Refer to the Baseball 2018 data given below, 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 National league (American League is 1 and National League is 0).a. Develop a correlation matrix. (i) Which independent variables have strong or weak correlations with the dependent variable. (ii) Do you see any problems with multicollinearity? Explain your answer.b. Use Excel to determine the multiple regression equation. (i) Write out the regression equation and determine its practical application (i.e., interpret the equation). (ii) Report and interpret the R-square.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? (i) If so, which ones?(ii) If so, what is your new equation?e. Develop a histogram of the residuals from the final regression equation developed in part (d-ii). Is it reasonable to conclude that the normality assumption has been met? Why or Why not?f. Plot the residuals against the fitted values from the final regression equation developed in part (d-ii). Plot the residuals on the vertical axis and the fitted values on the horizontal axis. What regression assumption is supported? Why is it supported? АВDEFHKLMN12Team SalaryYear StadiumAttendanceNet Worth3TeamLeague($ mil)HRВАWinsERAOpenedmil$ bil4 Arizona DiamondbacksNational143.321760.235823.7219982.2426951.215Atlanta BravesNational130.61750.257903.7520172.5557811.6256Baltimore OriolesAmerican127.631880.239475.1819921.5641921.27Boston Red SoxAmerican227.42080.2681083.7519122.8955752.88 Chicago Cubs9 Chicago White Sox10 Cincinnati Reds11 Cleveland Indians12 Colorado Rockies13 Detroit Tigers14 Houston Astros15 Kansas City Royals16 Los Angeles Angels17 Los Angeles Dodgers18 Miami Marlins19 Milwaukee BrewersNational194.261670.258953.6519143.1810892.9American71.841820.241624.8419911.6088171.5National100.311720.254674.6320031.6293561.01American142.82160.259913.7719941.9267011.045National143.972100.256914.3319953.015881.1American130.961350.241644.5820001.856971.225American163.522050.2551033.1120002.9805491.65American129.941550.245584.9419731.6651071.015American173.782140.242804.1519663.0202161.8National199.582350.25923.3819623.85753National91.821280.237634.7620120.8111041National108.982180.252963.7320012.8508751.0320 Minnesota Twins21 New York Mets22 New York Yankees23 Oakland AthleticsAmerican115.511660.25784.520101.9591971.15National150.191700.234774.0720092.2249952.1American179.62670.2491003.7820093.4828554American80.322270.252973.8119661.5736161.0224 Philadelphia Phillies25 Pittsburgh Pirates26 San Diego PadresNational104.31860.234804.1420042.1581241.7National91.031570.25482420011.4653161.26National101.341620.235664.420042.1685361.2727 San Francisco Giants28 Seattle MarinersAmerican205.671760.254894.1320002.2994892.85National160.991330.239733.9519993.1561851.4529 St. Louis Cardinals30 Tampa Bay Rays31 Texas Rangers32 Toronto Blue JaysNational163.782050.249883.8520063.4035871.9American68.811500.258903.7419901.1549730.9American140.631940.24674.9219942.1071071.6American150.952170.244734.8519892.3252811.3533 Washington NationalsNational181.381910.254824.0420082.5296041.6753435363738392018 Baseball Data+

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Refer to the Baseball 2018 data given below, 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 National league (American League is 1 and National League is 0). a. Develop a correlation matrix. (i) Which independent variables have strong or weak correlations with the dependent variable. (ii) Do you see any problems with multicollinearity? Explain your answer. b. Use Excel to determine the multiple regression equation. (i) Write out the regression equation and determine its practical application (i.e., interpret the equation). (ii) Report and interpret the R-square. 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? (i) If so, which ones? (ii) If so, what is your new equation? e. Develop a histogram of the residuals from the final regression equation developed in part (d-ii). Is it reasonable to conclude that the normality assumption has been met? Why or Why not? f. Plot the residuals against the fitted values from the final regression equation developed in part (d-ii). Plot the residuals on the vertical axis and the fitted values on the horizontal axis. What regression assumption is supported? Why is it supported?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Refer to the Baseball 2018 data given below, 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 National league (American League is 1 and National League is 0).

a. Develop a correlation matrix.

