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 that belong to the Football Bowl Subdivision. 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.

Using Euclidean distance to compute dissimilarity between observations, apply hierarchical clustering with 10 clusters using latitude and longitude as variables. Execute the clustering two timesonce with single linkage and once with group average linkage. Compute the cluster sizes and visualize the clusters by creating a scatter plot with longitude as the x-variable and latitude as the y-variable.

In the Data tab of the Rattle GUI - R window, uncheck the box next to Partition. For the Latitude and Longitude variables, select the Input button. Select the Ignore button for the other variables and then click Execute button. In the Cluster tab, in the Type: row, select Hierarchical. In the Build Options: row, select euclidean in the Distance: box and select single (average in the second analysis) in Agglomerate: box. Enter 1 in the Processors: box. In Cluster Options: row, enter 10 in the Clusters: box, and then click the Execute button. To generate various statistics on the cluster, on the Cluster tab, click Stats. The visualization based on the latitude and longitude values can be generated using the Data Plot button in the Cluster tab.

Air Force Falcons ,52480,-104.759899,38.8632,39823782,56600,4413 Akron Zips ,30000,-81.521499,41.0804,25583730,171513,27470 Alabama Crimson Tide,101821,-87.540979,33.2377,124498616,995147,31647 Arizona State Sun Devils,73379,-111.930639,33.38835,55294113,514724,72254 Arizona Wildcats,57803,-110.891717,32.195816,59663128,552351,39236 Arkansas Razorbacks,76000,-94.155684,36.0718,91768112,788668,23199 Arkansas State Red Wolves ,30964,-90.685768,35.821828,13374507,39479,13900 Army Black Knights ,40000,-74.027317,41.362343,34342038,73190,4624 Auburn Tigers,87451,-85.480322,32.5929,103982441,471851,25469 Ball State Cardinals,22500,-87.842539,40.115904,20483476,140275,22147 Baylor Bears ,50000,-97.183198,31.56895,,1003929,15029 Boise State Broncos,37000,-116.2261,43.606651,37524722,72507,19664 Boston College Eagles ,44500,-71.017892,42.336029,,1726100,13906 Bowling Green Falcons,23724,-83.6514,41.3747,20157361,141788,17577 Buffalo Bulls,29013,-78.859684,42.8898,26228030,494791,28860 BYU Cougars,63725,-111.642674,40.24715,,920149,34101 California Golden Bears,62717,-122.29729,37.86725,65243053,3257667,25885 Central Michigan Chippewas ,30199,-84.778251,43.596552,23500552,85267,28194 Charlotte 49ers,15300,-80.834514,35.19755,,140913,25277 Cincinnati Bearcats ,35000,-84.505957,39.139801,42724841,1004368,32264 Clemson Tigers,81500,-82.812853,34.684019,61174977,473748,19914 Colorado Buffaloes ,53750,-105.251025,40.026881,60923253,784580,32252 Colorado State Rams ,34400,-105.068481,40.55555,29372783,221231,30450 Connecticut Huskies,40000,-72.256675,41.806054,63089340,312329,25868 Duke Blue Devils ,33941,-78.914969,35.980433,,5747377,15427 East Carolina Pirates ,50000,-77.374398,35.599826,34048869,128551,27386 Eastern Michigan Eagles ,30200,-83.621106,42.2442,27717621,47101,23341 Florida International Golden Panthers,20000,-80.210845,25.775667,23849954,136237,44686 Florida Atlantic Owls ,30000,-80.106624,26.3727,19438422,179739,29290 Florida Gators,92548,-82.336277,29.67415,123514257,1295313,49589 Florida State Seminoles,82300,-84.281399,30.457,78575788,525260,41087 Fresno State Bulldogs ,41031,-119.792874,36.7806,30190480,127293,21981 Georgia Bulldogs,92746,-83.393701,33.9553,92341067,745765,34816 Georgia State Panthers,71149,-84.422592,33.7629,22895575,113199,32022 Georgia Tech Yellow