Pengantar Data Sains
Tugas Pengantar Data Sains
Naufal Fadhlullah
April 28, 2024
Email          : naufal.fadhlullah@student.matanauniversity.ac.id
Instagram     : https://www.instagram.com/naaufald
RPubs       Â
 : https://rpubs.com/naaufaldd/
Address     : ARA
Center, Matana University Tower
             Jl. CBD
Barat Kav, RT.1, Curug Sangereng, Kelapa Dua, Tangerang, Banten
15810.
1 Partition Clustering
Metode partitional clustering adalah metode yang membagi data menjadi sejumlah non-overlapping subset atau cluster tanpa struktur hierarki tertentu. Metode ini mencakup teknik-teknik seperti K-Means, K-Medoids, dan CLARA.
2 Hierarchial Clustering
Agglomerative Hierarchical Clustering adalah metode pengelompokan data yang dimulai dengan setiap satu pengamatan sebagai clusternya sendiri kemudian terus mengelompokkan pengamatan ke dalam kelompok yang semakin besar.
3 Melakukan proses klastering
dengan metod Partion dan Hirarchical dengan menggunakan data USArrest yang berisi data statistik penangkapan per 100.000 data penduduk untuk kasus , , dan pada tiap 50 negara bagian di US pada tahun 1973.
3.1 partitional clustering
## Murder Assault UrbanPop Rape
## Alabama 1.24256408 0.78283935 -0.52090661 -0.003416473
## Alaska 0.50786248 1.10682252 -1.21176419 2.484202941
## Arizona 0.07163341 1.47880321 0.99898006 1.042878388
## Arkansas 0.23234938 0.23086801 -1.07359268 -0.184916602
## California 0.27826823 1.26281442 1.75892340 2.067820292
## Colorado 0.02571456 0.39885929 0.86080854 1.864967207
## Connecticut -1.03041900 -0.72908214 0.79172279 -1.081740768
## Delaware -0.43347395 0.80683810 0.44629400 -0.579946294
## Florida 1.74767144 1.97077766 0.99898006 1.138966691
## Georgia 2.20685994 0.48285493 -0.38273510 0.487701523
## Hawaii -0.57123050 -1.49704226 1.20623733 -0.110181255
## Idaho -1.19113497 -0.60908837 -0.79724965 -0.750769945
## Illinois 0.59970018 0.93883125 1.20623733 0.295524916
## Indiana -0.13500142 -0.69308401 -0.03730631 -0.024769429
## Iowa -1.28297267 -1.37704849 -0.58999237 -1.060387812
## Kansas -0.41051452 -0.66908525 0.03177945 -0.345063775
## Kentucky 0.43898421 -0.74108152 -0.93542116 -0.526563903
## Louisiana 1.74767144 0.93883125 0.03177945 0.103348309
## Maine -1.30593210 -1.05306531 -1.00450692 -1.434064548
## Maryland 0.80633501 1.55079947 0.10086521 0.701231086
## Massachusetts -0.77786532 -0.26110644 1.34440885 -0.526563903
## Michigan 0.99001041 1.01082751 0.58446551 1.480613993
## Minnesota -1.16817555 -1.18505846 0.03177945 -0.676034598
## Mississippi 1.90838741 1.05882502 -1.48810723 -0.441152078
## Missouri 0.27826823 0.08687549 0.30812248 0.743936999
## Montana -0.41051452 -0.74108152 -0.86633540 -0.515887425
## Nebraska -0.80082475 -0.82507715 -0.24456358 -0.505210947
## Nevada 1.01296983 0.97482938 1.06806582 2.644350114
## New Hampshire -1.30593210 -1.36504911 -0.65907813 -1.252564419
## New Jersey -0.08908257 -0.14111267 1.62075188 -0.259651949
## New Mexico 0.82929443 1.37080881 0.30812248 1.160319648
## New York 0.76041616 0.99882813 1.41349461 0.519730957
## North Carolina 1.19664523 1.99477641 -1.41902147 -0.547916860
## North Dakota -1.60440462 -1.50904164 -1.48810723 -1.487446939
## Ohio -0.11204199 -0.60908837 0.65355127 0.017936483
## Oklahoma -0.27275797 -0.23710769 0.16995096 -0.131534211
## Oregon -0.66306820 -0.14111267 0.10086521 0.861378259
## Pennsylvania -0.34163624 -0.77707965 0.44629400 -0.676034598
## Rhode Island -1.00745957 0.03887798 1.48258036 -1.380682157
## South Carolina 1.51807718 1.29881255 -1.21176419 0.135377743
## South Dakota -0.91562187 -1.01706718 -1.41902147 -0.900240639
