K-Means Clustering
To begin the analysis k-means clustering is used with 6 different groups to differentiate the colleges initially. The following lists the colleges and the cluster they are in and then puts them in order by those clusters.
set.seed(1)
grpEdu <- kmeans(edu[,c(-1,-2)], centers=6, nstart=10) #solve for 6 grps but start with 10 grps
clusEdu<-cbind(edu,cluster=grpEdu$cluster)
head(clusEdu)
## College State Public MathSAT VerbSAT ACT Received
## 1 Christendom College VA 0 568 568 23 81
## 2 Mount Vernon College DC 0 440 402 20 149
## 3 King's College NY 0 442 465 25 356
## 4 Alaska Pacific University AK 0 490 482 20 193
## 5 Sierra Nevada College NV 0 400 400 21 200
## 6 Trinity College DC 0 470 480 22 247
## Accepted Enrolled Pct10 Pct25 FTUG PTUG ISTuit OSTuit Books PhDs SFRatio
## 1 72 51 33 71 139 3 8730 8730 400 92 9.3
## 2 70 61 15 35 203 138 13780 13780 500 84 5.7
## 3 233 53 16 24 246 18 8190 8190 500 100 7.0
## 4 146 55 16 44 249 869 7560 7560 800 76 11.9
## 5 160 100 5 25 300 50 7500 7500 500 45 7.5
## 6 189 100 19 49 309 639 11412 11412 500 89 8.3
## cluster
## 1 6
## 2 2
## 3 6
## 4 6
## 5 6
## 6 6
o=order(grpEdu$cluster)
data.frame(edu$College[o],grpEdu$cluster[o]) #shows college and what cluster it is in
## edu.College.o. grpEdu.cluster.o.
## 1 Webber College 1
## 2 Kendall College 1
## 3 Bartlesville Wesleyan College 1
## 4 College of the Southwest 1
## 5 Tennessee Wesleyan College 1
## 6 Pacific Christian College 1
## 7 Huston-Tillotson College 1
## 8 Texas College 1
## 9 Concordia Lutheran College 1
## 10 Jarvis Christian College 1
## 11 Bennett College 1
## 12 Bluefield College 1
## 13 Voorhees College 1
## 14 Univ. of Texas of the Permian Basin 1
## 15 Dallas Baptist University 1
## 16 McMurry University 1
## 17 John Brown University 1
## 18 Mars Hill College 1
## 19 Freed-Hardeman University 1
## 20 Howard Payne University 1
## 21 Texas Wesleyan University 1
## 22 Cumberland College 1
## 23 Flagler College 1
## 24 Hardin-Simmons University 1
## 25 Oklahoma Christian University 1
## 26 Bluefield State College 1
## 27 Montana College of Mineral Sci. & Tech. MT 1
## 28 Castleton State College 1
## 29 University of Minnesota at Morris 1
## 30 University of South Carolina at Aiken 1
## 31 Spelman College 1
## 32 University of North Carolina at Asheville 1
## 33 Lander University 1
## 34 University of Texas at Dallas 1
## 35 Bethune Cookman College 1
## 36 Cedarville College 1
## 37 Univ. of South Carolina at Spartanburg 1
## 38 Grove City College 1
## 39 Western State College of Colorado 1
## 40 Shepherd College 1
## 41 Xavier University of Louisiana 1
## 42 Morehouse College 1
## 43 Longwood College 1
## 44 Harding University 1
## 45 Winthrop University 1
## 46 Mesa State College 1
## 47 SUNY College at Potsdam 1
## 48 University of Southern Colorado 1
## 49 University of West Florida 1
## 50 University of Colorado at Denver 1
## 51 University of North Florida 1
## 52 University of Missouri at Rolla 1
## 53 West Texas A&M University 1
## 54 SUNY College at Fredonia 1
## 55 Angelo State University 1
## 56 University of Southern Indiana 1
## 57 Salisbury State University 1
## 58 Troy State University at Troy 1
## 59 South Carolina State University 1
## 60 Prairie View A. and M. University 1
## 61 SUNY College at Plattsburgh 1
## 62 Lamar University 1
## 63 Michigan Technological University 1
## 64 Winona State University 1
## 65 Mount Vernon College 2
## 66 Albertus Magnus College 2
## 67 Wells College 2
## 68 Chatham College 2
## 69 Sweet Briar College 2
## 70 Scripps College 2
## 71 Stephens College 2
## 72 Randolph-Macon Woman's College 2
## 73 Monmouth College 2
## 74 Albertson College 2
## 75 Hood College 2
## 76 Bethany College 2
## 77 Antioch University 2
## 78 Ripon College 2
## 79 Pitzer College 2
## 80 Oglethorpe University 2
## 81 Cedar Crest College 2
## 82 Hollins College 2
## 83 Claremont McKenna College 2
## 84 Heidelberg College 2
## 85 Knox College 2
## 86 Albright College 2
## 87 Hiram College 2
## 88 Earlham College 2
## 89 Pacific University 2
## 90 Beloit College 2
## 91 Elmira College 2
## 92 Muskingum College 2
## 93 Coe College 2
## 94 University of the South 2
## 95 Cornell College 2
## 96 Simmons College 2
## 97 Reed College 2
## 98 Whitman College 2
## 99 Westmont College 2
## 100 Grinnell College 2
## 101 Wheaton College 2
## 102 Hamline University 2
## 103 Lycoming College 2
## 104 Eckerd College 2
## 105 Carthage College 2
## 106 Guilford College 2
## 107 California Lutheran University 2
## 108 University of La Verne 2
## 109 Kenyon College 2
## 110 Hartwick College 2
## 111 West Virginia Wesleyan College 2
## 112 Linfield College 2
## 113 Amherst College 2
## 114 Willamette University 2
## 115 Davidson College 2
## 116 Muhlenberg College 2
## 117 Chapman University 2
## 118 Rollins College 2
## 119 College of Wooster 2
## 120 Colby College 2
## 121 Franklin and Marshall College 2
## 122 Ohio Wesleyan University 2
## 123 Illinois Wesleyan University 2
## 124 Mount Holyoke College 2
## 125 Illinois Institute of Technology 2
## 126 Buena Vista College 2
## 127 Wittenberg University 2
## 128 Azusa Pacific University 2
## 129 Vassar College 2
## 130 Luther College 2
## 131 Gustavus Adolphus College 2
## 132 Skidmore College 2
## 133 Pepperdine University 2
## 134 Ohio Northern University 2
## 135 Gonzaga University 2
## 136 Pacific Lutheran University 2
## 137 Oberlin College 2
## 138 Butler University 2
## 139 Colgate University 2
## 140 University of Denver 2
## 141 Wesleyan University 2
## 142 University of Puget Sound 2
## 143 Worcester Polytechnic Institute 2
## 144 Saint Olaf College 2
## 145 Fairfield University 2
## 146 Seattle University 2
## 147 Drake University 2
## 148 Providence College 2
## 149 University of San Francisco 2
## 150 SUNY College at New Paltz 3
## 151 SUNY College at Cortland 3
## 152 SUNY College at Geneseo 3
## 153 Texas Southern University 3
## 154 SUNY College at Brockport 3
## 155 University of Maryland at Baltimore County 3
## 156 University of North Carolina at Wilmington 3
## 157 East Tennessee State University 3
## 158 College of Charleston 3
## 159 SUNY College at Oswego 3
## 160 University of Idaho 3
## 161 Marshall University 3
## 162 Cleveland State University 3
## 163 Radford University 3
## 164 University of North Dakota 3
## 165 University of Northern Colorado 3
## 166 Univ. of Wisconsin at Eau Claire 3
## 167 SUNY at Binghamton 3
## 168 Indiana State University 3
## 169 Montana State University 3
## 170 Western Washington University 3
## 171 Indiana Univ.