Question

 

The Football Bowl Subdivision (FBS) level of the National Collegiate Athletic Association (NCAA) consists of over 100 schools. Most of these schools belong to one of several conferences, or collections of schools, that compete with each other on a regular basis in collegiate sports. Suppose the NCAA has commissioned a study that will propose the formation of conferences based on the similarities of the constituent schools. The file FBS contains data on schools belong to the Football Bowl Subdivision (FBS). Each row in this file contains information on a school. The variables include football stadium capacity, latitude, longitude, athletic department revenue, endowment, and undergraduate enrollment.

School	StadiumCapacity	Latitude	Longitude	AthleticRevenue ($)	Endowment ($000)	Enrollment
Air Force Falcons	52,480	38.86	-104.76	39,823,782	56,600	4,413
Akron Zips	30,000	41.08	-81.52	25,583,730	171,513	27,470
Alabama Crimson Tide	101,821	33.24	-87.54	124,498,616	995,147	31,647
Arizona State Sun Devils	73,379	33.39	-111.93	55,294,113	514,724	72,254
Arizona Wildcats	57,803	32.20	-110.89	59,663,128	552,351	39,236
Arkansas Razorbacks	76,000	36.07	-94.16	91,768,112	788,668	23,199
Arkansas State Red Wolves	30,964	35.82	-90.69	13,374,507	39,479	13,900
Army Black Knights	40,000	41.36	-74.03	34,342,038	73,190	4,624
Auburn Tigers	87,451	32.59	-85.48	103,982,441	471,851	25,469
Ball State Cardinals	22,500	40.12	-87.84	20,483,476	140,275	22,147
Baylor Bears	50,000	31.57	-97.18		1,003,929	15,029
Boise State Broncos	37,000	43.61	-116.23	37,524,722	72,507	19,664
Boston College Eagles	44,500	42.34	-71.02		1,726,100	13,906
Bowling Green Falcons	23,724	41.37	-83.65	20,157,361	141,788	17,577
Buffalo Bulls	29,013	42.89	-78.86	26,228,030	494,791	28,860
BYU Cougars	63,725	40.25	-111.64		920,149	34,101
California Golden Bears	62,717	37.87	-122.30	65,243,053	3,257,667	25,885
Central Michigan Chippewas	30,199	43.60	-84.78	23,500,552	85,267	28,194
Charlotte 49ers	15,300	35.20	-80.83		140,913	25,277
Cincinnati Bearcats	35,000	39.14	-84.51	42,724,841	1,004,368	32,264
Clemson Tigers	81,500	34.68	-82.81	61,174,977	473,748	19,914
Colorado Buffaloes	53,750	40.03	-105.25	60,923,253	784,580	32,252
Colorado State Rams	34,400	40.56	-105.07	29,372,783	221,231	30,450
Connecticut Huskies	40,000	41.81	-72.26	63,089,340	312,329	25,868
Duke Blue Devils	33,941	35.98	-78.91		5,747,377	15,427
East Carolina Pirates	50,000	35.60	-77.37	34,048,869	128,551	27,386
Eastern Michigan Eagles	30,200	42.24	-83.62	27,717,621	47,101	23,341
Florida International Golden Panthers	20,000	25.78	-80.21	23,849,954	136,237	44,686
Florida Atlantic Owls	30,000	26.37	-80.11	19,438,422	179,739	29,290
Florida Gators	92,548	29.67	-82.34	123,514,257	1,295,313	49,589
Florida State Seminoles	82,300	30.46	-84.28	78,575,788	525,260	41,087
Fresno State Bulldogs	41,031	36.78	-119.79	30,190,480	127,293	21,981
Georgia Bulldogs	92,746	33.96	-83.39	92,341,067	745,765	34,816
Georgia State Panthers	71,149	33.76	-84.42	22,895,575	113,199	32,022
Georgia Tech Yellow Jackets	55,000	33.76	-84.42	54,354,409	1,619,718	20,941
Hawaiʻi Warriors	50,000	19.70	-155.09	36,801,458	215,119	20,429
Houston Cougars	32,000	29.77	-95.39	34,614,033	662,984	39,820
Idaho Vandals	16,000	46.73	-117.00	17,545,304	192,003	12,312