## Tennessee 1.24256408 0.20686926 -0.45182086 0.605142783
## Texas 1.12776696 0.36286116 0.99898006 0.455672088
## Utah -1.05337842 -0.60908837 0.99898006 0.178083656
## Vermont -1.28297267 -1.47304350 -2.31713632 -1.071064290
## Virginia 0.16347111 -0.17711080 -0.17547783 -0.056798864
## Washington -0.86970302 -0.30910395 0.51537975 0.530407436
## West Virginia -0.47939280 -1.07706407 -1.83353601 -1.273917376
## Wisconsin -1.19113497 -1.41304662 0.03177945 -1.113770203
## Wyoming -0.22683912 -0.11711392 -0.38273510 -0.601299251
## attr(,"scaled:center")
## Murder Assault UrbanPop Rape
## 7.788 170.760 65.540 21.232
## attr(,"scaled:scale")
## Murder Assault UrbanPop Rape
## 4.355510 83.337661 14.474763 9.366385## K-means clustering with 3 clusters of sizes 20, 13, 17
##
## Cluster means:
## Murder Assault UrbanPop Rape
## 1 1.0049340 1.0138274 0.1975853 0.8469650
## 2 -0.9615407 -1.1066010 -0.9301069 -0.9667633
## 3 -0.4469795 -0.3465138 0.4788049 -0.2571398
##
## Clustering vector:
## Alabama Alaska Arizona Arkansas California
## 1 1 1 3 1
## Colorado Connecticut Delaware Florida Georgia
## 1 3 3 1 1
## Hawaii Idaho Illinois Indiana Iowa
## 3 2 1 3 2
## Kansas Kentucky Louisiana Maine Maryland
## 3 2 1 2 1
## Massachusetts Michigan Minnesota Mississippi Missouri
## 3 1 2 1 1
## Montana Nebraska Nevada New Hampshire New Jersey
## 2 2 1 2 3
## New Mexico New York North Carolina North Dakota Ohio
## 1 1 1 2 3
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 3 3 3 3 1
## South Dakota Tennessee Texas Utah Vermont
## 2 1 1 3 2
## Virginia Washington West Virginia Wisconsin Wyoming
## 3 3 2 2 3
##
## Within cluster sum of squares by cluster:
## [1] 46.74796 11.95246 19.62285
## (between_SS / total_SS = 60.0 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"## Murder Assault UrbanPop Rape
## 1 1.0049340 1.0138274 0.1975853 0.8469650
## 2 -0.9615407 -1.1066010 -0.9301069 -0.9667633
## 3 -0.4469795 -0.3465138 0.4788049 -0.2571398## Alabama Alaska Arizona Arkansas California
## 1 1 1 3 1
## Colorado Connecticut Delaware Florida Georgia
## 1 3 3 1 1
## Hawaii Idaho Illinois Indiana Iowa
## 3 2 1 3 2
## Kansas Kentucky Louisiana Maine Maryland
## 3 2 1 2 1
## Massachusetts Michigan Minnesota Mississippi Missouri
## 3 1 2 1 1
## Montana Nebraska Nevada New Hampshire New Jersey
## 2 2 1 2 3
## New Mexico New York North Carolina North Dakota Ohio
## 1 1 1 2 3
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 3 3 3 3 1
## South Dakota Tennessee Texas Utah Vermont
## 2 1 1 3 2
## Virginia Washington West Virginia Wisconsin Wyoming
## 3 3 2 2 3## Murder Assault UrbanPop Rape
## Alabama 13.2 236 58 21.2
## Alaska 10.0 263 48 44.5
## Arizona 8.1 294 80 31.0
## Arkansas 8.8 190 50 19.5
## California 9.0 276 91 40.6
## Colorado 7.9 204 78 38.7## Murder Assault UrbanPop Rape
## Alabama 1.24256408 0.78283935 -0.52090661 -0.003416473
## Alaska 0.50786248 1.10682252 -1.21176419 2.484202941
## Arizona 0.07163341 1.47880321 0.99898006 1.042878388
## Arkansas 0.23234938 0.23086801 -1.07359268 -0.184916602
## California 0.27826823 1.26281442 1.75892340 2.067820292
## Colorado 0.02571456 0.39885929 0.86080854 1.864967207
## Connecticut -1.03041900 -0.72908214 0.79172279 -1.081740768
## Delaware -0.43347395 0.80683810 0.44629400 -0.579946294
## Florida 1.74767144 1.97077766 0.99898006 1.138966691
## Georgia 2.20685994 0.48285493 -0.38273510 0.487701523
## Hawaii -0.57123050 -1.49704226 1.20623733 -0.110181255
## Idaho -1.19113497 -0.60908837 -0.79724965 -0.750769945
## Illinois 0.59970018 0.93883125 1.20623733 0.295524916
## Indiana -0.13500142 -0.69308401 -0.03730631 -0.024769429
## Iowa -1.28297267 -1.37704849 -0.58999237 -1.060387812
## Kansas -0.41051452 -0.66908525 0.03177945 -0.345063775
## Kentucky 0.43898421 -0.74108152 -0.93542116 -0.526563903
## Louisiana 1.74767144 0.93883125 0.03177945 0.103348309
## Maine -1.30593210 -1.05306531 -1.00450692 -1.434064548
## Maryland 0.80633501 1.55079947 0.10086521 0.701231086
## Massachusetts -0.77786532 -0.26110644 1.34440885 -0.526563903
## Michigan 0.99001041 1.01082751 0.58446551 1.480613993
## Minnesota -1.16817555 -1.18505846 0.03177945 -0.676034598
## Mississippi 1.90838741 1.05882502 -1.48810723 -0.441152078
## Missouri 0.27826823 0.08687549 0.30812248 0.743936999
## Montana -0.41051452 -0.74108152 -0.86633540 -0.515887425
## Nebraska -0.80082475 -0.82507715 -0.24456358 -0.505210947
## Nevada 1.01296983 0.97482938 1.06806582 2.644350114
## New Hampshire -1.30593210 -1.36504911 -0.65907813 -1.252564419
## New Jersey -0.08908257 -0.14111267 1.62075188 -0.259651949
## New Mexico 0.82929443 1.37080881 0.30812248 1.160319648
## New York 0.76041616 0.99882813 1.41349461 0.519730957
## North Carolina 1.19664523 1.99477641 -1.41902147 -0.547916860
## North Dakota -1.60440462 -1.50904164 -1.48810723 -1.487446939
## Ohio -0.11204199 -0.60908837 0.65355127 0.017936483
## Oklahoma -0.27275797 -0.23710769 0.16995096 -0.131534211
## Oregon -0.66306820 -0.14111267 0.10086521 0.861378259
## Pennsylvania -0.34163624 -0.77707965 0.44629400 -0.676034598
## Rhode Island -1.00745957 0.03887798 1.48258036 -1.380682157
## South Carolina 1.51807718 1.29881255 -1.21176419 0.135377743
## South Dakota -0.91562187 -1.01706718 -1.41902147 -0.900240639
## Tennessee 1.24256408 0.20686926 -0.45182086 0.605142783
## Texas 1.12776696 0.36286116 0.99898006 0.455672088
## Utah -1.05337842 -0.60908837 0.99898006 0.178083656
## Vermont -1.28297267 -1.47304350 -2.31713632 -1.071064290
## Virginia 0.16347111 -0.17711080 -0.17547783 -0.056798864
## Washington -0.86970302 -0.30910395 0.51537975 0.530407436
## West Virginia -0.47939280 -1.07706407 -1.83353601 -1.273917376
## Wisconsin -1.19113497 -1.41304662 0.03177945 -1.113770203
## Wyoming -0.22683912 -0.11711392 -0.38273510 -0.601299251
## attr(,"scaled:center")
## Murder Assault UrbanPop Rape
## 7.788 170.760 65.540 21.232
## attr(,"scaled:scale")
## Murder Assault UrbanPop Rape
## 4.355510 83.337661 14.474763 9.366385## K-means clustering with 4 clusters of sizes 8, 13, 16, 13
##
## Cluster means:
## Murder Assault UrbanPop Rape
## 1 1.4118898 0.8743346 -0.8145211 0.01927104
## 2 -0.9615407 -1.1066010 -0.9301069 -0.96676331
## 3 -0.4894375 -0.3826001 0.5758298 -0.26165379
## 4 0.6950701 1.0394414 0.7226370 1.27693964
##
## Clustering vector:
## Alabama Alaska Arizona Arkansas California
## 1 4 4 1 4
## Colorado Connecticut Delaware Florida Georgia
## 4 3 3 4 1
## Hawaii Idaho Illinois Indiana Iowa
## 3 2 4 3 2
## Kansas Kentucky Louisiana Maine Maryland
## 3 2 1 2 4
## Massachusetts Michigan Minnesota Mississippi Missouri
## 3 4 2 1 4
## Montana Nebraska Nevada New Hampshire New Jersey
## 2 2 4 2 3
## New Mexico New York North Carolina North Dakota Ohio
## 4 4 1 2 3
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 3 3 3 3 1
## South Dakota Tennessee Texas Utah Vermont
## 2 1 4 3 2
## Virginia Washington West Virginia Wisconsin Wyoming
## 3 3 2 2 3
##
## Within cluster sum of squares by cluster:
## [1] 8.316061 11.952463 16.212213 19.922437
## (between_SS / total_SS = 71.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"3.2 hierarchial clustering
metode clustering yang digunakan untuk mengelompokkan objek-objek ke dalam kelompok berdasarkan kemiripan atau jarak antara objek-objek