-Purdue Univ. at Indianapolis 3
## 172 University of Southern Mississippi 3
## 173 University of Texas at San Antonio 3
## 174 Metropolitan State College 3
## 175 Stephen F. Austin State University 3
## 176 Appalachian State University 3
## 177 University of North Carolina at Charlotte 3
## 178 Florida International University 3
## 179 Utah State University 3
## 180 University of Texas at Arlington 3
## 181 University of Cincinnati 3
## 182 Northern Arizona University 3
## 183 University of Central Florida 3
## 184 University of South Carolina at Columbia 3
## 185 Oklahoma State University 3
## 186 California Polytechnic-San Luis 3
## 187 East Carolina University 3
## 188 Bowling Green State University 3
## 189 Southwest Texas State University 3
## 190 University of Utah 3
## 191 University of North Texas 3
## 192 University of South Florida 3
## 193 University of Missouri at Columbia 3
## 194 Ohio University 3
## 195 Kent State University 3
## 196 Colorado State University 3
## 197 University of Tennessee at Knoxville 3
## 198 Ball State University 3
## 199 Auburn University-Main Campus 3
## 200 Louisiana State University at Baton Rouge 3
## 201 San Diego State University 3
## 202 University of Nebraska at Lincoln 3
## 203 University of Minnesota Twin Cities 3
## 204 Johns Hopkins University 4
## 205 Carnegie Mellon University 4
## 206 Massachusetts Institute of Technology 4
## 207 Vanderbilt University 4
## 208 Emory University 4
## 209 Brown University 4
## 210 Duke University 4
## 211 Hofstra University 4
## 212 Northwestern University 4
## 213 University of Pennsylvania 4
## 214 Northeastern University 4
## 215 University of Southern California 4
## 216 Boston University 4
## 217 University of Arizona 5
## 218 University of Michigan at Ann Arbor 5
## 219 Arizona State University Main campus 5
## 220 Indiana University at Bloomington 5
## 221 University of Illinois - Urbana 5
## 222 Michigan State University 5
## 223 University of Texas at Austin 5
## 224 Texas A&M Univ. at College Station 5
## 225 Christendom College 6
## 226 King's College 6
## 227 Alaska Pacific University 6
## 228 Sierra Nevada College 6
## 229 Trinity College 6
## 230 Montreat-Anderson College 6
## 231 Saint Mary-of-the-Woods College 6
## 232 Notre Dame College of Ohio 6
## 233 Centenary College 6
## 234 Covenant College 6
## 235 Huntington College 6
## 236 St. Martin's College 6
## 237 Virginia Intermont College 6
## 238 Nyack College 6
## 239 Saint Francis College 6
## 240 Schreiner College 6
## 241 Center for Creative Studies 6
## 242 Salem College 6
## 243 Huntingdon College 6
## 244 Concordia College 6
## 245 Phillips University 6
## 246 Newberry College 6
## 247 Southwestern Adventist College 6
## 248 Maryville College 6
## 249 Queens College 6
## 250 Sterling College 6
## 251 Union College 6
## 252 Concordia University 6
## 253 Defiance College 6
## 254 North Carolina Wesleyan College 6
## 255 Avila College 6
## 256 Tiffin University 6
## 257 University of Dubuque 6
## 258 Kentucky Wesleyan College 6
## 259 Westminster College 6
## 260 Ursuline College 6
## 261 Fresno Pacific College 6
## 262 College of Mount St. Vincent 6
## 263 Northland College 6
## 264 Bethel College 6
## 265 Belhaven College 6
## 266 Keuka College 6
## 267 Briar Cliff College 6
## 268 Rocky Mountain College 6
## 269 Davis & Elkins College 6
## 270 Bluffton College 6
## 271 University of Charleston 6
## 272 Centenary College of Louisiana 6
## 273 Southern California College 6
## 274 Thiel College 6
## 275 Alderson-Broaddus College 6
## 276 Emory & Henry College 6
## 277 Concordia College 6
## 278 Saint Joseph's College 6
## 279 Franklin College 6
## 280 William Woods University 6
## 281 Transylvania University 6
## 282 College of Santa Fe 6
## 283 North Park College 6
## 284 Hilbert College 6
## 285 Texas Lutheran College 6
## 286 Manchester College 6
## 287 Illinois College 6
## 288 Mount Mary College 6
## 289 Centre College 6
## 290 Hendrix College 6
## 291 Wheeling Jesuit College 6
## 292 Tri-State University 6
## 293 Tusculum College 6
## 294 Marymount Manhattan College 6
## 295 University of St. Thomas 6
## 296 Graceland College 6
## 297 Cazenovia College 6
## 298 Hanover College 6
## 299 Mount St. Mary's College 6
## 300 Central Wesleyan College 6
## 301 Missouri Valley College 6
## 302 Eastern College 6
## 303 University of Dallas 6
## 304 Dowling College 6
## 305 Wofford College 6
## 306 Christian Brothers University 6
## 307 Quincy University 6
## 308 Millsaps College 6
## 309 D'Youville College 6
## 310 Carroll College 6
## 311 Asbury College 6
## 312 Austin College 6
## 313 Presbyterian College 6
## 314 Hillsdale College 6
## 315 College of Mount St. Joseph 6
## 316 Mount Saint Mary College 6
## 317 Point Park College 6
## 318 Southwestern University 6
## 319 Lenoir-Rhyne College 6
## 320 Bellarmine College 6
## 321 Wingate College 6
## 322 Northwestern College 6
## 323 Houghton College 6
## 324 Whitworth College 6
## 325 Nazareth College of Rochester 6
## 326 William Jewell College 6
## 327 Wartburg College 6
## 328 Franciscan University of Steubenville 6
## 329 Geneva College 6
## 330 North Central College 6
## 331 Maryville University 6
## 332 College of St. Scholastica 6
## 333 Birmingham-Southern College 6
## 334 Westminster College 6
## 335 University of Indianapolis 6
## 336 Saint Mary's College 6
## 337 Florida Southern College 6
## 338 LeTourneau University 6
## 339 Gardner Webb University 6
## 340 Malone College 6
## 341 Northwood University 6
## 342 St. Joseph's College 6
## 343 Incarnate Word College 6
## 344 St. John Fisher College 6
## 345 St. Bonaventure University 6
## 346 Saint John's University 6
## 347 College of Saint Catherine 6
## 348 College of Saint Benedict 6
## 349 St. Edward's University 6
## 350 Webster University 6
## 351 Taylor University 6
## 352 Millikin University 6
## 353 Barry University 6
## 354 Anderson University 6
## 355 Ashland University 6
## 356 Point Loma Nazarene College 6
## 357 Savannah Coll. of Art and Design 6
## 358 St. Norbert College 6
## 359 Belmont University 6
## 360 Augsburg College 6
## 361 University of Detroit Mercy 6
## 362 St. Mary's University of San Antonio 6
## 363 Lindenwood College 6
## 364 Widener University 6
## 365 Messiah College 6
## 366 Indiana Wesleyan University 6
## 367 Oral Roberts University 6
## 368 Siena College 6
## 369 Gannon University 6
## 370 Baldwin-Wallace College 6
## 371 Loyola University 6
## 372 Xavier University 6
## 373 University of Tulsa 6
## 374 Mercer University 6
## 375 John Carroll University 6
## 376 Calvin College 6
## 377 Marist College 6
## 378 Iona College 6
## 379 University of St. Thomas 6
## 380 Bradley University 6
## 381 Embry Riddle Aeronautical University 6
## 382 Loyola University Chicago 6
## 383 University of Dayton 6
## 384 DePaul University 6
## 385 Marquette University 6
The number of applications received is plotted against the school’s in-state tuition. This is done to look for any relationships between variables.
summary(edu$Received)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 77 682 1272 2691 3270 20192
plot(edu$Received, edu$ISTuit, type="n", xlim=c(70,20200), xlab="Applications Received", ylab="Tuition (In-State)")
text(x=edu$Received, y=edu$ISTuit, labels=edu$College, col=rainbow(6)[grpEdu$cluster])
The graph is difficult to read but some overarching conclusions can be drawn from it. The six clusters are condensed in three general areas so using three clusters could generate better results. There also seems to be a large number of public schools listed in the lower right corner. So, to see if being a public or private institution is significant in distinguishing the clusters the following code is run.
m1 <- aov(Public ~ as.factor(cluster), data=clusEdu)
summary(m1)
## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(cluster) 5 53.08 10.616 223.9 <2e-16 ***
## Residuals 379 17.97 0.047
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Whether an institution is public or private does prove statistically significant enough to distinguish the clusters. To see other patterns that could distinguish the clusters the group means for each cluster is procured.
