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The file ClassificationData.xlsx (Screenshot attached below) contains the following information about the top 25 MBA programs: percentage of applicants accepted, percentage of accepted applicants who enroll, mean GMAT score of enrollees, mean undergraduate GPA of enrollees, annual cost of school (for state schools, this is the cost for out-of-state students), percentage of students who are minorities, percentage of students who are non-U.S. residents, and mean starting salary of graduates (in thousands of dollars).Use these data to divide the top 25 schools into 4 clusters, using for example the K-Means clustering algorithm, and interpret your clusters. The method is explained in our textbook: Section 8.8 in the Fourth and Fifth Edition or Section 14.3 in the Sixth Edition. More precisely, use Evolutionary Solver to find 4 schools to be used as cluster centers and to assign all other schools to one of these cluster centers. Each school is then assigned to the nearest cluster center, where nearest is defined in terms of the eight attributes. The objective is to minimize the sum of the distances from each school to its cluster center.

The file ClassificationData.xlsx (Screenshot attached below) contains the following information about the top 25 MBA programs: percentage of applicants accepted, percentage of accepted applicants who enroll, mean GMAT score of enrollees, mean undergraduate GPA of enrollees, annual cost of school (for state schools, this is the cost for out-of-state students), percentage of students who are minorities, percentage of students who are non-U.S. residents, and mean starting salary of graduates (in thousands of dollars).Use these data to divide the top 25 schools into 4 clusters, using for example the K-Means clustering algorithm, and interpret your clusters. The method is explained in our textbook: Section 8.8 in the Fourth and Fifth Edition or Section 14.3 in the Sixth Edition. More precisely, use Evolutionary Solver to find 4 schools to be used as cluster centers and to assign all other schools to one of these cluster centers. Each school is then assigned to the nearest cluster center, where nearest is defined in terms of the eight attributes. The objective is to minimize the sum of the distances from each school to its cluster center.

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The file ClassificationData.xlsx (Screenshot attached below) contains the following information about the top 25 MBA programs: percentage of applicants accepted, percentage of accepted applicants who enroll, mean GMAT score of enrollees, mean undergraduate GPA of enrollees, annual cost of school (for state schools, this is the cost for out-of-state students), percentage of students who are minorities, percentage of students who are non-U.S. residents, and mean starting salary of graduates (in thousands of dollars).Use these data to divide the top 25 schools into 4 clusters, using
for example the K-Means clustering algorithm, and interpret your clusters. The method is explained in our textbook: Section 8.8 in the Fourth and Fifth Edition or Section 14.3 in the Sixth Edition. More precisely, use Evolutionary Solver to find 4 schools to be used as cluster centers and to assign all other schools to one of these cluster centers. Each school is then assigned to the nearest cluster center, where nearest is defined in terms of the eight attributes. The objective is to minimize the sum of the distances from each school to its cluster center.


Hint: Your model will have four decision variables (changing cells) corresponding to the indexes of the four schools chosen as cluster centers.
In addition, please note that you need to first standardize the value of each attribute by subtracting the attribute’s mean and dividing the difference by the attribute’s standard deviation.

A C D E G H 1 School % accepted d who enroll Mean GMAT Mean GPA Total Cost % minority % non-US štarting Salary Wharton 15 71 662 3.42 32400 16 30 102 3 Michigan 28 44 645 3.3 29800 15 26 86 4 Northwestern 14 69 660 3.3 32600 9 24 99 Harvard 13 88 680 3.5 30100 19 27 114 6 Virginia 19 49 660 3.1 31200 20 12 93 7 Columbia 14 70 660 3.3 32200 12 24 93 8 Stanford 7 81 690 3.6 34500 25 25 111 9 Chicago 23 57 685 3.4 34200 5 23 90 10 MIT 14 12 650 3.5 36700 15 37 101 11 Dartmouth 14 49 669 3.39 32700 9 16 104 12 Duke 17 50 646 3.33 30100 12 19 84 13 UCLA 17 55 651 3.5 27100 10 20 91 14 Berkeley 13 51 652 3.42 29100 11 35 91 15 NYU 20 11 646 3.3 32700 8 35 79 16 Indiana 45 20 630 3.2 21000 8 16 68 17 Washington U 43 40 606 3.2 28000 39 62 18 Carnegie-Mell 31 65 638 3.2 27200 38 86 19 Cornell 25 38 634 3.3 29600 11 28 55 20 UNC 19 55 630 3.3 17500 16 19 80 21 Texas 18 12 631 3.3 19100 14 17 69 22 Rochester 36 34 630 3.22 28200 46 68 23 Yale 23 54 676 3.38 32000 15 31 88 24 SMU 62 48 601 3 26300 5 22 63 25 Vanderbilt 42 47 615 3.2 29700 7 23 63 26 Thunderbird 75 64 572 3.41 23800 10 33 57 27
Transcribed Image Text:A C D E G H 1 School % accepted d who enroll Mean GMAT Mean GPA Total Cost % minority % non-US štarting Salary Wharton 15 71 662 3.42 32400 16 30 102 3 Michigan 28 44 645 3.3 29800 15 26 86 4 Northwestern 14 69 660 3.3 32600 9 24 99 Harvard 13 88 680 3.5 30100 19 27 114 6 Virginia 19 49 660 3.1 31200 20 12 93 7 Columbia 14 70 660 3.3 32200 12 24 93 8 Stanford 7 81 690 3.6 34500 25 25 111 9 Chicago 23 57 685 3.4 34200 5 23 90 10 MIT 14 12 650 3.5 36700 15 37 101 11 Dartmouth 14 49 669 3.39 32700 9 16 104 12 Duke 17 50 646 3.33 30100 12 19 84 13 UCLA 17 55 651 3.5 27100 10 20 91 14 Berkeley 13 51 652 3.42 29100 11 35 91 15 NYU 20 11 646 3.3 32700 8 35 79 16 Indiana 45 20 630 3.2 21000 8 16 68 17 Washington U 43 40 606 3.2 28000 39 62 18 Carnegie-Mell 31 65 638 3.2 27200 38 86 19 Cornell 25 38 634 3.3 29600 11 28 55 20 UNC 19 55 630 3.3 17500 16 19 80 21 Texas 18 12 631 3.3 19100 14 17 69 22 Rochester 36 34 630 3.22 28200 46 68 23 Yale 23 54 676 3.38 32000 15 31 88 24 SMU 62 48 601 3 26300 5 22 63 25 Vanderbilt 42 47 615 3.2 29700 7 23 63 26 Thunderbird 75 64 572 3.41 23800 10 33 57 27
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