## Alabama Alaska Arizona Arkansas California Colorado
## Alaska 2.7037541
## Arizona 2.2935197 2.7006429
## Arkansas 1.2898102 2.8260386 2.7177583
## California 3.2631104 3.0125415 1.3104842 3.7636409
## Colorado 2.6510673 2.3265187 1.3650307 2.8310512 1.2876185
## Connecticut 3.2152975 4.7399125 3.2628575 2.6076395 4.0663898 3.3279920
## Delaware 2.0192927 3.6213633 1.9093696 1.8003239 3.0737852 2.5547456
## Florida 2.2981353 2.9967642 1.7493928 3.3721968 2.0250039 2.4458600
## Georgia 1.1314351 2.8194388 2.7871963 2.2117614 3.3780585 2.8649105
## Hawaii 3.3885300 4.5301340 3.2621208 2.9723097 3.6589083 2.8233524
## Idaho 2.9146623 4.0580555 3.5210071 1.7687255 4.4879436 3.4767685
## Illinois 1.8734993 3.2670626 1.0825512 2.4626424 1.9117469 1.7898322
## Indiana 2.0761411 3.3655952 2.6407486 1.4450503 3.4061273 2.3655622
## Iowa 3.4878952 4.7251910 4.1157513 2.4252661 4.9708591 3.9406898
## Kansas 2.2941096 3.6808173 2.7762838 1.5718411 3.6071725 2.6272281
## Kentucky 1.8475879 3.5440903 3.3567681 1.0598104 4.2463809 3.2274013
## Louisiana 0.7722224 2.9631431 2.2178519 2.0254276 3.0176625 2.6546743
## Maine 3.4851115 4.8322605 4.2961903 2.3621893 5.2699843 4.2713441
## Maryland 1.2896460 2.2777590 1.2117356 2.0582244 2.2312581 1.9667562
## Massachusetts 2.9874810 4.3729925 2.5162281 2.6881270 3.2156499 2.6522793
## Michigan 1.8814771 2.1154937 1.1940906 2.5895050 1.5146739 1.2363108
## Minnesota 3.2314338 4.4266606 3.5388450 2.3300992 4.3123134 3.3283853
## Mississippi 1.2831907 3.2554326 3.4551406 1.9318631 4.4200736 3.8491042
## Missouri 1.6309686 2.5360573 1.5958731 1.6717500 2.2891751 1.3127406
## Montana 2.3317271 3.6575988 3.3270869 1.2290066 4.2494176 3.1845338
## Nebraska 2.6625170 3.9136902 3.1641791 1.7240495 4.0197242 3.0034613
## Nevada 3.1024305 2.3443182 1.9260292 3.7086787 1.1968261 1.3988595
## New Hampshire 3.5619825 4.8650686 4.2430411 2.4949861 5.1270892 4.1126287
## New Jersey 2.6980230 4.1791832 2.1755787 2.7398478 2.7463023 2.3229870
## New Mexico 1.5993970 2.0580889 1.0376848 2.3183196 1.8010201 1.5467439
## New York 2.0723680 3.2903769 1.0725219 2.7478626 1.6787069 1.7363385
## North Carolina 1.6043662 3.2403071 3.1478947 2.0717938 4.2802569 3.8649275
## North Dakota 4.0614988 5.2110254 4.9319844 2.8756492 5.8660699 4.8014019
## Ohio 2.2698519 3.5903348 2.3585705 1.9617104 3.0133425 2.1188236
## Oklahoma 1.9570874 3.3416664 2.2648377 1.4224574 3.1488712 2.2263966
## Oregon 2.3705678 2.6990696 2.0008664 1.8477626 2.6574019 1.5331980
## Pennsylvania 2.5161340 4.1239537 2.9188907 1.9739986 3.7144562 2.8541709
## Rhode Island 3.3951297 5.0629572 3.0570151 3.0883430 3.8883995 3.4810739
## South Carolina 0.9157968 2.5640542 2.7992041 1.7074195 3.7546959 3.2131137
## South Dakota 3.0835587 4.2467198 4.1020099 1.8724822 5.0529153 3.9667318
## Tennessee 0.8407489 2.3362541 2.2989846 1.4254486 3.0119267 2.1972111
## Texas 1.6463225 3.1527905 1.6448574 2.3505545 2.1698156 1.7947199
## Utah 3.0906007 3.9480881 2.5244431 2.6049855 3.0701663 2.2461228
## Vermont 3.9791527 4.8707876 5.1003665 2.7442984 6.0323504 4.8924735
## Virginia 1.4859733 3.0492081 2.3106550 0.9971035 3.2159723 2.2622539
## Washington 2.6481824 3.2715253 2.1399117 2.1313402 2.7746720 1.7897920
## West Virginia 3.1243471 4.5004558 4.4974190 1.9951691 5.4883565 4.4210375
## Wisconsin 3.5047330 4.8711543 3.9425867 2.6102451 4.7354960 3.7846917
## Wyoming 1.8291027 3.4993456 2.6923028 0.9912639 3.7242766 2.8211492
## Connecticut Delaware Florida Georgia Hawaii Idaho
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware 1.7568475