Jackets,55000,-84.422592,33.7629,54354409,1619718,20941 Hawaii Warriors,50000,-155.087501,19.696151,36801458,215119,20429 Houston Cougars ,32000,-95.386728,29.7687,34614033,662984,39820 Idaho Vandals,16000,-116.996844,46.729767,17545304,192003,12312 Illinois Fighting Illini,60670,-88.264949,40.113,77863883,1600603,44407 Indiana Hoosiers ,52929,-86.5264,39.1653,71017355,1574815,42731 Iowa Hawkeyes,70585,-91.535124,41.65825,93353561,1044097,29810 Iowa State Cyclones,55000,-93.625622,42.02335,48591617,612283,29611 Kansas Jayhawks ,50071,-95.255405,38.96285,74850203,1250443,27939 Kansas State Wildcats ,50000,-96.589981,39.1901,69947834,337460,23863 Kent State Golden Flashes ,30520,-81.362487,41.147067,21448821,37250,27855 Kentucky Wildcats,67606,-84.45946,38.042746,84878311,915924,27226 Louisiana Tech Bulldogs ,30600,-92.639625,32.531802,17146559,63314,11518 LouisianaLafayette Ragin' Cajuns ,31000,-92.029499,30.21525,13556901,69627,16885 LouisianaMonroe Warhawks ,30427,-92.084921,32.51165,11661727,23158,8583 Louisville Cardinals,56000,-85.741156,38.22475,87736323,772157,21153 LSU Tigers,92542,-91.126043,30.448967,107259352,692556,29718 Marshall Thundering Herd ,38016,-82.433767,38.41295,27444906,83810,13966 Maryland Terrapins ,54000,-76.934785,38.996062,61634829,791809,37580 Massachusetts Minutemen,17000,-71.248359,42.06515,27248277,210101,28084 Memphis Tigers,62380,-90.006991,35.1056,40384265,195060,22725 Miami Hurricanes,74916,-80.210845,25.775667,,719852,16068 Miami University RedHawks,24386,-84.747241,39.505667,26745727,403070,17395 Michigan State Spartans,75025,-84.48432,42.73595,122739052,317721,47954 Michigan Wolverines,114804,-83.730841,42.27535,84510199,7834752,42716 Middle Tennessee Blue Raiders ,31000,-86.394592,35.853391,27125185,64570,26442 Minnesota Golden Gophers,50805,-93.266849,44.96185,78924683,2503305,52557 Mississippi State Bulldogs,55082,-88.82216,33.456723,58981769,346676,20424 Missouri Tigers,71004,-92.326696,38.9541,64146530,1119032,33805 Navy Midshipmen ,34000,-76.503033,38.97165,,89780,4576 NC State Wolfpack,57583,-78.658753,35.82195,51076345,617632,34767 Nebraska Cornhuskers,81091,-96.688171,40.8164,83679756,1241577,24593 Nevada Wolf Pack,33400,-119.748882,39.438391,22652490,235404,18004 New Mexico Lobos,40094,-106.613892,35.11265,40287108,349145,28977 New Mexico State Aggies ,30343,-106.755756,32.336067,26997597,186737,18024 North Carolina Tar Heels,62980,-79.040627,35.927613,75606311,2260970,29137 North Texas Mean Green ,30850,-97.130942,33.214204,11259222,110735,35574 Northern Illinois Huskies ,30998,-88.75191,41.930629,24148602,49890,22990 Northwestern Wildcats,49256,-87.694549,42.04635,,7182745,19968 Notre Dame Fighting Irish,80795,-86.265699,41.6753,,6259598,12004 Ohio Bobcats,24000,-82.096051,39.324177,25470296,336000,26201 Ohio State Buckeyes,102329,-82.987381,39.988933,131815821,2120714,56867 Oklahoma Sooners,82112,-97.513491,35.46705,104338844,1212023,30743 Oklahoma State Cowboys,60218,-97.513491,35.46705,82631915,681744,24231 Old Dominion Monarchs,19818,-76.244943,36.9232,32893744,170176,24753 Ole Miss Rebels,60580,-89.526155,34.359751,49180892,469006,18224 Oregon Ducks,53800,-123.112172,44.053,85819699,467211,24936 Oregon State Beavers ,45674,-122.656496,45.53825,55544015,411964,24977 Penn State Nittany Lions,107282,-76.884503,40.27605,116118025,1725138,45628 Pittsburgh Panthers,65050,-79.976702,40.439207,,2527398,28766 Purdue Boilermakers,62500,-86.911929,40.444667,66202493,2001601,39637 Rice Owls,70000,-95.386728,29.7687,,4451452,6224 Rutgers Scarlet Knights ,52454,-74.445133,40.4864,60190100,698507,39950 San Diego State Aztecs,70561,-117.13577,32.81495,45201703,135191,31303 