(i) Which independent variables have strong or weak correlations with the dependent variable.

(ii) Do you see any problems with multicollinearity? Explain your answer.

b. Use Excel to determine the multiple regression equation.

(i) Write out the regression equation and determine its practical application (i.e., interpret the equation).

(ii) Report and interpret the R-square.

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?

(i) If so, which ones?

(ii) If so, what is your new equation?

e. Develop a histogram of the residuals from the final regression equation developed in part (d-ii). Is it reasonable to conclude that the normality assumption has been met? Why or Why not?

f. Plot the residuals against the fitted values from the final regression equation developed in part (d-ii). Plot the residuals on the vertical axis and the fitted values on the horizontal axis. What regression assumption is supported? Why is it supported?

А
В
D
E
F
H
K
L
M
N
1
2
Team Salary
Year Stadium
Attendance
Net Worth
3
Team
League
($ mil)
HR
ВА
Wins
ERA
Opened
mil
$ bil
4 Arizona Diamondbacks
National
143.32
176
0.235
82
3.72
1998
2.242695
1.21
5
Atlanta Braves
National
130.6
175
0.257
90
3.75
2017
2.555781
1.625
6
Baltimore Orioles
American
127.63
188
0.239
47
5.18
1992
1.564192
1.2
7
Boston Red Sox
American
227.4
208
0.268
108
3.75
1912
2.895575
2.8
8 Chicago Cubs
9 Chicago White Sox
10 Cincinnati Reds
11 Cleveland Indians
12 Colorado Rockies
13 Detroit Tigers
14 Houston Astros
15 Kansas City Royals
16 Los Angeles Angels
17 Los Angeles Dodgers
18 Miami Marlins
19 Milwaukee Brewers
National
194.26
167
0.258
95
3.65
1914
3.181089
2.9
American
71.84
182
0.241
62
4.84
1991
1.608817
1.5
National
100.31
172
0.254
67
4.63
2003
1.629356
1.01
American
142.8
216
0.259
91
3.77
1994
1.926701
1.045
National
143.97
210
0.256
91
4.33
1995
3.01588
1.1
American
130.96
135
0.241
64
4.58
2000
1.85697
1.225
American
163.52
205
0.255
103
3.11
2000
2.980549
1.65
American
129.94
155
0.245
58
4.94
1973
1.665107
1.015
American
173.78
214
0.242
80
4.15
1966
3.020216
1.8
National
199.58
235
0.25
92
3.38
1962
3.8575
3
National
91.82
128
0.237
63
4.76
2012
0.811104
1
National
108.98
218
0.252
96
3.73
2001
2.850875
1.03
20 Minnesota Twins
21 New York Mets
22 New York Yankees
23 Oakland Athletics
American
115.51
166
0.25
78
4.5
2010
1.959197
1.15
National
150.19
170
0.234
77
4.07
2009
2.224995
2.1
American
179.6
267
0.249
100
3.78
2009
3.482855
4
American
80.32
227
0.252
97
3.81
1966
1.573616
1.02
24 Philadelphia Phillies
25 Pittsburgh Pirates
26 San Diego Padres
National
104.3
186
0.234
80
4.14
2004
2.158124
1.7
National
91.03
157
0.254
82
4
2001
1.465316
1.26
National
101.34
162
0.235
66
4.4
2004
2.168536
1.27
27 San Francisco Giants
28 Seattle Mariners
American
205.67
176
0.254
89
4.13
2000
2.299489
2.85
National
160.99
133
0.239
73
3.95
1999
3.156185
1.45
29 St. Louis Cardinals
30 Tampa Bay Rays
31 Texas Rangers
32 Toronto Blue Jays
National
163.78
205
0.249
88
3.85
2006
3.403587
1.9
American
68.81
150
0.258
90
3.74
1990
1.154973
0.9
American
140.63
194
0.24
67
4.92
1994
2.107107
1.6
American
150.95
217
0.244
73
4.85
1989
2.325281
1.35
33 Washington Nationals
National
181.38
191
0.254
82
4.04
2008
2.529604
1.675
34
35
36
37
38
39
2018 Baseball Data
+

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