## Florida 4.4700701 3.0614170
## Georgia 3.9738227 2.9838715 2.1812958
## Hawaii 1.3843291 2.4748807 4.3596338 3.8105218
## Idaho 1.6354214 2.0382540 4.6999827 3.8005715 2.3658101
## Illinois 2.7400560 1.5584719 1.7711863 2.3135778 2.7329756 3.2728945
## Indiana 1.6147898 1.6973340 3.6150778 2.6924143 1.5460727 1.4923351
## Iowa 1.5470089 2.6068606 5.2682765 4.2517889 2.1564575 0.8584962
## Kansas 1.2280424 1.5510864 3.8424558 3.0071474 1.4648766 1.2103118
## Kentucky 2.3346386 2.2514939 3.9474983 2.4408198 2.5203345 1.6565236
## Louisiana 3.5329409 2.3266996 1.7529677 0.8592544 3.5687157 3.5283772
## Maine 1.8792141 2.6560808 5.3946798 4.3334217 2.7160558 0.8486112
## Maryland 3.4968269 1.9624834 1.4355204 1.8388691 3.6148670 3.4014584
## Massachusetts 0.9468199 1.4382527 3.7753087 3.6706708 1.3276676 2.2201020
## Michigan 3.7037870 2.5165292 1.3357020 1.9185489 3.4123472 3.7775301
## Minnesota 0.9843793 2.1652930 4.7635252 3.9621842 1.4673850 1.0124936
## Mississippi 4.1762631 3.0510628 3.0886673 1.5828594 4.4777223 3.6002946
## Missouri 2.4383227 1.6723281 2.5182466 2.1021909 2.1832480 2.4697182
## Montana 1.8584328 2.0306850 4.2696476 3.0967288 2.2488801 0.8286936
## Nebraska 1.2116949 1.8113430 4.3082894 3.4295510 1.6628657 0.7515014
## Nevada 4.5868149 3.5920897 1.9500388 2.9023041 4.0281974 4.7300228
## New Hampshire 1.6169000 2.6744233 5.3778074 4.3427351 2.3112009 0.9249563
## New Jersey 1.6108823 1.5808719 3.1900596 3.1989350 1.5050500 2.7425260
## New Mexico 3.6233659 2.2271650 1.2965798 1.9015384 3.5506088 3.5883476
## New York 3.0239174 1.8992106 1.5730970 2.3634498 2.9055803 3.5910319
## North Carolina 4.1894604 2.7475286 2.9994188 2.3351307 4.7330517 3.5929592
## North Dakota 2.5099838 3.3615239 6.0356613 4.8596758 3.1974906 1.4144557
## Ohio 1.4443671 1.5838515 3.3897305 2.8043208 1.1494313 1.9647327
## Oklahoma 1.4510623 1.1802929 3.3553471 2.7121515 1.6585736 1.5168111
## Oregon 2.1756954 1.7742778 3.3399718 2.9998878 2.0031861 1.9757247
## Pennsylvania 0.8721491 1.5894850 3.9389869 3.1817981 1.2119256 1.5171866
## Rhode Island 1.0756115 1.6230495 4.2314871 4.1832075 2.0590981 2.4592705
## South Carolina 4.0127954 2.7039667 2.5295912 1.3970074 4.2531214 3.4549959
## South Dakota 2.2397424 2.6722813 5.1015141 3.8729745 2.8044891 0.8070290
## Tennessee 3.2302375 2.3195070 2.3992285 1.0122252 3.0747375 2.9234395
## Texas 2.8734475 2.0031365 1.8537984 1.7575559 2.5901696 3.3172180
## Utah 1.2825907 1.8080931 3.9274528 3.7183994 1.0709720 2.0268663
## Vermont 3.2066152 3.7144653 6.0766416 4.7091538 3.7208347 1.7797462
## Virginia 1.9277004 1.4088230 3.1515587 2.2249559 2.0479238 1.6999289
## Washington 1.6963486 1.6350170 3.5570666 3.3016469 1.5452901 1.8861921
## West Virginia 2.7117590 3.0381601 5.3004067 3.8545331 3.2831874 1.4398440
## Wisconsin 1.0354597 2.4410507 5.1085370 4.2281611 1.6666970 1.2105401
## Wyoming 1.6218573 1.2586225 3.6325811 2.7329062 2.1883414 1.1687896
## Illinois Indiana Iowa Kansas Kentucky Louisiana
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana 2.2027081
