eBook Problem 4-3 The Football Bowl Subdivision (FBS) level of the National Coll

Question

eBook Problem 4-3 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. Click on the datafile logo to reference the data. DATA file (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 Choose the correct scatter plot diagrams below with longitude as the x-variable and latitude as the y-variable of single linkage method. (i) ch04_03a.png (ii) ch04_03b.png (iii) ch04_03c.png (iv) ch04_03d.png - Select your answer -IIIIIIIVItem 51 Write down the geographical span for the largest cluster. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (b) 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 Choose the correct scatter plot diagrams below with longitude as the x-variable and latitude as the y-variable of group average linkage method. (i) ch04_03b1.png (ii) ch04_03b2.png (iii) ch04_03b3.png (iv) ch04_03b4.png - Select your answer -IIIIIIIVItem 103 Compare the results of the two approaches. The input in the box below will not be graded, but may be reviewed and considered by your instructor. 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 Hawaii 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

Explanation / Answer

We can use R-software to analysis this data set.

x=read.csv("Book1.csv") # data file name
y=sapply(x, as.numeric ) ## which variable is numeric
c1=hclust(dist(y[, 2:7]),method='complete')
plot(c1)
cl1=cutree(c1, 10)

[1] 1 2 3 4 4 3 5 2 3 2 3 6 2 2 2 1 7 8 5 2 5 1 1 2 5
[26] 5 8 9 9 9 9 7 5 5 5 10 3 6 2 2 8 8 8 8 2 2 3 3 3 2
[51] 3 2 2 2 5 9 2 8 8 5 8 3 8 2 5 8 7 4 4 5 3 8 8 8 2
[76] 2 3 3 5 3 6 6 2 2 2 3 2 4 7 3 3 5 9 3 7 2 3 2 5 3
[101] 3 3 3 2 3 3 3 3 9 4 4 4 1 1 4 3 5 5 5 5 6 6 2 5 8
[126] 8 1

c2=hclust(dist(y[, 2:7]), method = 'average')
plot(c2)
cl2=cutree(c2, 10)

1 2 3 1 1 1 2 1 4 2 5 2 5 2 2 4 1 2 2 6 1 1 2 1 2
[26] 2 2 7 2 8 1 2 1 8 2 9 1 2 6 6 6 1 2 1 2 1 2 2 7 1
[51] 4 2 1 2 2 4 2 8 10 2 6 1 6 3 1 6 2 2 2 1 7 2 2 4 2
[76] 7 8 1 2 1 1 1 7 8 6 8 1 6 3 5 2 1 1 2 5 2 7 8 3 1
[101] 7 7 1 2 2 5 3 4 6 6 2 8 2 1 2 4 2 1 1 7 6 2 1 2 2
[126] 6 2

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