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

Question:

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.

TeamLeagueYear OpenedTeam SalaryAttendanceWinsERABAHRNet worth ($billion) 
Arizona DiamondbacksNational199889.081,043,010525.110.236144$1.320
Atlanta BravesNational2017134.462,300,247883.880.244239$1.875
Baltimore OriolesAmerican199245.70793,229525.840.239195$1.430
Boston Red SoxAmerican1912180.261,725,323924.260.261219$3.465
Chicago CubsNational1914149.671,978,934714.870.237210$3.360
Chicago White SoxAmerican1991125.991,596,385933.730.256190$1.685
Cincinnati RedsNational2003118.751,505,024834.400.249222$1.085
Cleveland IndiansAmerican199446.831,114,368804.340.238203$1.160
Colorado RockiesNational1995103.991,938,645744.820.249182$1.300
Detroit TigersAmerican200080.401,102,623774.320.242179$1.260
Houston AstrosAmerican2000171.022,068,509953.760.267221$1.870
Kansas City RoyalsAmerican197387.781,159,613744.650.249163$1.060
Los Angeles AngelsAmerican1966177.351,512,033774.690.245190$2.025
Los Angeles DodgersNational1962235.412,804,6931063.010.244237$3.570
Miami MarlinsNational201249.43642,617673.960.233158$0.990
Milwaukee BrewersNational200187.571,824,282953.500.233194$1.220
Minnesota TwinsAmerican2010121.001,310,199734.830.241228$1.325
New York MetsNational2009167.421,484,665773.900.238176$2.450
New York YankeesAmerican2009191.211,959,854923.740.237222$5.250
Oakland AthleticsAmerican196674.62701,430864.020.238199$1.125
Philadelphia PhilliesNational2004174.011,515,890824.390.24198$2.050
Pittsburgh PiratesNational200135.91859,498615.080.236124$1.285
San Diego PadresNational2004171.692,191,950794.100.242180$1.500
San Francisco GiantsAmerican2000127.891,679,4841073.240.249241$3.175
Seattle MarinersNational199964.551,215,985904.300.226199$1.630
St. Louis CardinalsNational2006135.052,102,530903.980.244198$2.245
Tampa Bay RaysAmerican199060.39761,0721003.670.242222$1.055
Texas RangersAmerican199484.872,110,258604.790.232167$1.785
Toronto Blue JaysAmerican1989137.13809,557913.910.266262$1.675
Washington NationalsNational2008161.911,465,543654.800.258182$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?

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Related Book For  book-img-for-question

Statistical Techniques In Business And Economics

ISBN: 9781265779696

19th Edition

Authors: Douglas Lind, William Marchal, Samuel Wathen

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