From 1946 to 1990, the Big Ten Conference consisted of the University of Illinois, Indiana University, University of Iowa, University of Michigan, Michigan State University, University of Minnesota, Northwestern University, Ohio State University, Purdue University, and University of Wisconsin. In 1990, the conference added Pennsylvania State University. In 2011, the conference added the University of Nebraska. In 2014, the University of Maryland and Rutgers University were added to the conference with speculation of more schools being added in the future.
The file BigTenExpand contains data on the football stadium capacity, latitude, longitude, endowment, and enrollment of 59 National Collegiate Athletic Association (NCAA) Football Bowl Subdivision (FBS) schools. Treat the 10 schools that were members of the Big Ten from 1946 to 1990 as being in a cluster and the other 49 schools as each being in their own cluster.
- Using Euclidean distance to measure dissimilarity between observations, determine which school (in its own cluster of one) that hierarchical clustering with complete linkage would recommend integrating into the Big Ten Conference. That is, which school is the most similar with respect to complete linkage to the cluster of ten schools that were members of the Big Ten from 1946 to 1990?
- Add the single school identified in (1) to create a cluster of 11 schools representing a hypothetical Big Ten Conference. Repeat the calculations to identify the school most similar with respect to complete linkage to this new cluster of 11 schools.
- Add the school identified in (2) to create a cluster of 12 schools representing a hypothetical Big Ten Conference. Repeat the calculations to identify the school most similar with respect to complete linkage to this new cluster of 12 schools.
- Add the school identified in (3) to create a cluster of 13 schools representing a hypothetical Big Ten Conference. Repeat the calculations to identify the school most similar with respect to complete linkage to this new cluster of 13 schools. Add this school to create a 14-school cluster.
- How does the hypothetical 14-team cluster created in (4) compare to the actual 14-team Big Ten Conference? For both the hypothetical 14-team Big Ten Conference and the actual 14-team Big Ten Conference, compute the cluster centroid, the distance from each cluster member to the cluster centroid, and average distance between the observations in the cluster. What do you observe when comparing these two clusters? Which cluster has the smaller average distance between observations? Is this surprising? Explain.
- Managerial Report, Excel .xlsx file, and PPT fileof the problem presentation with the problem solution analysis
Candidates:
School
StadiumCapacity
Latitude
Longitude
Endowment ($000)
Enrollment
1
Duke
-0.74515141
-1.300045853
0.915912002
2.544922985
-1.050282818
2
Maryland
0.111358164
-0.138951578
1.231986666
-0.2651109
0.911822867
3
North Carolina State
0.264350527
-1.361065861
0.956808902
-0.363877232
0.662673619
4
North Carolina
0.49479981
-1.320382904
0.895854619
0.567970634
0.164020841
5
Virginia
0.431604528
-0.50804171
0.984424237
1.98532706
-0.20886161
6
Virginia Tech
0.633701333
-0.817872556
0.674337675
-0.373507937
0.323359446
7
Wake Forest
-0.849380926
-1.253200947
0.70075523
-0.114026658
-1.765579415
8
Iowa State
0.154057679
1.026631711
-1.432185292
-0.36691036
0.20600333
9
Kansas
-0.056408231
-0.151739047
-1.692329355
-0.00504443
0.057913198
10
Kansas State
-0.059439896
-0.064241986
-1.905352822
-0.52274758
-0.303100786
11
Oklahoma
1.311726934
-1.497711435
-2.052762412
-0.026830328
0.30626531
12
Oklahoma State
0.376863749
-1.497711435
