Refer to the Baseball 2018 data, which report information on the 30 Major League Baseball teams for the 2018 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 (f). 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 (f). Plot the residuals on the vertical axis and the fitted values on the horizontal axis. What regression assumption is supported?

Data From Baseball 2018:

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Team League Year Opened Team Salary Attendance Wins ERA BA HR Net Worth Arizona Diamondbacks National 1998 143.32 2.243 82 3.72 0.235 176 1.210 Atlanta Braves National 2017 130.6 2.556 90 3.75 0.257 175 1.625 Baltimore Orioles American 1992 127.63 1.564 47 5.18 0.239 188 1.200 Boston Red Sox American 1912 227.4 2.896 108 3.75 0.268 208 2.800 Chicago Cubs Chicago White Sox Cincinnati Reds National American 1914 194.26 3.181 95 3.65 0.258 167 2.900 1991 71.84 1.609 62 4.84 0.241 182 1.500 National 2003 100.31 1.629 67 4.63 0.254 172 1.010 Cleveland Indians American 1994 142.8 1.927 91 3.77 0.259 216 1.045 Colorado Rockies National 1995 143.97 3.016 91 4.33 0.256 210 1.100 1.225 Detroit Tigers Houston Astros American 2000 130.96 1.857 64 4.58 0.241 135 American 2000 163.52 2.981 103 3.11 0.255 205 1.650 Kansas City Royals Los Angeles Angels Los Angeles Dodgers American 1973 129.94 1.665 58 4.94 155 0.245 0.242 1.015 3.020 3.858 American 1966 173.78 80 4.15 214 1.800 National 1962 199.58 92 3.38 0.25 235 3.000 Miami Marlins National 2012 91.82 0.811 63 4.76 0.237 128 1.000 Milwaukee Brewers National 2001 108.98 2.851 96 3.73 0.252 218 1.030 Minnesota Twins American 2010 115.51 1.959 78 4.50 0.25 166 1.150 New York Mets National 2009 150.19 2.225 3.483 77 4.07 0.234 170 2.100 New York Yankees Oakland Athletics American 2009 179.6 100 3.78 0.249 267 4.000 American 1966 80.32 1.574 97 3.81 0.252 227 1.020 Philadelphia Phillies Pittsburgh Pirates San Diego Padres San Francisco Giants National 2004 104.3 2.158 80 4.14 0.234 186 1.700 National 2001 91.03 1.465 82 4.00 0.254 157 1.260 National 2004 101.34 2.169 66 4.40 0.235 162 1.270 American 2000 205.67 160.99 2.299 89 4.13 0.254 176 2.850 Seattle Mariners National 1999 3.156 73 3.95 0.239 133 1.450 St. Louis Cardinals Tampa Bay Rays Texas Rangers Toronto Blue Jays Washington Nationals 2006 163.78 68.81 National 3.404 88 3.85 0.249 205 1.900 American 1990 1.155 90 3.74 0.258 150 0.900 American 1994 140.63 2.107 67 4.92 0.24 194 1.600 150.95 2.325 2.530 American 1989 73 4.85 0.244 217 1.350 National 2008 181.38 82 4.04 0.254 191 1.675