grpEdu$centers
## Public MathSAT VerbSAT ACT Received Accepted Enrolled
## 1 0.50000000 479.6719 436.9531 20.93750 1548.281 1067.7031 503.2812
## 2 0.01176471 553.3765 507.3647 24.61176 1810.671 1247.8706 404.0353
## 3 0.98148148 511.9074 456.6481 22.27778 6370.667 4363.1667 2128.8519
## 4 0.00000000 644.3846 564.8462 27.61538 10978.308 5620.4615 1806.0769
## 5 1.00000000 566.6250 490.1250 24.62500 15613.250 11946.0000 5332.7500
## 6 0.00000000 498.2360 458.9441 22.32919 1063.410 850.6584 322.8820
## Pct10 Pct25 FTUG PTUG ISTuit OSTuit Books
## 1 20.56250 46.82812 2297.000 680.0625 3911.781 5922.531 535.2188
## 2 36.47059 66.09412 1580.976 227.1294 15471.082 15471.082 531.2588
## 3 22.24074 53.79630 10753.741 3422.4815 2127.685 6677.074 569.8704
## 4 65.84615 86.00000 7520.462 1481.6154 17264.385 17264.385 629.5385
## 5 39.50000 73.12500 25598.375 3694.1250 2527.875 8605.500 581.2500
## 6 22.66460 50.02484 1400.565 490.5590 10011.745 10011.758 558.0745
## PhDs SFRatio
## 1 62.53125 16.29687
## 2 81.31765 12.10118
## 3 80.48148 17.90370
## 4 90.76923 8.40000
## 5 88.25000 18.18750
## 6 63.96894 14.09689
m2 <- aov(Books ~ as.factor(cluster), data=clusEdu)
summary(m2)
## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(cluster) 5 162464 32493 1.002 0.416
## Residuals 379 12291567 32432
The only variable whose group means don’t appear to variate greatly among the six clusters is estimated book cost and when a one-way ANOVA table is created the F value and p-statistic agree with that observation. The cost of books is not significant enough to distinguish the clusters.
Hierarchical Clustering
This data set can also be grouped using the hierarchical clustering method.
EduClus<-edu[,c(-1,-2)]
EduClus
## Public MathSAT VerbSAT ACT Received Accepted Enrolled Pct10 Pct25
## 1 0 568 568 23 81 72 51 33 71
## 2 0 440 402 20 149 70 61 15 35
## 3 0 442 465 25 356 233 53 16 24
## 4 0 490 482 20 193 146 55 16 44
## 5 0 400 400 21 200 160 100 5 25
## 6 0 470 480 22 247 189 100 19 49
## 7 0 443 427 20 263 223 103 10 24
## 8 0 370 437 20 280 143 79 5 27
## 9 0 420 450 18 150 150 121 15 15
## 10 0 422 392 20 150 130 88 23 50
## 11 0 430 440 22 149 114 81 19 41
## 12 0 460 390 19 77 61 27 7 38
## 13 0 415 423 19 136 107 42 12 36
## 14 0 500 470 19 369 312 90 12 46
## 15 0 440 370 19 232 182 99 7 29
## 16 0 474 426 22 167 142 89 9 41
## 17 0 460 430 23 353 340 103 17 45
## 18 0 590 490 24 318 240 130 40 85
## 19 0 336 450 16 261 159 114 7 20
## 20 0 536 512 24 407 317 181 21 48
## 21 0 481 491 22 212 197 91 28 56
## 22 0 480 422 21 450 430 125 20 46
## 23 0 480 460 19 191 165 63 5 25
## 24 0 427 410 19 411 354 138 14 42
## 25 0 330 290 16 254 189 189 15 26
## 26 0 472 433 21 460 283 160 15 34
## 27 0 450 410 21 213 166 85 13 36
## 28 0 470 420 22 584 413 131 19 51
## 29 0 470 450 21 601 396 203 1 20
## 30 0 510 500 24 462 402 146 36 68
## 31 0 469 402 20 232 216 106 16 34
## 32 0 508 494 24 335 284 132 28 69
## 33 0 513 446 23 608 520 127 26 47
## 34 0 341 316 11 575 482 206 9 18
## 35 0 500 485 20 180 171 74 19 39
## 36 0 590 560 26 855 632 139 60 83
## 37 0 465 423 22 692 576 174 19 50
## 38 0 466 418 20 872 722 154 14 36
## 39 0 474 426 21 450 405 194 17 34
## 40 0 419 395 21 321 318 172 11 27
## 41 0 505 448 23 1464 888 176 26 52
## 42 0 514 491 26 516 392 154 32 62
## 43 0 441 402 22 479 373 127 20 43
## 44 0 440 390 20 484 384 177 9 45
## 45 0 485 420 22 688 497 144 30 75
## 46 0 438 381 21 571 461 174 10 26
## 47 0 432 394 20 812 689 195 7 24
## 48 0 395 385 17 774 542 193 17 38
## 49 0 450 450 22 373 298 86 14 43
## 50 0 431 388 20 377 358 181 15 30
## 51 0 517 502 25 696 616 169 35 66
## 52 0 372 308 19 845 734 254 5 21
## 53 0 480 430 22 576 558 137 11 39
## 54 0 450 410 22 584 497 175 20 49
## 55 0 520 480 24 662 553 184 20 43
## 56 0 470 470 23 601 503 204 28 57
## 57 0 524 487 24 587 479 158 38 62
## 58 0 434 404 21 325 260 86 21 47
## 59 0 340 330 16 1465 1006 188 10 30
## 60 0 532 476 22 346 274 146 51 87
## 61 0 474 454 23 946 648 177 23 46
## 62 0 509 485 24 699 565 176 36 64
## 63 0 479 448 23 664 515 210 12 44
## 64 0 504 516 24 713 661 252 25 44
## 65 0 490 475 21 907 802 200 15 30
## 66 0 490 453 22 495 415 267 15 37
## 67 0 557 513 24 587 501 211 28 52
## 68 0 455 467 23 248 197 121 24 51
## 69 0 495 451 22 461 381 174 10 43
## 70 0 410 385 22 392 351 155 16 44
## 71 0 444 426 21 560 392 270 11 31
## 72 0 590 560 26 1133 630 220 37 73
## 73 0 437 399 19 629 501 183 10 26
## 74 0 512 438 23 692 514 209 20 50
## 75 0 570 549 27 792 649 186 56 87
## 76 0 505 443 21 682 535 204 22 43
## 77 0 550 500 25 495 434 210 35 55
## 78 0 466 443 21 385 340 193 18 38
## 79 0 444 418 20 1154 951 253 15 31
## 80 0 490 470 21 776 607 198 25 58
## 81 0 502 505 23 602 498 215 26 58
## 82 0 443 394 20 582 498 172 21 44
## 83 0 485 445 23 765 646 226 30 60
## 84 0 466 434 19 299 206 81 26 40
## 85 0 494 423 22 920 684 225 24 42
## 86 0 532 481 22 804 632 281 29 72
## 87 1 438 401 19 116 90 59 14 46
## 88 0 497 435 22 360 314 155 37 64
## 89 0 482 459 21 469 435 227 17 39
## 90 0 564 532 26 759 729 244 57 81
## 91 0 480 484 21 546 447 189 16 42
## 92 0 526 466 22 465 361 176 19 39
## 93 0 500 408 21 578 411 187 25 50
## 94 0 670 600 28 1860 767 227 71 93
## 95 0 350 350 18 238 235 108 2 13
## 96 0 498 436 22 497 423 215 27 57
## 97 0 508 442 22 1004 802 239 23 63
## 98 0 545 470 23 894 787 262 28 63
## 99 0 520 510 20 235 217 121 12 32
## 100 0 575 534 27 1013 888 288 55 82
## 101 0 564 525 26 823 721 274 52 87
## 102 0 509 484 23 605 405 284 24 53
## 103 0 500 420 22 738 687 241 20 44
## 104 0 570 530 25 1040 845 286 48 77
## 105 0 479 433 22 