In the chapter, we mentioned the use of correlation-based distance and Euclidean distance as dissimilarity measures for hierarchical clustering. It turns out that these two measures are almost equivalent: if each observation has been centered to have mean zero and standard deviation one, and if we let rij denote the correlation between the ith and jth observations, then the quantity \(1 − r_{ij}\) is proportional to the squared Euclidean distance between the ith and jth observations.
On the USArrests data, show that this proportionality holds.
Hint: The Euclidean distance can be calculated using the dist() function, and correlations can be calculated using the cor() function.
library(ISLR)
set.seed(1)names(USArrests)## [1] "Murder" "Assault" "UrbanPop" "Rape"dsc <- scale(USArrests)head(dsc)## Murder Assault UrbanPop Rape
## Alabama 1.24256408 0.7828393 -0.5209066 -0.003416473
## Alaska 0.50786248 1.1068225 -1.2117642 2.484202941
## Arizona 0.07163341 1.4788032 0.9989801 1.042878388
## Arkansas 0.23234938 0.2308680 -1.0735927 -0.184916602
## California 0.27826823 1.2628144 1.7589234 2.067820292
## Colorado 0.02571456 0.3988593 0.8608085 1.864967207a <- dist(dsc)^2
b <- as.dist(1 - cor(t(dsc)))
summary(b / a)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000086 0.069135 0.133943 0.234193 0.262589 4.887686a## Alabama Alaska Arizona Arkansas California
## Alaska 7.31028609
## Arizona 5.26023278 7.29347205
## Arkansas 1.66361028 7.98649428 7.38621016
## California 10.64788918 9.07540626 1.71736889 14.16499276
## Colorado 7.02815781 5.41268921 1.86330880 8.01485074 1.65796150
## Connecticut 10.33813789 22.46677045 10.64623933 6.79978363 16.53552607
## Delaware 4.07754307 13.11427242 3.64569237 3.24116621 9.44815517
## Florida 5.28142566 8.98059543 3.06037530 11.37171123 4.10064060
## Georgia 1.28014540 7.94923506 7.76846344 4.89188867 11.41127921
## Hawaii 11.48213585 20.52211419 10.64143234 8.83462477 13.38760961
## Idaho 8.49525655 16.46781442 12.39749070 3.12838990 20.14163739
## Illinois 3.50999964 10.67369811 1.17191703 6.06460748 3.65477638
## Indiana 4.31036167 11.32723119 6.97355332 2.08817050 11.60170337
## Iowa 12.16541263 22.32742956 16.93940863 5.88191549 24.70944059
## Kansas 5.26293868 13.54841569 7.70775193 2.47068453 13.01169377
## Kentucky 3.41358096 12.56057601 11.26789198 1.12319808 18.03175051
## Louisiana 0.59632751 8.78021688 4.91886698 4.10235707 9.10628726
## Maine 12.14600188 23.35074194 18.45725130 5.57993812 27.77273418
## Maryland 1.66318693 5.18818595 1.46830307 4.23628759 4.97851292
## Massachusetts 8.92504280 19.12306325 6.33140382 7.22602687 10.34040454
## Michigan 3.53995592 4.47531360 1.42585234 6.70553617 2.29423689
## Minnesota 10.44216437 19.59532401 12.52342409 5.42936227 18.59604712
## Mississippi 1.64657827 10.59784130 11.93799654 3.73209520 19.53705043
## Missouri 2.66005864 6.43158652 2.54681087 2.79474818 5.24032265
## Montana 5.43695119 13.37802891 11.06950744 1.51045714 18.05754995
## Nebraska 7.08899655 15.31697104 10.01202932 2.97234668 16.15818272
## Nevada 9.62507498 5.49582762 3.70958842 13.75429806 1.43239266
## New Hampshire 12.68771958 23.66889235 18.00339737 6.22495555 26.28704345
## New Jersey 7.27932787 17.46557261 4.73314255 7.50676610 7.54217630
## New Mexico 2.55807090 4.23572974 1.07678966 5.37460577 3.24367338
## New York 4.29470910 10.82658009 1.15030330 7.55074861 2.81805702
## North Carolina 2.57399095 10.49958985 9.90924086 4.29232957 18.32059908
## North Dakota 16.49577270 27.15478586 24.32446969 8.26935844 34.41077602
## Ohio 5.15222767 12.89050377 5.56285484 3.84830773 9.08023330
## Oklahoma 3.83019123 11.16673433 5.12948980 2.02338516 9.91538983
## Oregon 5.61959184 7.28497679 4.00346648 3.41422652 7.06178489
## Pennsylvania 6.33093011 17.00699373 8.51992298 3.89667037 13.79718497
## Rhode Island 11.52690580 25.63353589 9.34534128 9.53786230 15.11965101
## South Carolina 0.83868385 6.57437373 7.83554381 2.91528136 14.09774107
## South Dakota 9.50833401 18.03462912 16.82648492 3.50618977 25.53195296
## Tennessee 0.70685875 5.45808328 5.28533038 2.03190371 9.07170233
## Texas 2.71037787 9.94008765 2.70555598 5.52510645 4.70809967
## Utah 9.55181256 15.58739966 6.37281277 6.78594964 9.42592130
## Vermont 15.83365636 23.72457189 26.01373812 7.53117389 36.38925099
## Virginia 2.20811667 9.29766981 5.33912675 0.99421537 10.34247768
## Washington 7.01286989 10.70287758 4.57922199 4.54261108 7.69880444
## West Virginia 9.76154469 20.25410214 20.22677731 3.98069981 30.12205684
## Wisconsin 12.28315357 23.72814438 15.54398956 6.81337957 22.42492239
## Wyoming 3.34561684 12.24541987 7.24849420 0.98260421 13.87023590
## Colorado Connecticut Delaware Florida Georgia
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut 11.07553068