Illinois Fighting Illini	60,670	40.11	-88.26	77,863,883	1,600,603	44,407
Indiana Hoosiers	52,929	39.17	-86.53	71,017,355	1,574,815	42,731
Iowa Hawkeyes	70,585	41.66	-91.54	93,353,561	1,044,097	29,810
Iowa State Cyclones	55,000	42.02	-93.63	48,591,617	612,283	29,611
Kansas Jayhawks	50,071	38.96	-95.26	74,850,203	1,250,443	27,939
Kansas State Wildcats	50,000	39.19	-96.59	69,947,834	337,460	23,863
Kent State Golden Flashes	30,520	41.15	-81.36	21,448,821	37,250	27,855
Kentucky Wildcats	67,606	38.04	-84.46	84,878,311	915,924	27,226
Louisiana Tech Bulldogs	30,600	32.53	-92.64	17,146,559	63,314	11,518
Louisiana–Lafayette Ragin' Cajuns	31,000	30.22	-92.03	13,556,901	69,627	16,885
Louisiana–Monroe Warhawks	30,427	32.51	-92.08	11,661,727	23,158	8,583
Louisville Cardinals	56,000	38.22	-85.74	87,736,323	772,157	21,153
LSU Tigers	92,542	30.45	-91.13	107,259,352	692,556	29,718
Marshall Thundering Herd	38,016	38.41	-82.43	27,444,906	83,810	13,966
Maryland Terrapins	54,000	39.00	-76.93	61,634,829	791,809	37,580
Massachusetts Minutemen	17,000	42.07	-71.25	27,248,277	210,101	28,084
Memphis Tigers	62,380	35.11	-90.01	40,384,265	195,060	22,725
Miami Hurricanes	74,916	25.78	-80.21		719,852	16,068
Miami University RedHawks	24,386	39.51	-84.75	26,745,727	403,070	17,395
Michigan State Spartans	75,025	42.74	-84.48	122,739,052	317,721	47,954
Michigan Wolverines	114,804	42.28	-83.73	84,510,199	7,834,752	42,716
Middle Tennessee Blue Raiders	31,000	35.85	-86.39	27,125,185	64,570	26,442
Minnesota Golden Gophers	50,805	44.96	-93.27	78,924,683	2,503,305	52,557
Mississippi State Bulldogs	55,082	33.46	-88.82	58,981,769	346,676	20,424
Missouri Tigers	71,004	38.95	-92.33	64,146,530	1,119,032	33,805
Navy Midshipmen	34,000	38.97	-76.50		89,780	4,576
NC State Wolfpack	57,583	35.82	-78.66	51,076,345	617,632	34,767
Nebraska Cornhuskers	81,091	40.82	-96.69	83,679,756	1,241,577	24,593
Nevada Wolf Pack	33,400	39.44	-119.75	22,652,490	235,404	18,004
New Mexico Lobos	40,094	35.11	-106.61	40,287,108	349,145	28,977
New Mexico State Aggies	30,343	32.34	-106.76	26,997,597	186,737	18,024
North Carolina Tar Heels	62,980	35.93	-79.04	75,606,311	2,260,970	29,137
North Texas Mean Green	30,850	33.21	-97.13	11,259,222	110,735	35,574
Northern Illinois Huskies	30,998	41.93	-88.75	24,148,602	49,890	22,990
Northwestern Wildcats	49,256	42.05	-87.69		7,182,745	19,968
Notre Dame Fighting Irish	80,795	41.68	-86.27		6,259,598	12,004
Ohio Bobcats	24,000	39.32	-82.10	25,470,296	336,000	26,201
Ohio State Buckeyes	102,329	39.99	-82.99	131,815,821	2,120,714	56,867
Oklahoma Sooners	82,112	35.47	-97.51	104,338,844	1,212,023	30,743
Oklahoma State Cowboys	60,218	35.47	-97.51	82,631,915	681,744	24,231
Old Dominion Monarchs	19,818	36.92	-76.24	32,893,744	170,176	24,753
Ole Miss Rebels	60,580	34.36	-89.53	49,180,892	469,006	18,224
Oregon Ducks	53,800	44.05	-123.11	85,819,699	467,211	24,936
Oregon State Beavers	45,674	45.54	-122.66	55,544,015	411,964	24,977
Penn State Nittany Lions	107,282	40.28	-76.88	116,118,025	1,725,138	45,628
Pittsburgh Panthers	65,050	40.44	-79.98		2,527,398	28,766
Purdue Boilermakers	62,500	40.44	-86.91	66,202,493	2,001,601	39,637
Rice Owls	70,000	29.77	-95.39		4,451,452	6,224
Rutgers Scarlet Knights	52,454	40.49	-74.45	60,190,100	698,507	39,950
San Diego State Aztecs	70,561	32.81	-117.14	45,201,703	135,191	31,303