903 755 213 15 49
## 106 0 537 486 24 1038 839 227 30 63
## 107 0 502 409 21 1262 1102 276 14 40
## 108 0 420 370 19 626 372 145 12 34
## 109 0 500 460 24 695 535 239 21 30
## 110 0 560 500 26 374 280 185 45 77
## 111 0 502 447 22 555 414 242 14 41
## 112 0 540 510 24 922 729 244 37 66
## 113 0 392 375 19 3847 3433 527 9 35
## 114 0 541 486 24 1006 837 317 33 65
## 115 0 570 550 25 1358 1006 274 35 63
## 116 0 506 466 21 657 537 113 37 90
## 117 0 542 479 24 943 849 288 41 71
## 118 0 429 384 18 174 146 88 8 29
## 119 0 400 400 18 1310 983 316 5 35
## 120 0 479 452 23 458 369 165 16 42
## 121 0 593 550 26 681 588 246 44 74
## 122 0 440 400 18 1011 829 410 9 33
## 123 0 564 517 24 1501 935 273 51 83
## 124 0 530 480 24 880 520 224 16 42
## 125 0 528 496 23 1025 707 297 22 66
## 126 0 570 550 26 905 834 319 32 61
## 127 0 497 435 22 866 619 157 18 47
## 128 0 575 549 26 1320 923 284 26 54
## 129 0 450 500 23 529 492 261 29 55
## 130 0 496 463 23 1457 1045 345 27 50
## 131 0 513 476 23 643 509 280 26 56
## 132 0 442 406 20 1056 873 385 15 38
## 133 0 490 436 22 1109 922 375 24 46
## 134 0 554 498 24 948 798 295 42 74
## 135 0 560 500 25 1006 742 275 29 60
## 136 0 601 557 27 1445 966 326 46 83
## 137 0 580 520 26 1082 832 302 34 63
## 138 0 550 520 24 920 745 347 35 66
## 139 0 560 510 25 1538 1329 383 33 68
## 140 0 480 460 24 1003 782 295 23 53
## 141 0 480 440 21 798 620 238 14 41
## 142 0 450 450 19 1170 695 238 14 48
## 143 0 424 418 21 875 744 207 7 38
## 144 0 485 458 22 895 548 314 20 54
## 145 0 577 526 25 1244 912 352 44 77
## 146 0 482 439 21 979 743 259 25 46
## 147 0 515 474 23 807 707 308 39 63
## 148 0 632 603 28 1966 1436 327 47 80
## 149 0 458 405 20 516 454 322 13 34
## 150 0 426 415 20 592 501 279 19 44
## 151 0 442 400 22 1239 1017 383 10 34
## 152 0 488 456 22 699 601 352 17 43
## 153 0 535 508 24 949 786 302 30 70
## 154 0 600 550 27 1861 998 359 45 77
## 155 0 544 490 24 1121 926 372 43 70
## 156 0 540 494 24 947 798 266 36 68
## 157 1 550 501 24 950 713 351 42 72
## 158 0 550 510 24 663 547 315 32 67
## 159 0 557 478 24 1231 1074 345 34 66
## 160 0 516 488 24 553 452 228 22 49
## 161 0 502 460 22 668 534 237 19 39
## 162 0 470 420 21 995 789 398 26 47
## 163 0 556 483 25 1127 884 308 30 64
## 164 0 642 602 29 2039 1389 432 56 91
## 165 0 550 530 24 1738 1373 417 21 55
## 166 0 506 457 24 549 397 169 26 51
## 167 0 513 476 23 1415 714 338 18 52
## 168 0 487 443 23 672 596 278 29 60
## 169 0 575 535 25 1006 825 328 34 73
## 170 0 493 451 21 1286 1005 363 16 37
## 171 0 559 517 25 1422 1109 366 33 65
## 172 0 510 470 22 467 424 350 16 40
## 173 0 575 525 26 805 588 287 67 88
## 174 0 520 460 22 1616 1427 434 20 43
## 175 0 530 500 24 1202 1054 326 18 44
## 176 0 530 470 24 996 866 377 29 58
## 177 0 487 432 21 1487 1276 388 26 51
## 178 0 480 440 22 776 765 351 22 44
## 179 0 495 436 21 563 247 247 23 52
## 180 0 472 431 22 1597 969 226 16 38
## 181 0 538 488 25 888 734 393 26 60
## 182 0 593 570 27 2212 1538 408 44 75
## 183 1 420 370 19 1046 832 518 15 57
## 184 0 524 478 23 2083 1725 430 22 49
## 185 1 575 481 22 572 544 320 45 72
## 186 0 505 478 23 1381 1040 374 20 44
## 187 0 489 439 23 1566 1400 483 28 55
## 188 0 552 491 24 477 417 204 29 54
## 189 1 459 416 21 1257 940 363 9 22
## 190 0 556 495 25 1561 1188 458 48 72
## 191 0 685 639 25 4302 992 418 83 96
## 192 0 575 525 25 1658 1327 395 49 80
## 193 0 650 580 29 2373 956 452 77 96
## 194 0 445 400 19 1110 930 332 18 36
## 195 0 479 433 21 874 758 428 21 46
## 196 0 370 450 20 1093 998 285 5 25
## 197 0 565 506 24 2519 1836 462 30 61
## 198 0 501 456 22 959 771 351 23 48
## 199 0 557 502 25 1777 1151 382 31 55
## 200 0 483 442 19 707 512 222 17 44
## 201 0 480 441 21 1163 927 386 16 49
## 202 0 525 465 22 1368 1064 354 19 51
## 203 0 535 478 25 1489 1313 375 13 45
## 204 0 555 465 24 933 800 444 18 45
## 205 0 469 482 22 511 411 186 23 51
## 206 0 570 530 24 2100 1883 553 29 65
## 207 0 526 484 23 938 864 511 29 62
## 208 0 610 560 26 2848 1319 456 58 84
## 209 0 483 438 22 1272 1012 375 20 45
## 210 0 494 511 23 665 462 226 17 44
## 211 0 600 500 26 3270 2120 508 46 80
## 212 0 579 513 25 1769 1092 437 41 80
## 213 0 575 528 25 2190 1700 458 36 65
## 214 0 541 511 24 1444 1261 456 29 62
## 215 0 470 430 20 990 784 279 18 45
## 216 0 617 534 28 3050 1342 471 55 86
## 217 0 462 423 21 1216 908 423 19 40
## 218 1 650 550 26 1458 874 588 56 86
## 219 1 480 425 21 848 560 377 14 24
## 220 0 438 410 21 1454 1267 424 20 41
## 221 0 472 425 21 809 687 428 20 43
## 222 0 571 549 27 1800 1314 526 47 79
## 223 0 515 490 23 1109 688 386 20 65
## 224 0 603 499 25 1756 1360 478 42 77
## 225 0 526 493 24 860 688 285 32 70
## 226 0 614 553 24 1334 1243 568 30 56
## 227 0 522 490 24 1220 974 481 28 67
## 228 0 515 487 23 3713 1237 443 47 83
## 229 0 577 524 25 1979 1739 575 42 68
## 230 0 474 428 21 1080 948 504 25 56
## 231 1 550 504 24 1757 979 394 32 74
## 232 0 580 460 22 662 513 257 12 30
## 233 1 455 406 18 1166 1009 510 9 33
## 234 1 632 556 27 1089 780 410 46 79
## 235 0 408 367 16 1646 1150 542 12 30
## 236 0 498 439 21 927 731 415 24 50
## 237 0 516 454 22 1243 1020 414 33 60
## 238 0 435 435 22 810 484 356 6 33
## 239 0 625 603 27 3550 1877 653 53 87
## 240 0 521 491 20 2139 1492 502 24 64
## 241 0 524 486 24 1307 1090 616 25 55
## 242 1 459 411 19 885 553 381 13 38
## 243 0 607 537 27 2491 1110 573 57 88
## 244 0 555 509 24 1742 1382 607 30 64
## 245 0 590 520 25 1549 1392 587 38 72
## 246 0 585 520 25 1709 1385 634 36 72
## 247 1 470 420 21 2702 1623 604 7 24
## 248 0 570 520 25 4293 2728 591 25 62
## 249 0 455 408 21 735 423 366 20 48
## 250 0 