San Jose State Spartans ,30456,-121.849783,37.304,18861113,73100,30236 SMU Mustangs ,32000,-96.765249,32.794151,,1196508,10982 South Alabama Jaguars,40646,-88.088959,30.67745,17432045,283496,14769 South Carolina Gamecocks,80250,-80.886341,34.039236,83813226,494358,30721 South Florida Bulls,65647,-82.48212,27.959,41948123,349320,39596 Southern Miss Golden Eagles ,36000,-89.306919,31.31275,6799370,58745,11604 Stanford Cardinal ,50000,-122.164887,37.42405,,16502606,19945 Syracuse Orange,49262,-76.144067,43.041059,,913662,20829 TCU Horned Frogs,45000,-97.336249,32.753901,,1191900,9518 Temple Owls,68532,-75.134678,40.006817,,280731,36855 Tennessee Volunteers,102455,-83.946288,35.97455,104368992,848329,30194 Texas A&M Aggies,82600,-96.3342,30.6278,87296532,358946,49861 Texas Longhorns,101624,-97.750522,30.30588,150295926,2852959,38437 Texas State Bobcats ,30000,-97.929043,29.880178,21741489,119711,34087 Texas Tech Red Raiders,60454,-98.117429,29.704347,59534895,890930,32327 Toledo Rockets,26248,-83.581649,41.66395,19485449,197374,22610 Troy Trojans ,30000,-85.97,31.8086,15246720,30640,28322 Tulane Green Wave,73208,-89.931355,30.065846,,1014985,13359 Tulsa Golden Hurricane ,35542,-95.916407,36.12775,,800925,4092 UAB Blazers,70100,-86.799223,33.527746,25690048,326970,17575 UCF Knights ,45301,-81.374248,28.504748,42762625,127129,58587 UCLA Bruins,94118,-118.411201,34.112101,66003893,2975615,40675 UNLV Rebels,36800,-115.33381,36.208287,59544869,168560,27378 USC Trojans,93607,-118.411201,34.112101,,3517173,38810 Utah State Aggies,25513,-111.835125,41.74004,22777944,208986,26657 Utah Utes ,45634,-111.929921,40.777267,38091538,668683,31660 UTEP Miners,51500,-106.437549,31.84925,27694358,174922,22640 UTSA Roadrunners,65000,-98.505355,29.45765,16675632,81760,30968 Vanderbilt Commodores ,39790,-86.784829,36.17155,,3414514,12836 Virginia Cavaliers,61500,-78.485745,38.03745,78439006,4760515,24927 Virginia Tech Hokies,66233,-80.428414,37.232748,66909557,600648,30936 Wake Forest Demon Deacons ,31500,-80.26291,36.1021,,1058250,7351 Washington Huskies,72500,-122.350326,47.6218,70231336,2154494,42428 Washington State Cougars ,35117,-117.161959,46.733253,39983482,722717,27327 West Virginia Mountaineers,60540,-79.949772,39.635649,60451426,392001,29617 Western Kentucky Hilltoppers,22000,-86.441242,36.973703,22269484,114415,21036 Western Michigan Broncos ,30100,-85.588287,42.2747,25627752,198436,25086 Wisconsin Badgers,80321,-89.387519,43.0798,96288191,1872933,42441 Wyoming Cowboys ,32580,-105.583037,41.31088,27577001,321781,12925

Cluster Size ** That's 1 2 4 5 6 X 7 8 9 10 Choose the correct scatter plot diagrams below with longitude as the x-variable and latitude as the y-variable of single linkage method. (i) Single Linkage Clusters 45 40 T Oo o OO 00 0 35 . T Latitude 8oo 0008 % 30 T 00 8 25 - 20 -140 -120 -100 -80 Longitude (ii) Single Linkage Clusters 45 T o 00 o 40 00 o 35 Latitude 08 09 000.8% 30 3 8 25 20 -140 -120 -100 -80 (iv) Latitude 20 25 30 35 40 45 -140 - 120 Longitude Single Linkage Clusters o 0 000 -100 O O o 00008 @ 8 o og -80 8 0000 oo Cluster Size ** That's 1 2 4 5 6 X 7 8 9 10 Choose the correct scatter plot diagrams below with longitude as the x-variable and latitude as the y-variable of single linkage method. (i) Single Linkage Clusters 45 40 T Oo o OO 00 0 35 . T Latitude 8oo 0008 % 30 T 00 8 25 - 20 -140 -120 -100 -80 Longitude (ii) Single Linkage Clusters 45 T o 00 o 40 00 o 35 Latitude 08 09 000.8% 30 3 8 25 20 -140 -120 -100 -80 (iv) Latitude 20 25 30 35 40 45 -140 - 120 Longitude Single Linkage Clusters o 0 000 -100 O O o 00008 @ 8 o og -80 8 0000 oo