## Iowa 3.7380070 1.7786548
## Kansas 2.3228505 0.4287712 1.4699265
## Kentucky 2.8478883 1.1790552 1.9426473 1.3020180
## Louisiana 1.6535178 2.4957547 4.0359614 2.7284126 2.4221964
## Maine 3.9342034 2.1029158 0.6457158 1.7913753 1.9925855 4.0901924
## Maryland 1.3429997 2.5430878 4.0642448 2.7400943 2.8229479 1.2739137
## Massachusetts 2.0080982 1.6615695 2.3510287 1.4343401 2.6284451 3.1524549
## Michigan 1.3959090 2.6118471 4.3248636 2.9020920 3.1163494 1.6677999
## Minnesota 3.1558788 1.3184866 0.7644384 0.9745872 1.9333640 3.6905974
## Mississippi 3.0869477 3.0859068 4.1603272 3.2683740 2.3898884 1.6268879
## Missouri 1.3552973 1.2203931 2.9398546 1.5192717 1.9677184 1.8362172
## Montana 2.9659043 1.0033431 1.2403561 0.9170466 0.8523702 2.9444756
## Nebraska 2.7962196 0.8570429 0.9821819 0.5279092 1.4219429 3.1706333
## Nevada 2.3891753 3.5278633 5.2227312 3.8391728 4.1644286 2.8410670
## New Hampshire 3.8490624 1.9278736 0.2058539 1.6084091 2.0093558 4.1168122
## New Jersey 1.4562775 1.7638332 2.9122979 1.7071034 2.6914828 2.6826380
## New Mexico 1.3393276 2.5909993 4.2131394 2.8356373 3.0007332 1.4911656
## New York 0.3502188 2.4628527 4.0411586 2.6096016 3.1213366 1.7495096
## North Carolina 3.0124311 3.3437548 4.2973973 3.4387635 2.8798080 1.9868618
## North Dakota 4.6139615 2.6587932 1.0534375 2.3970805 2.4482563 4.6977846
## Ohio 1.8124981 0.6976320 2.1610242 0.7817000 1.7726720 2.4996969
## Oklahoma 1.8439860 0.5303259 1.9391446 0.5198728 1.4623483 2.3535566
## Oregon 2.0743434 1.1780815 2.4662295 1.3426890 2.1388677 2.7490592
## Pennsylvania 2.3134187 0.8412900 1.5708895 0.5456840 1.5944097 2.8440845
## Rhode Island 2.5057761 2.3335609 2.5453686 2.0087021 3.0457816 3.5648047
## South Carolina 2.6163680 2.8469842 4.1015324 3.0609333 2.4166385 1.3151908
## South Dakota 3.8004708 1.8411735 0.9886706 1.6701106 1.5114990 3.7457555
## Tennessee 1.9478353 1.8100316 3.4176329 2.1533060 1.7489942 1.1298534
## Texas 0.8241352 2.0035762 3.6962443 2.2378289 2.5297839 1.3325285
## Utah 2.2771632 1.4019666 2.1682069 1.2751603 2.5461745 3.3440990
## Vermont 4.8624402 2.8667983 1.7298425 2.7298377 2.3888326 4.6795933
## Virginia 1.8624960 0.6127246 2.1704984 0.8351949 1.0918624 1.9554079
## Washington 2.0612962 1.1405746 2.2502832 1.1579118 2.2630242 2.9705622
## West Virginia 4.1148082 2.2478563 1.5256890 2.1244674 1.5236299 3.7947215
## Wisconsin 3.4790637 1.6806129 0.6318069 1.3242947 2.0950212 3.9559184
## Wyoming 2.2643574 0.8898783 1.7194683 0.7588728 1.0694408 2.3837077
## Maine Maryland Massachusetts Michigan Minnesota
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky
## Louisiana
## Maine
## Maryland 4.1259083
## Massachusetts 2.6920282 2.9743193
## Michigan 4.5333420 1.0800988 3.0576915
## Minnesota 1.2980362 3.6448929 1.6587245 3.7995101
## Mississippi 4.0014591 2.2992240 4.1217248 2.9722824 4.1067600
## Missouri 3.2055955 1.5705755 1.9810531 1.4068840 2.4088795
## Montana 1.3271199 3.0249456 2.2919046 3.3348908 1.2662635
## Nebraska 1.3218907 3.1309065 1.6863806 3.3478988 0.6083415
## Nevada 5.5153139 2.2551337 3.8556049 1.2609417 4.6391114
## New Hampshire 0.4995971 4.1663744 2.4573524 4.4646172 0.9279247
## New Jersey 3.2532459 2.6263456 0.7977642 2.5678440 2.2254151
## New Mexico 4.3460538 0.5353893 3.0274701 0.5782474 3.7377675
## New York 4.2595904 1.4362170 2.2479437 1.2897453 3.4391596
## North Carolina 4.0631653 2.0542355 4.0773401 3.0232021 4.2219622
## North Dakota 0.7305609 4.7423030 3.3446903 5.1171939 1.8065731
## Ohio 2.5455752 2.5061694 1.1567960 2.4459855 1.5216293
## Oklahoma 2.1929825 2.2492942 1.3383233 2.4336743 1.4198434
## Oregon 2.7813372 2.2466329 1.8709252 2.1626274 1.9270100
## Pennsylvania 1.9197571 2.9585539 1.1337883 3.1048542 1.0106613
## Rhode Island 2.7331079 3.4379146 0.9440940 3.7320501 2.0310592
## South Carolina 4.0015575 1.6165582 3.8310425 2.3233363 3.9484630
## South Dakota 0.7812991 3.7991896 2.8925136 4.1744724 1.4990317
## Tennessee 3.5420469 1.5202431 2.9678843 1.5970196 3.1023238
## Texas 3.9386296 1.5431868 2.2593978 1.2888621 3.1438264
## Utah 2.6218087 3.0338001 0.9015809 2.9441421 1.4177147
## Vermont 1.4253680 4.7430576 3.9277625 5.1250778 2.4019924
## Virginia 2.3474650 2.0124420 1.8503795 2.2439957 1.7932233
## Washington 2.6292546 2.5434911 1.3472994 2.4715215 1.5955418
## West Virginia 1.1818120 4.0251562 3.3782752 4.4668346 2.0791705
## Wisconsin 1.1485830 4.0091486 1.8882704 4.2034334 0.4940832
## Wyoming 1.7665064 2.4041294 1.8201580 2.8324573 1.4845967
## Mississippi Missouri Montana Nebraska Nevada
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky
## Louisiana
## Maine
## Maryland
## Massachusetts
## Michigan
## Minnesota
## Mississippi
## Missouri 2.8692946
## Montana 3.0015255 2.0313649
## Nebraska 3.5269565 1.9651798 0.7389936
## Nevada 4.1064793 2.3489003 4.3243112 4.2628916
## New Hampshire 4.1895936 3.0885710 1.3329504 1.1300720 5.3871427
## New Jersey 3.8894324 1.7079555 2.5912431 2.1246377 3.3464214
## New Mexico 2.6557350 1.4579057 3.1915871 3.2494088 1.7234839
## New York 3.2655822 1.5284764 3.2662661 3.0925340 2.1674148
## North Carolina 1.1826891 3.0224849 3.2209267 3.6500186 4.1773437
## North Dakota 4.4753078 3.7811273 1.8291157 1.9038740 6.0519445
## Ohio 3.4148987 1.1327425 1.6436336 1.2654510 3.2930712
## Oklahoma 3.0466140 1.0927654 1.2225315 0.9674809 3.4108696
## Oregon 3.5033774 0.9974171 1.8044622 1.5727910 2.8581280
## Pennsylvania 3.4971746 1.7793568 1.3246445 0.8483058 4.0392694
## Rhode Island 4.3875001 2.7475003 2.6888576 2.1303973 4.6185330
## South Carolina 0.7865674 2.3846001 2.9024302 3.3517226 3.4427701
## South Dakota 3.5355186 2.8862448 0.8857149 1.2591419 5.1416772
## Tennessee 1.8269569 1.2413874 2.2494023 2.5526834 2.6666268
## Texas 2.8431727 1.1654171 2.8298991 2.7568751 2.2765693
## Utah 4.2571173 1.7478909 2.0956369 1.4573012 3.5868975
## Vermont 4.2046660 3.8803394 1.9261350 2.2952287 6.0437845
## Virginia 2.5383053 0.9787310 1.1556682 1.2472262 3.3001850
## Washington 3.8140404 1.2502752 1.8442691 1.3859985 3.1570805
## West Virginia 3.3281129 3.2538044 1.2758193 1.8117833 5.4963193
## Wisconsin 4.2987974 2.8171535 1.4916365 0.9719877 5.0751736
## Wyoming 2.6813279 1.6073860 0.8150071 0.9268202 3.9202716
## New Hampshire New Jersey New Mexico New York North Carolina
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky
## Louisiana
## Maine
## Maryland
## Massachusetts
## Michigan
## Minnesota
## Mississippi
## Missouri
## Montana
## Nebraska
## Nevada
## New Hampshire
## New Jersey 3.0269198
## New Mexico 4.3360809 2.6208087
## New York 4.1586415 1.6344744 1.3324096
## North Carolina 4.3157112 3.9418824 2.5348334 3.2163998
## North Dakota 0.9231894 3.9166205 4.9450519 4.9325292 4.5836787
## Ohio 2.3095495 1.1099823 2.4960904 2.0434995 3.6205693
## Oklahoma 2.0697098 1.4711183 2.3426252 2.1367108 3.1366639
## Oregon 2.6377191 1.9738854 2.1553130 2.2727718 3.5095191
## Pennsylvania 1.6822035 1.4216058 3.0619915 2.5949374 3.6803956
## Rhode Island 2.5813199 1.4668378 3.6032966 2.7682543 4.2185789
## South Carolina 4.1596914 3.5826726 1.9596343 2.7755634 1.0476313
## South Dakota 0.9874611 3.3318222 3.9969513 4.1124693 3.6955387
## Tennessee 3.5298430 2.6339707 1.5528304 2.0847931 2.3374653
## Texas 3.8178258 1.6226525 1.4418241 0.8457697 3.0857436
## Utah 2.3304873 1.3141843 2.9843796 2.4826984 4.2680823
## Vermont 1.6716127 4.4005416 4.9416825 5.1704762 4.3880034
## Virginia 2.2878085 1.8255601 2.1341562 2.1439207 2.7517523
## Washington 2.4214987 1.5759539 2.4796057 2.2747965 3.8055684
## West Virginia 1.4648924 3.7402121 4.2681325 4.4279608 3.5978058
## Wisconsin 0.7155628 2.4671212 4.1327758 3.7687073 4.4429456
## Wyoming 1.7950754 2.0372127 2.6286722 2.5890441 2.7501141
## North Dakota Ohio Oklahoma Oregon Pennsylvania
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky
## Louisiana
## Maine
## Maryland
## Massachusetts
## Michigan
## Minnesota
## Mississippi
## Missouri
## Montana
## Nebraska
## Nevada
## New Hampshire
## New Jersey
## New Mexico
## New York
## North Carolina
## North Dakota
## Ohio 3.1448279
## Oklahoma 2.8246690 0.6483903
## Oregon 3.2862071 1.2407607 1.0734082
## Pennsylvania 2.5555137 0.7781298 0.8180221 1.7293732
## Rhode Island 3.4042300 1.9659747 1.9746699 2.6621371 1.6369255
## South Carolina 4.5104172 3.1289884 2.7470931 3.0134453 3.3429642
## South Dakota 1.0324944 2.4394250 2.0340486 2.4988870 1.9790714
## Tennessee 4.0623149 2.0167804 1.8500296 2.0306758 2.4343114
## Texas 4.5749422 1.6711510 1.8312655 2.1053000 2.2460705
## Utah 3.1738212 1.0154223 1.2372916 1.2825152 1.2529078
## Vermont 0.9824857 3.4825859 3.1010306 3.4262789 3.0270572
## Virginia 2.9443461 0.9774388 0.5646254 1.2664430 1.1769236
## Washington 3.1725909 0.9725013 0.9586525 0.5935343 1.3993323
## West Virginia 1.2716808 2.8650371 2.4631736 3.0349855 2.3799278
## Wisconsin 1.6216339 1.8649801 1.7916829 2.4088700 1.2204658
## Wyoming 2.4170757 1.3086480 0.7366465 1.6013015 1.0684605
## Rhode Island South Carolina South Dakota Tennessee Texas
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky
## Louisiana
## Maine
## Maryland
## Massachusetts
## Michigan
## Minnesota
## Mississippi
## Missouri
## Montana
## Nebraska
## Nevada
## New Hampshire
## New Jersey
## New Mexico
## New York
## North Carolina
## North Dakota
## Ohio
## Oklahoma
## Oregon
## Pennsylvania
## Rhode Island
## South Carolina 4.1861320
## South Dakota 3.1262712 3.5215978
## Tennessee 3.5743861 1.4375120 3.0589938
## Texas 2.8757996 2.4532276 3.7101039 1.4712840
## Utah 1.7565845 3.8912317 2.6823382 2.8678113 2.4039834
## Vermont 4.1104165 4.2668977 1.0856574 3.9356721 4.7444455
## Virginia 2.4330133 2.2636538 2.0316897 1.3514491 1.6921625
## Washington 2.1743525 3.3802314 2.5083824 2.3809584 2.1635337
## West Virginia 3.5400858 3.4651680 0.7108812 3.1707450 3.9586581
## Wisconsin 2.0779526 4.2190973 1.5437375 3.4257189 3.4539515
## Wyoming 2.1726807 2.5059056 1.5644785 1.9298669 2.2564704
## Utah Vermont Virginia Washington West Virginia Wisconsin
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky
## Louisiana
## Maine
## Maryland
## Massachusetts
## Michigan
## Minnesota
## Mississippi
## Missouri
## Montana
## Nebraska
## Nevada
## New Hampshire
## New Jersey
## New Mexico
## New York
## North Carolina
## North Dakota
## Ohio
## Oklahoma
## Oregon
## Pennsylvania
## Rhode Island
## South Carolina
## South Dakota
## Tennessee
## Texas
## Utah
## Vermont 3.6546040
## Virginia 1.7612066 3.0638337
## Washington 0.6940667 3.4804319 1.3809295
## West Virginia 3.2680139 1.0380554 2.3353210 3.0846553
## Wisconsin 1.8082282 2.3518637 2.1266497 2.0637823 2.0308890
## Wyoming 1.8552036 2.6299335 0.7038309 1.5929546 1.8821600 1.7446366
## Alabama Alaska Arizona Arkansas California
## 1 1 1 2 1
## Colorado Connecticut Delaware Florida Georgia
## 1 2 2 1 1
## Hawaii Idaho Illinois Indiana Iowa
## 2 3 1 2 3
## Kansas Kentucky Louisiana Maine Maryland
## 2 2 1 3 1
## Massachusetts Michigan Minnesota Mississippi Missouri
## 2 1 3 1 2
## Montana Nebraska Nevada New Hampshire New Jersey
## 3 3 1 3 2
## New Mexico New York North Carolina North Dakota Ohio
## 1 1 1 3 2
## Oklahoma Oregon Pennsylvania Rhode Island South Carolina
## 2 2 2 2 1
## South Dakota Tennessee Texas Utah Vermont
## 3 1 1 2 3
## Virginia Washington West Virginia Wisconsin Wyoming
## 2 2 3 3 2