481 422 24 1405 1167 557 20 65
## 251 0 585 514 25 3821 2037 680 86 96
## 252 0 541 465 24 2936 2342 669 35 62
## 253 0 539 492 25 1886 1524 526 31 67
## 254 0 531 474 23 1603 1392 504 31 68
## 255 0 623 596 29 4778 2767 678 50 89
## 256 0 544 484 25 2362 2037 700 40 68
## 257 0 520 490 23 1223 650 632 13 37
## 258 0 623 563 27 4856 2492 727 46 75
## 259 0 540 470 24 2974 2001 580 29 60
## 260 0 560 491 24 2961 1932 628 24 68
## 261 0 518 464 23 2464 1908 678 24 57
## 262 0 660 620 29 4772 1973 712 60 86
## 263 0 529 468 23 1690 1366 662 30 61
## 264 0 581 520 26 4044 2826 688 51 83
## 265 0 540 510 25 1891 1698 719 24 80
## 266 0 469 438 21 2097 1915 695 34 61
## 267 0 660 540 28 2768 2314 682 49 86
## 268 0 521 475 24 1959 1805 695 24 47
## 269 0 538 488 24 3708 1678 722 41 66
## 270 1 497 455 23 2747 1870 724 12 47
## 271 0 580 520 26 2248 1673 745 38 73
## 272 0 576 525 24 1712 1557 696 41 68
## 273 0 529 473 24 2286 1668 564 37 70
## 274 0 560 498 25 4784 3346 781 30 66
## 275 0 525 464 24 2115 1540 494 28 72
## 276 0 530 490 24 1721 1068 806 35 75
## 277 0 561 502 23 2421 2109 820 27 57
## 278 0 540 490 25 2799 2573 839 34 65
## 279 1 516 470 18 2320 1805 769 24 61
## 280 0 567 505 25 1784 1512 913 29 56
## 281 1 451 400 20 1584 1456 891 6 18
## 282 0 515 475 25 4731 3171 830 12 31
## 283 0 686 606 30 8474 3446 911 75 94
## 284 1 540 500 23 3150 2289 650 16 51
## 285 1 480 428 20 1401 1239 605 10 34
## 286 0 537 485 25 5139 3346 973 20 55
## 287 1 496 452 22 1558 1254 472 20 57
## 288 1 529 478 23 1199 562 261 30 74
## 289 1 533 484 22 1800 1253 560 44 85
## 290 0 457 410 19 4892 3530 913 13 33
## 291 1 655 547 27 1877 1826 823 49 77
## 292 0 530 464 23 2057 1807 828 26 53
## 293 1 450 440 21 1950 1506 1023 7 35
## 294 1 525 472 23 4877 2798 814 13 48
## 295 1 509 441 22 3540 2001 1016 24 54
## 296 0 679 555 28 8728 5201 1191 60 89
## 297 1 429 384 18 2379 2133 1292 8 25
## 298 1 554 491 22 4216 2290 736 20 52
## 299 0 514 463 21 2306 1721 538 23 48
## 300 1 510 470 20 1471 1281 824 18 67
## 301 1 373 330 17 2556 1752 946 7 16
## 302 0 742 639 31 6411 2140 1078 96 99
## 303 0 590 530 25 3767 3414 1061 30 58
## 304 1 377 332 17 2405 2234 1061 10 22
## 305 1 537 479 24 8399 3609 656 19 53
## 306 0 544 461 25 3151 2584 958 14 40
## 307 1 520 460 22 5549 3583 853 9 40
## 308 1 524 460 23 7888 3519 1036 6 40
## 309 1 608 541 26 8598 4562 1143 56 93
## 310 0 529 482 24 3579 2959 868 25 55
## 311 1 459 413 20 2336 1725 1043 10 27
## 312 0 640 559 28 7791 4690 1499 71 92
## 313 1 620 512 26 2618 2288 1032 42 77
## 314 0 650 570 28 8506 4168 1236 76 97
## 315 1 390 420 19 4345 3245 2604 15 85
## 316 0 680 620 28 12586 3239 1462 87 95
## 317 1 506 446 22 7294 3564 904 7 34
## 318 1 490 460 22 3325 2047 1301 20 45
## 319 0 578 504 25 6361 5293 1507 26 51
## 320 0 554 511 25 4815 3551 1227 30 58
## 321 0 687 615 30 13789 3893 1583 90 98
## 322 1 578 505 23 4269 2594 985 27 57
## 323 0 540 470 24 7428 5860 1349 25 63
## 324 1 494 441 21 6071 3856 1449 15 67
## 325 1 450 400 21 3330 2730 1303 15 36
## 326 1 532 489 22 4772 3140 1265 22 55
## 327 1 550 480 24 8000 4556 1464 17 70
## 328 0 561 492 25 5152 4600 1685 36 71
## 329 1 517 463 23 3133 2799 1337 24 49
## 330 0 670 600 29 12289 5200 1902 85 98
## 331 0 465 450 23 4226 3666 2007 14 60
## 332 1 440 408 20 2407 2296 1304 5 19
## 333 1 490 460 22 5702 4894 1742 15 37
## 334 1 535 465 23 2777 2249 1652 20 54
## 335 1 480 440 22 5530 4007 1697 12 37
## 336 1 525 460 23 5729 4520 1957 20 52
## 337 1 615 533 26 14463 6166 1757 60 94
## 338 1 434 391 20 5659 4761 3147 10 31
## 339 1 520 440 23 3500 2836 1779 15 42
## 340 1 530 470 24 5548 3563 1549 30 71
## 341 0 680 594 29 12394 5232 2464 85 100
## 342 1 428 388 19 4630 3655 2301 5 27
## 343 1 531 449 22 2850 2044 1046 20 50
## 344 1 484 423 21 4217 3100 1686 17 46
## 345 1 448 407 20 3512 2975 1662 6 23
## 346 1 467 472 21 5870 4461 2272 12 32
## 347 1 519 471 22 7313 4664 1910 20 63
## 348 1 491 435 21 5803 4441 1730 19 62
## 349 1 543 476 23 3306 2079 1071 42 89
## 350 1 520 480 22 4281 3825 2426 26 53
## 351 1 506 434 21 3281 2559 1448 19 43
## 352 1 533 464 23 6855 5553 2408 26 57
## 353 0 531 467 23 11901 8492 2517 16 42
## 354 1 495 444 22 5891 4931 1973 23 48
## 355 1 533 464 23 6986 2959 1918 25 60
## 356 1 520 465 22 7693 5815 2328 30 66
## 357 1 540 477 24 4522 3913 2181 29 57
## 358 1 547 455 21 7811 3817 1650 47 73
## 359 1 486 435 18 9274 6362 2435 14 44
## 360 0 592 498 25 12229 8498 2477 45 71
## 361 1 497 449 22 9251 7333 3076 14 45
## 362 1 482 425 21 8532 5316 2421 14 48
## 363 1 543 484 24 5095 4491 2400 27 53
## 364 1 526 467 23 4418 2737 2049 23 51
## 365 1 553 492 23 7589 4676 1876 29 63
## 366 1 564 502 25 6574 4637 2940 32 62
## 367 1 520 473 24 11023 8298 3183 21 54
## 368 0 600 550 26 20192 13007 3810 45 80
## 369 1 462 424 21 9210 3040 7425 10 30
## 370 1 545 479 25 9478 6312 2194 29 65
## 371 1 525 468 23 7473 5372 3013 27 53
## 372 1 473 422 21 9361 7910 3849 38 50
## 373 1 575 501 24 7548 6791 3070 25 57
## 374 1 529 468 23 5996 4993 3079 29 57
## 375 1 457 394 20 9402 7020 2151 20 70
## 376 1 513 447 22 6277 6003 3526 33 63
## 377 1 568 484 23 11054 6397 3524 26 55
## 378 1 526 462 23 14079 12238 4529 29 57
## 379 1 634 543 27 19152 12940 4893 66 92
## 380 1 521 453 23 12809 10308 3761 24 49
## 381 1 530 466 24 16587 13243 5873 25 72
## 382 1 617 522 27 14939 11652 5705 52 88
## 383 1 524 461 23 18114 15096 6180 23 57
## 384 1 603 523 25 14752 9572 5329 48 85
## 385 1 578 491 25 14474 10519 6392 49 85
## FTUG PTUG ISTuit OSTuit Books PhDs SFRatio
## 1 139 3 8730 8730 400 92 9.3
## 2 203 138 13780 13780 