
San Francisco Giants	American	2000	127.89	1,679,484	107	3.24	0.249	241	$3.175
Seattle Mariners	National	1999	64.55	1,215,985	90	4.30	0.226	199	$1.630
St. Louis Cardinals	National	2006	135.05	2,102,530	90	3.98	0.244	198	$2.245
Tampa Bay Rays	American	1990	60.39	761,072	100	3.67	0.242	222	$1.055
Texas Rangers	American	1994	84.87	2,110,258	60	4.79	0.232	167	$1.785
Toronto Blue Jays	American	1989	137.13	809,557	91	3.91	0.266	262	$1.675
Washington Nationals	National	2008	161.91	1,465,543	65	4.80	0.258	182	$1.925

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? Report the final regression equation.

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. What regression assumption is supported?