San Jose State Spartans	30,456	37.30	-121.85	18,861,113	73,100	30,236
SMU Mustangs	32,000	32.79	-96.77		1,196,508	10,982
South Alabama Jaguars	40,646	30.68	-88.09	17,432,045	283,496	14,769
South Carolina Gamecocks	80,250	34.04	-80.89	83,813,226	494,358	30,721
South Florida Bulls	65,647	27.96	-82.48	41,948,123	349,320	39,596
Southern Miss Golden Eagles	36,000	31.31	-89.31	6,799,370	58,745	11,604
Stanford Cardinal	50,000	37.42	-122.16		16,502,606	19,945
Syracuse Orange	49,262	43.04	-76.14		913,662	20,829
TCU Horned Frogs	45,000	32.75	-97.34		1,191,900	9,518
Temple Owls	68,532	40.01	-75.13		280,731	36,855
Tennessee Volunteers	102,455	35.97	-83.95	104,368,992	848,329	30,194
Texas A&M Aggies	82,600	30.63	-96.33	87,296,532	358,946	49,861
Texas Longhorns	101,624	30.31	-97.75	150,295,926	2,852,959	38,437
Texas State Bobcats	30,000	29.88	-97.93	21,741,489	119,711	34,087
Texas Tech Red Raiders	60,454	29.70	-98.12	59,534,895	890,930	32,327
Toledo Rockets	26,248	41.66	-83.58	19,485,449	197,374	22,610
Troy Trojans	30,000	31.81	-85.97	15,246,720	30,640	28,322
Tulane Green Wave	73,208	30.07	-89.93		1,014,985	13,359
Tulsa Golden Hurricane	35,542	36.13	-95.92		800,925	4,092
UAB Blazers	70,100	33.53	-86.80	25,690,048	326,970	17,575
UCF Knights	45,301	28.50	-81.37	42,762,625	127,129	58,587
UCLA Bruins	94,118	34.11	-118.41	66,003,893	2,975,615	40,675
UNLV Rebels	36,800	36.21	-115.33	59,544,869	168,560	27,378
USC Trojans	93,607	34.11	-118.41		3,517,173	38,810
Utah State Aggies	25,513	41.74	-111.84	22,777,944	208,986	26,657
Utah Utes	45,634	40.78	-111.93	38,091,538	668,683	31,660
UTEP Miners	51,500	31.85	-106.44	27,694,358	174,922	22,640
UTSA Roadrunners	65,000	29.46	-98.51	16,675,632	81,760	30,968
Vanderbilt Commodores	39,790	36.17	-86.78		3,414,514	12,836
Virginia Cavaliers	61,500	38.04	-78.49	78,439,006	4,760,515	24,927
Virginia Tech Hokies	66,233	37.23	-80.43	66,909,557	600,648	30,936
Wake Forest Demon Deacons	31,500	36.10	-80.26		1,058,250	7,351
Washington Huskies	72,500	47.62	-122.35	70,231,336	2,154,494	42,428
Washington State Cougars	35,117	46.73	-117.16	39,983,482	722,717	27,327
West Virginia Mountaineers	60,540	39.64	-79.95	60,451,426	392,001	29,617
Western Kentucky Hilltoppers	22,000	36.97	-86.44	22,269,484	114,415	21,036
Western Michigan Broncos	30,100	42.27	-85.59	25,627,752	198,436	25,086
Wisconsin Badgers	80,321	43.08	-89.39	96,288,191	1,872,933	42,441
Wyoming Cowboys	32,580	41.31	-105.58	27,577,001	321,781	12,925

A) Apply hierarchical clustering with 10 clusters using latitude and longitude as variables. Be sure to Normalize Input Data in Step 2 of the XLMiner Hierarchical Clustering procedure. Compute the cluster sizes, as well as the minimum and maximum of the latitude and longitude of single linkage method. If required, round your answers to one decimal places. If your answer is negative, use minus sign.

Cluster Id	Cluster Size	Min of Latitude	Max of Latitude	Min of Longitude	Max of Longitude
1
2
3
4
5
6
7
8
9
10

B) Write down the geographical span for the largest cluster.

C) Compute the cluster sizes, as well as the minimum and maximum of the latitude and longitude of group average linkage method.

Cluster Id	Cluster Size	Min of Latitude	Max of Latitude	Min of Longitude	Max of Longitude
1
2
3
4
5
6
7
8
9
10

D) Compare the results of the two approaches.

Answer 1