500 84 5.7
## 3 246 18 8190 8190 500 100 7.0
## 4 249 869 7560 7560 800 76 11.9
## 5 300 50 7500 7500 500 45 7.5
## 6 309 639 11412 11412 500 89 8.3
## 7 316 20 8438 8438 500 42 11.1
## 8 327 110 5590 5590 650 53 15.1
## 9 338 33 6900 6900 800 24 15.9
## 10 341 768 10300 10300 500 44 10.2
## 11 344 150 5950 5950 500 38 8.4
## 12 352 147 3120 3120 400 24 14.3
## 13 377 373 8064 8064 650 61 8.7
## 14 396 526 11400 11400 500 41 9.5
## 15 402 237 7070 7070 400 59 8.9
## 16 414 165 6500 6500 500 38 10.7
## 17 416 230 13290 13290 500 90 11.5
## 18 416 19 14900 14900 600 93 8.3
## 19 455 84 5180 5180 500 55 11.0
## 20 468 31 9700 9700 470 73 19.0
## 21 471 148 13500 13500 400 95 9.3
## 22 488 43 9950 9950 300 76 11.8
## 23 494 574 11550 11550 300 43 14.5
## 24 495 61 8170 8170 600 32 12.3
## 25 503 40 3605 3605 300 37 18.4
## 26 508 34 7950 7950 600 35 11.6
## 27 513 247 8670 8670 450 43 12.5
## 28 521 99 8955 8955 500 51 11.8
## 29 525 323 11230 11230 2340 8 6.8
## 30 527 41 14500 14500 500 91 6.5
## 31 534 172 6900 6900 450 67 12.1
## 32 534 216 10475 10475 500 68 11.2
## 33 538 126 8080 8080 500 63 11.4
## 34 542 9 3750 3750 350 48 12.1
## 35 562 18 10430 10430 400 55 11.6
## 36 569 7 17238 17238 600 95 8.2
## 37 597 83 10500 10500 600 58 11.6
## 38 601 36 10194 10194 500 57 11.4
## 39 614 388 13900 13900 450 46 10.9
## 40 620 280 7536 7536 430 44 13.0
## 41 624 128 11200 11200 500 80 11.1
## 42 630 549 11020 11020 610 73 14.0
## 43 631 133 8280 8280 500 50 16.1
## 44 634 78 7800 7800 500 60 14.1
## 45 641 101 10800 10800 570 55 13.1
## 46 645 283 10850 10850 400 58 12.8
## 47 646 84 8242 8242 600 77 12.7
## 48 650 14 5600 5600 750 63 12.1
## 49 651 490 8950 8950 500 57 10.6
## 50 653 129 7150 7150 450 61 17.8
## 51 653 56 13970 13970 370 88 9.2
## 52 662 351 7600 7600 600 59 19.0
## 53 662 131 10430 10430 400 85 16.5
## 54 662 121 8000 8000 500 57 11.3
## 55 665 37 10720 10720 600 66 12.5
## 56 671 11 13000 13000 400 91 11.6
## 57 678 41 13500 13500 500 67 9.4
## 58 699 717 9600 9600 450 39 10.5
## 59 703 20 4450 4450 500 43 22.9
## 60 704 63 9900 9900 630 59 10.5
## 61 707 432 11790 11790 500 75 11.9
## 62 710 399 13960 13960 450 82 14.4
## 63 712 10 15700 15700 400 80 13.0
## 64 712 23 15476 15476 400 69 11.3
## 65 726 61 9570 9570 350 58 15.9
## 66 733 402 9300 9300 500 51 14.6
## 67 735 28 15200 15200 350 87 9.4
## 68 736 347 7600 7600 600 60 15.8
## 69 738 55 9600 9600 600 55 13.3
## 70 738 430 10260 10260 600 39 13.1
## 71 743 118 8734 8734 600 56 11.3
## 72 750 30 17688 17688 650 100 10.4
## 73 754 187 9400 9400 400 64 12.8
## 74 760 81 9900 9900 400 76 13.3
## 75 769 377 12900 12900 600 91 13.1
## 76 771 611 9500 9500 400 26 2.5
## 77 775 44 8950 8950 600 86 11.3
## 78 784 127 9520 9520 630 63 18.6
## 79 791 140 11172 11172 700 68 11.6
## 80 791 764 14340 14340 500 58 11.7
## 81 795 74 13470 13470 500 78 11.1
## 82 799 78 10468 10468 660 40 11.5
## 83 809 32 8578 8578 700 79 13.9
## 84 811 206 9600 9600 500 56 14.3
## 85 815 222 11200 11200 600 55 14.8
## 86 840 68 10390 10390 525 54 12.5
## 87 841 704 840 5130 600 84 15.5
## 88 848 1542 5400 5400 500 48 14.4
## 89 851 120 10535 10535 550 39 12.9
## 90 867 51 10900 10900 500 81 12.1
## 91 873 683 11138 11138 600 40 14.0
## 92 879 156 12580 12580 400 76 13.1
## 93 880 477 6930 6930 400 57 11.0
## 94 887 1 17000 17000 500 99 9.6
## 95 888 390 7500 7500 600 31 14.3
## 96 895 429 7850 7850 490 54 13.8
## 97 909 51 10440 10440 525 63 11.8
## 98 909 28 8050 8050 600 75 15.6
## 99 931 487 8950 8950 550 51 10.7
## 100 943 7 11850 11850 600 95 11.4
## 101 954 6 8800 8800 500 82 13.1
## 102 961 99 6398 6398 400 68 13.3
## 103 964 242 13780 13780 500 68 12.5
## 104 967 24 15747 15747 400 88 12.7
## 105 971 305 10500 10500 600 66 14.1
## 106 973 306 15595 15595 300 79 11.3
## 107 978 98 9456 9456 468 53 12.8
## 108 983 40 7700 7700 450 70 21.9
## 109 988 785 10200 10200 350 63 11.7
## 110 995 408 8550 8550 500 75 12.6
## 111 996 2281 9100 9100 550 51 23.6
## 112 1000 275 14067 14067 400 75 10.6
## 113 1010 12 9384 9384 600 22 14.3
## 114 1024 15 8200 8200 500 84 10.6
## 115 1028 13 15036 15036 600 90 10.6
## 116 1039 466 12474 12474 630 53 11.9
## 117 1041 35 14210 14210 450 76 10.9
## 118 1047 33 8300 8300 600 62 15.2
## 119 1057 175 8550 8550 400 35 17.4
## 120 1057 355 11190 11190 450 60 13.6
## 121 1058 73 10760 10760 500 85 13.4
## 122 1059 2458 9000 9000 450 77 12.4
## 123 1059 34 12680 12680 605 91 15.3
## 124 1068 364 9300 9300 600 81 11.1
## 125 1070 72 10100 10100 450 69 16.3
## 126 1073 179 11320 11320 550 82 12.7
## 127 1074 336 8920 8920 680 68 14.6
## 128 1085 81 16304 16304 355 87 11.1
## 129 1093 322 8650 8650 390 49 14.1
## 130 1109 502 14990 14990 450 77 21.5
## 131 1110 39 8988 8988 500 61 12.1
## 132 1111 244 6950 6950 600 60 11.9
## 133 1115 70 13240 13240 600 73 13.4
## 134 1120 15 11280 11280 400 81 13.0
## 135 1127 205 13925 13925 500 73 12.7
## 136 1129 24 15350 15350 450 89 10.3
## 137 1133 30 11859 11859 554 80 13.4
## 138 1133 42 11090 11090 400 80 12.0
## 139 1140 10 15248 15248 550 71 12.2
## 140 1144 160 16160 16160 500 74 8.9
## 141 1165 1232 9800 9800 400 46 11.1
## 142 1170 429 7470 7470 250 74 15.3
## 143 1173 1402 9700 9700 400 45 14.5
## 144 1174 50 5500 5500 600 68 16.1
## 145 1177 43 11850 11850 600 83 11.3
## 146 1188 166 10100 10100 400 88 12.0
## 147 1198 605 8840 8840 750 74 13.1
## 148 1199 61 19960 19960 500 90 11.8
## 149 1201 214 5190 5190 400 59 12.7
## 150 1204 392 6400 6400 600 80 14.5
## 151 1207 157 7820 7820 550 69 13.9
## 152 1209 33 11328 11328 400 45 14.5
## 153 1210 26 9990 9990 500 85 15.0
## 154 1220 46 16670 16670 750 