-2.052762412
-0.327522793
-0.270506785
13
West Virginia
0.390612993
0.107305772
0.750737953
-0.491820337
0.206534754
14
Cincinnati
-0.699932623
-0.083608387
0.023485011
-0.144580218
0.440981274
15
Louisville
0.196757195
-0.43592642
-0.173676014
-0.276254484
-0.543127256
16
Pittsburgh
0.583187807
0.416696149
0.746439418
0.719047505
0.131161128
17
Rutgers
0.045344714
0.43486666
1.629382017
-0.318017405
1.121735316
18
Syracuse
-0.090952138
1.418475699
1.358200152
-0.196014672
-0.571824148
19
Temple
0.731867518
0.250214942
1.519317648
-0.55491552
0.847609144
20
Nebraska
1.268130729
0.561925099
-1.921025795
-0.010071857
-0.238444209
21
Penn State
2.38647373
0.353876532
1.24001262
0.264129363
1.624639486
22
Charlotte
-1.541113072
-1.601475827
0.609516466
-0.634198726
-0.177861882
23
East Carolina
-0.059439896
-1.44658928
1.161816151
-0.641208545
0.008933626
24
Marshall
-0.571150886
-0.363464608
0.354245565
-0.66657874
-1.179684542
25
Memphis
0.469180101
-1.636878928
-0.854583627
-0.603494898
-0.403894189
26
Old Dominion
-1.348196662
-0.937056451
1.342098442
-0.617605265
-0.224272904
27
Tulsa
-0.676789486
-1.243325041
-1.797837725
-0.259941711
-2.054231174
28
Army
-0.486435048
0.772127113
1.696073321
-0.672600767
-2.007111586
29
Navy
-0.742632139
-0.148350822
1.300902417
-0.663193477
-2.011362978
30
Notre Dame
1.255491673
0.892623561
-0.257402957
2.835375737
-1.353460164
31
Akron
-0.913430199
0.663571849
0.49986072
-0.616847125
0.016373561
32
Ball State
-1.233676563
0.292216227
-0.50909632
-0.634560501
-0.455088027
33
Bowling Green
-1.181412356
0.776884874
0.159888404
-0.633702561
-0.859855913
34
Buffalo
-0.955574621
1.360237116
0.92473653
-0.433533702
0.13948677
35
Central Michigan
-0.904932996
1.632354708
-0.01997824
-0.665752555
0.080498714
36
Eastern Michigan
-0.904890296
1.111664608
0.164723897
-0.687394424
-0.349334667
37
Kent State
-0.891226451
0.689240349
0.525242031
-0.692980392
0.050473263
38
Miami University
-1.153145277
0.057259378
-0.01502846
-0.485543707
-0.875975772
39
Northern Illinois
-0.870816083
0.990931755
-0.65424906
-0.685812933
-0.380422966
40
Ohio
-1.16962729
-0.012618913
0.4081514
-0.523575467
-0.096022598
41
Toledo
-1.07363878
0.888253521
0.171021978
-0.602182754
-0.414079814
42
Western Michigan
-0.909160248
1.123407888
-0.149275242
-0.601580552
-0.194778876
43
Kentucky
0.692327767
-0.506002614
0.030906808
-0.194732014
-0.005237678
44
Missouri
0.83742072
-0.155108021
-1.224852237
-0.079560482
0.577468651
45
Tennessee
2.180363171
-1.302310959
0.112818725
-0.233061473
0.257640021
46
Vanderbilt
-0.495401946
-1.226460921
-0.340265882
1.222082883
-1.279769381
47
Arkansas State
-0.872267866
-1.361112834
-0.962929221
-0.691716447
-1.185530205
48
Middle Tennessee
-0.870730684
-1.348960272
-0.277976707
-0.677488701
-0.07467707
49
Western Kentucky
-1.25502632
-0.917611505
-0.285422926
-0.649224305
-0.553490023
Big Ten
School
StadiumCapacity
Latitude
Longitude
Endowment ($000)
Enrollment
1
Illinois
0.39616393
0.291098113
-0.576520912
0.193512318
1.516494718
2
Indiana
0.065626984
-0.07379062
-0.299015746
0.178889342
1.368050303
3
Iowa
0.819529623
0.886058875
-1.098502436
-0.122052057
0.22362889
4
Michigan State
1.00911547
1.301000932
0.026938684
-0.533940497
1.830654826
5
Michigan
2.707659483
1.123658154
0.147208124
3.728560154
1.366721743
6
Minnesota
-0.025066787
2.158029349
-1.374918363
0.705385671
2.238345543
7
Northwestern
-0.091208336
1.035487299
-0.485474329
3.358842341
-0.648083481
8
Ohio State
2.174983032
0.243329145
0.265878343
0.488439062
2.62008506
9
Purdue
0.474304043
0.418798388
-0.360553436
0.420896539
1.094012701
10
Wisconsin
1.235252102
1.433391974
-0.755704228
0.347935893
1.342364813