80 10.5
## 155 1270 160 12660 12660 678 80 16.9
## 156 1274 471 10850 10850 550 77 13.6
## 157 1276 9 14320 14320 490 77 14.9
## 158 1279 75 10060 10060 500 74 11.2
## 159 1295 105 11600 11600 400 66 12.4
## 160 1301 242 9650 9650 600 57 14.9
## 161 1306 258 9476 9476 500 67 20.1
## 162 1306 122 6230 6230 400 42 13.0
## 163 1310 766 11718 11718 450 73 16.4
## 164 1333 30 15688 15688 400 88 9.5
## 165 1335 30 18460 18460 700 92 13.2
## 166 1343 1751 9250 9250 425 52 13.1
## 167 1345 44 5120 5120 500 52 18.1
## 168 1350 275 11844 11844 450 54 11.6
## 169 1362 102 13252 13252 450 89 13.0
## 170 1363 74 13900 13900 500 75 14.0
## 171 1363 23 15360 15360 600 82 12.8
## 172 1365 334 6300 6300 700 75 13.7
## 173 1376 207 11660 11660 400 74 14.0
## 174 1405 580 13125 13125 500 74 15.9
## 175 1410 299 13404 13404 450 78 15.6
## 176 1411 72 12065 12065 430 62 12.5
## 177 1417 1646 11120 11120 525 55 11.1
## 178 1419 228 6400 6400 500 58 16.2
## 179 1427 432 12950 12950 612 72 12.4
## 180 1431 1522 13540 13540 630 66 14.1
## 181 1433 27 12730 12730 500 74 9.9
## 182 1445 1 19240 19240 750 95 11.1
## 183 1463 1150 1856 4498 600 24 16.3
## 184 1464 67 17480 17480 500 75 12.3
## 185 1470 416 2013 6073 550 71 16.4
## 186 1506 970 8025 8025 400 65 17.4
## 187 1509 170 14200 14200 450 58 16.4
## 188 1532 77 8840 8840 600 58 20.8
## 189 1547 294 3660 7656 400 89 14.7
## 190 1548 840 13380 13380 500 89 17.8
## 191 1593 5 19760 19760 660 93 8.4
## 192 1595 159 14800 14800 400 91 13.3
## 193 1601 6 17295 17295 600 95 12.0
## 194 1603 374 8180 8180 500 65 15.2
## 195 1605 246 9858 9858 450 42 17.6
## 196 1650 5180 9450 9450 600 33 91.8
## 197 1656 352 16975 16975 600 76 12.8
## 198 1662 209 16624 16624 600 72 12.8
## 199 1668 1052 16425 16425 955 81 13.3
## 200 1671 1512 7350 7350 600 52 13.6
## 201 1685 556 8840 8840 750 67 11.4
## 202 1687 677 10570 10570 400 86 14.5
## 203 1688 131 10456 10456 500 91 17.7
## 204 1691 72 12247 12247 500 76 12.0
## 205 1692 562 12224 12224 450 63 11.5
## 206 1704 1 16240 16240 500 84 11.1
## 207 1715 103 12247 12247 500 70 13.1
## 208 1720 35 18930 18930 500 83 10.2
## 209 1732 936 9428 9428 600 76 15.7
## 210 1739 1550 9160 9160 500 68 20.6
## 211 1748 40 24940 24940 590 93 10.9
## 212 1757 81 10965 10965 450 60 14.2
## 213 1780 48 16732 16732 550 93 12.1
## 214 1788 95 11910 11910 450 60 11.4
## 215 1811 3144 11290 11290 600 76 12.6
## 216 1818 23 14360 14360 400 77 12.9
## 217 1819 281 10100 10100 550 48 12.1
## 218 1846 154 3330 9843 600 74 14.6
## 219 1855 1412 2320 5800 500 62 14.8
## 220 1874 757 11431 11431 600 43 17.4
## 221 1889 217 10176 10178 800 71 16.1
## 222 1891 40 19300 19300 750 79 9.0
## 223 1897 208 8325 8325 1200 14 16.1
## 224 1911 626 14550 14550 500 80 12.3
## 225 1928 442 13306 13306 450 62 8.8
## 226 1946 95 12140 12140 425 74 15.1
## 227 1964 623 7800 7800 650 61 11.1
## 228 1971 107 7000 7000 660 73 12.5
## 229 1980 144 15948 15948 400 82 12.8
## 230 2032 122 15500 15500 250 47 12.8
## 231 2033 1078 608 5972 600 77 13.0
## 232 2074 726 11902 11902 540 65 12.8
## 233 2074 341 3340 4938 528 67 17.0
## 234 2106 2919 784 4536 645 91 20.8
## 235 2128 82 5188 5188 650 48 13.8
## 236 2149 2217 11130 11130 600 72 13.5
## 237 2149 418 8678 8678 700 82 16.2
## 238 2155 191 9200 9200 1000 65 24.1
## 239 2164 77 18920 18920 600 90 9.7
## 240 2186 2171 12350 12350 500 88 12.6
## 241 2196 82 7344 7344 570 50 15.3
## 242 2207 1058 2295 5739 312 70 15.9
## 243 2213 35 5224 5224 525 65 18.4
## 244 2258 53 10300 10300 475 68 14.1
## 245 2269 85 13240 13240 600 73 13.8
## 246 2281 50 14125 14125 400 79 12.5
## 247 2315 146 1819 5918 500 76 19.4
## 248 2322 263 18710 18710 500 87 12.7
## 249 2448 707 9210 9210 700 49 39.8
## 250 2452 1113 2064 4694 700 57 16.5
## 251 2488 625 18200 18200 500 95 11.6
## 252 2502 66 15990 15990 600 73 14.5
## 253 2523 296 13000 13000 600 78 14.7
## 254 2580 302 13312 13312 600 78 11.0
## 255 2587 120 19670 19670 575 77 10.1
## 256 2607 148 13130 13130 500 77 10.9
## 257 2645 167 7950 7950 480 51 15.5
## 258 2649 25 19510 19510 500 95 10.5
## 259 2666 554 15192 15192 400 84 15.9
## 260 2669 616 10800 10800 575 71 14.1
## 261 2693 691 10970 10970 500 47 13.3
## 262 2714 27 19130 19130 1400 90 12.1
## 263 2718 1460 10995 10995 1000 68 17.6
## 264 2738 138 16230 16230 630 79 15.0
## 265 2740 761 11100 11100 600 77 11.7
## 266 2793 166 6900 6900 617 67 14.4
## 267 2802 86 15884 15884 530 92 15.2
## 268 2849 1107 11520 11520 600 73 13.3
## 269 2852 153 7050 7050 250 71 17.8
## 270 2874 118 2606 7920 550 74 18.4
## 271 2888 105 14350 14350 550 82 10.0
## 272 2936 433 11750 11750 1200 94 11.5
## 273 2943 1260 11985 11985 400 93 9.2
## 274 2984 1037 15000 15000 700 86 15.1
## 275 2993 347 12825 12825 500 85 12.2
## 276 3128 213 5504 5504 700 71 17.7
## 277 3168 392 11700 11700 600 89 14.5
## 278 3322 726 13420 13420 560 88 15.0
## 279 3395 670 3620 6400 580 71 12.8
## 280 3401 136 10230 10230 400 75 14.8
## 281 3471 911 1434 5016 540 48 28.8
## 282 3557 658 10700 10700 550 74 17.6
## 283 3566 1569 18800 18800 500 96 3.3
## 284 3598 234 2650 6840 500 71 15.1
## 285 3716 675 1644 7100 540 63 19.4
## 286 3717 1358 14400 14400 450 66 18.4
## 287 3754 2477 1597 6172 541 83 23.4
## 288 3805 2728 1828 9244 520 89 18.1
## 289 3876 3588 1732 6634 600 82 17.8
## 290 3906 1446 10690 10690 570 66 16.0
## 291 3926 561 3030 9057 700 88 14.4
## 292 4106 982 11712 11712 500 80 13.8
## 293 4111 1301 672 4104 500 70 21.9
## 294 4123 298 2650 6550 620 82 16.3
## 295 4190 1512 840 5130 500 60 23.1
## 296 4265 291 17900 17900 450 86 9.2
## 297 4283 2973 2040 4973 500 56 22.0
## 298 4296 1027 2328 5130 600 73 17.9
## 299 4309 549 13226 13226 750 86 13.6
## 300 4343 990 1697 2883 300 50 23.0
## 301 4396 515 2200 4380 600 60 18.3
## 302 4481 28 20100 20100 725 99 10.1
## 303 4531 643 10870 10870 2000 75 14.4
## 304 4564 448 840 4290 598 55 19.4
## 305 4658 1478 2650 6550 550 85 15.3
## 306 4772 856 7800 7800 570 37 16.5
## 307 5004 475 2650 6550 600 80 17.9
## 308 5011 346 2650 6550 630 82 17.8
## 309 5060 146 2650 6550 600 79 19.1
## 310 5244 3417 11500 11500 700 94 6.2
## 311 5438 4058 864 4752 508 48 18.4
## 312 5500 90 17865 17865 630 93 5.8
## 313 5524 414 3510 8127 900 82 17.0
## 314 5544 192 17600 17600 600 97 5.0
## 315 5584 3101 780 7860 600 65 18.2
## 316 5643 349 19528 19528 720 99 7.6
## 317 5758 1363 2650 6550 500 79 19.0
## 318 5800 872 2200 4200 300 53 20.2
## 319 5889 665 11380 11380 500 81 14.8
## 320 6069 3719 11214 11214 600 69 16.1
## 321 6188 53 18590 18590 625 95 5.0
## 322 6476 2592 3338 8594 494 82 18.4
## 323 6534 1350 11600 11600 1000 81 13.9
## 324 6635 1145 1492 7558 500 82 19.1
## 325 6706 2640 1800 5800 600 73 14.0
## 326 6851 1200 3060 6120 666 73 17.2
## 327 6943 869 2650 6550 500 69 22.0
## 328 7016 804 11610 11610 600 86 13.5
## 329 7242 1431 1548 5962 832 82 13.5
## 330 7450 45 16404 16404 759 96 6.8
## 331 7703 2339 1660 5094 700 77 16.6
## 332 7749 3961 3231 6462 808 91 18.5
## 333 8077 472 2924 6684 500 73 19.6
## 334 8334 1435 2110 5634 450 97 15.9
## 335 8463 1498 1829 7731 540 75 21.5
## 336 8516 1264 2208 6996 279 80 19.3
## 337 8544 671 2650 6550 700 83 18.0
## 338 8596 1949 2802 6892 600 72 16.6
## 339 8730 993 1576 5552 550 75 17.6
## 340 8909 506 2406 8124 639 83 22.7
## 341 9205 531 17020 17020 500 95 6.3
## 342 9216 11176 2766 8490 600 69 10.4
## 343 9260 1387 2392 4652 500 78 18.7
## 344 9375 5457 672 4104 452 94 25.3
## 345 9544 8177 1494 5790 500 75 21.1
## 346 9851 1289 780 4860 200 85 21.4
## 347 9940 1035 740 6806 96 83 18.3
## 348 10099 3255 764 7248 600 79 16.8
## 349 10208 9310 1695 6597 800 81 13.9
## 350 10657 4257 1650 5775 700 83 18.7
## 351 10975 8431 1206 4422 500 73 21.0
## 352 11036 2011 3234 8907 556 89 10.8
## 353 11160 10221 13380 13380 600 73 12.9
## 354 11249 2682 1828 6746 620 78 21.7
## 355 12330 7152 1716 6618 700 80 22.2
## 356 12594 3661 3196 8074 495 84 16.9
## 357 12830 1658 1889 5336 800 84 15.3
## 358 12911 1404 2033 7380 612 72 19.8
## 359 13171 1687 764 7248 500 74 13.2
## 360 13259 1429 17230 17230 600 90 11.4
## 361 13699 1213 3070 7452 600 81 21.1
## 362 13806 4277 840 4860 500 70 21.2
## 363 13894 8374 1954 6857 858 89 12.8
## 364 14047 5134 672 4104 450 86 22.6
## 365 14770 10962 1856 6760 500 84 17.0
## 366 14782 1583 3030 9057 600 87 12.7
## 367 14861 1310 3552 7629 550 79 20.4
## 368 14971 3113 18420 18420 475 80 11.9
## 369 15615 3230 3927 7854 500 81 20.8
## 370 15646 1829 2124 8412 470 87 19.2
## 371 15749 3237 1830 5764 750 86 16.5
## 372 16148 2207 2864 7244 500 69 17.7
## 373 16262 1716 2100 6300 600 85 16.7
## 374 16269 3757 2625 5925 600 83 15.9
## 375 16407 5550 1742 8384 612 87 19.5
## 376 16454 3171 2055 5595 500 86 15.1
## 377 16502 21836 3171 8949 714 88 12.2
## 378 21664 4894 1828 7434 620 91 19.6
## 379 22045 1339 5040 15732 476 90 11.5
## 380 22593 7585 1828 7434 700 88 18.9
## 381 24763 2717 2984 9766 600 77 21.3
## 382 25422 911 2760 7560 500 87 17.4
## 383 26640 4120 4103 10658 504 93 14.0
## 384 30017 5189 840 5130 650 91 19.7
## 385 31643 2798 840 5130 600 89 23.1
Although difficult to read the general layout of the upper portion of the diagram points to three or four major groupings. Since it looked like three clusters should be tried when the k-means method was used, 3 clusters will be now tested to see if there is any change in the outcomes.
set.seed(1)
grpEdu <- kmeans(edu[,c(-1,-2)], centers=3, nstart=10) #solve for 3 grps but start with 10 grps
clusEdu<-cbind(edu,cluster=grpEdu$cluster)
head(clusEdu)
## College State Public MathSAT VerbSAT ACT Received
## 1 Christendom College VA 0 568 568 23 81
## 2 Mount Vernon College DC 0 440 402 20 149
## 3 King's College NY 0 442 465 25 356
## 4 Alaska Pacific University AK 0 490 482 20 193
## 5 Sierra Nevada College NV 0 400 400 21 200
## 6 Trinity College DC 0 470 480 22 247
## Accepted Enrolled Pct10 Pct25 FTUG PTUG ISTuit OSTuit Books PhDs SFRatio
## 1 72 51 33 71 139 3 8730 8730 400 92 9.3
## 2 70 61 15 35 203 138 13780 13780 500 84 5.7
## 3 233 53 16 24 246 18 8190 8190 500 100 7.0
## 4 146 55 16 44 249 869 7560 7560 800 76 11.9
## 5 160 100 5 25 300 50 7500 7500 500 45 7.5
## 6 189 100 19 49 309 639 11412 11412 500 89 8.3
## cluster
## 1 3
## 2 1
## 3 3
## 4 3
## 5 3
## 6 3
plot(edu$Received, edu$ISTuit, type="n", xlim=c(70,20200), xlab="Applications Received", ylab="Tuition (In-State)")
text(x=edu$Received, y=edu$ISTuit, labels=edu$College, col=rainbow(3)[grpEdu$cluster])
Two new versions of the ANOVA tables from above are produced looking at public institutions and average price of books.
m1 <- aov(Public ~ as.factor(cluster), data=clusEdu)
summary(m1)
## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(cluster) 2 39.76 19.878 242.7 <2e-16 ***
## Residuals 382 31.29 0.082
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
m2 <- aov(Books ~ as.factor(cluster), data=clusEdu)
summary(m2)
## Df Sum Sq Mean Sq F value Pr(>F)
## as.factor(cluster) 2 32050 16025 0.493 0.611
## Residuals 382 12421982 32518
The new table for public colleges has a slightly higher F value and the p-statistic remains significant. The new table for books has a lower F value and a higher p-statistic, meaning it has an even smaller significance and doesn’t differentiate the clusters.