## Delaware 6.52672513 3.08651312
## Florida 5.98223097 19.98152656 9.37227420
## Georgia 8.20771199 15.79126676 8.90348920 4.75805123
## Hawaii 7.97131856 1.91636702 6.12503464 19.00640730 14.52007651
## Idaho 12.08791906 2.67460320 4.15447951 22.08983753 14.44434344
## Illinois 3.20349937 7.50790667 2.42883468 3.13710100 5.35264212
## Indiana 5.59588463 2.60754615 2.88094279 13.06878725 7.24909451
## Iowa 15.52903598 2.39323648 6.79572222 27.75473724 18.07770851
## Kansas 6.90232753 1.50808805 2.40586899 14.76446625 9.04293557
## Kentucky 10.41611905 5.45053733 5.06922482 15.58274268 5.95760124
## Louisiana 7.04729559 12.48167150 5.41353118 3.07289585 0.73831819
## Maine 18.24438016 3.53144577 7.05476523 29.10257068 18.77854388
## Maryland 3.86813010 12.22779824 3.85134128 2.06071870 3.38143975
## Massachusetts 7.03458569 0.89646785 2.06857093 14.25295574 13.47382394
## Michigan 1.52846446 13.71803806 6.33291945 1.78409971 3.68083002
## Minnesota 11.07814842 0.96900264 4.68849362 22.69117192 15.69890364
## Mississippi 14.81560328 17.44117384 9.30898393 9.53986573 2.50544394
## Missouri 1.72328786 5.94541768 2.79668143 6.34156581 4.41920649
## Montana 10.14125584 3.45377251 4.12368175 18.22989072 9.58972949
## Nebraska 9.02077965 1.46820464 3.28096358 18.56135781 11.76182001
## Nevada 1.95680782 21.03887110 12.90310820 3.80265151 8.42336888
## New Hampshire 16.91371460 2.61436548 7.15253998 28.92081279 18.85934822
## New Jersey 5.39626853 2.59494163 2.49915588 10.17648033 10.23318484
## New Mexico 2.39241657 13.12878022 4.96026386 1.68111907 3.61584816
## New York 3.01487151 9.14407633 3.60700083 2.47463407 5.58589499
## North Carolina 14.93766452 17.55157860 7.54891363 8.99651331 5.45283520
## North Dakota 23.05346036 6.30001869 11.29984311 36.42920793 23.61644843
## Ohio 4.48941342 2.08619625 2.50858566 11.49027253 7.86421495
## Oklahoma 4.95684195 2.10558179 1.39309130 11.25835446 7.35576590
## Oregon 2.35069605 4.73365045 3.14806170 11.15541196 8.99932660
## Pennsylvania 8.14629147 0.76064399 2.52646255 15.51561791 10.12383891
## Rhode Island 12.11787531 1.15694003 2.63428960 17.90548280 17.49922478
## South Carolina 10.32409956 16.10252721 7.31143611 6.39883155 1.95162981
## South Dakota 15.73496135 5.01644621 7.14108735 26.02544595 14.99993185
## Tennessee 4.82773647 10.43443400 5.38011250 5.75629754 1.02459987
## Texas 3.22101946 8.25670065 4.01255601 3.43656855 3.08900282
## Utah 5.04506762 1.64503880 3.26920062 15.42488523 13.82649431
## Vermont 23.93629683 10.28238080 13.79725222 36.92557268 22.17612925
## Virginia 5.11779268 3.71602886 1.98478227 9.93232210 4.95042892
## Washington 3.20335541 2.87759861 2.67328071 12.65272280 10.90087257
## West Virginia 19.54557221 7.35363691 9.23041666 28.09431110 14.85742544
## Wisconsin 14.32389159 1.07217680 5.95872868 26.09715038 17.87734606
## Wyoming 7.95888274 2.63042110 1.58413047 13.19564549 7.46877639
## Hawaii Idaho Illinois Indiana Iowa
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho 5.59705761
## Illinois 7.46915588 10.71183870
## Indiana 2.39034065 2.22706397 4.85192310
## Iowa 4.65030909 0.73701571 13.97269651 3.16361273
## Kansas 2.14586355 1.46485465 5.39563441 0.18384472 2.16068385
## Kentucky 6.35208601 2.74407044 8.11046765 1.39017124 3.77387850
## Louisiana 12.73573209 12.44944547 2.73412117 6.22879147 16.28898461
## Maine 7.37695910 0.72014100 15.47795616 4.42225495 0.41694885
## Maryland 13.06726342 11.56991907 1.80364809 6.46729543 16.51808558
## Massachusetts 1.76270117 4.92885269 4.03245856 2.76081309 5.52733614
## Michigan 11.64411364 14.26973368 1.94856185 6.82174551 18.70444536
## Minnesota 2.15321861 1.02514329 9.95957129 1.73840680 0.58436614
## Mississippi 20.04999676 12.96212148 9.52924636 9.52282094 17.30832209
## Missouri 4.76657180 6.09950785 1.83683080 1.48935924 8.64274489
## Montana 5.05746152 0.68673312 8.79658837 1.00669736 1.53848336
## Nebraska 2.76512238 0.56475433 7.81884414 0.73452252 0.96468138
## Nevada 16.22637449 22.37311541 5.70815885 12.44581973 27.27692155
## New Hampshire 5.34164971 0.85554409 14.81528146 3.71669649 0.04237581
## New Jersey 2.26517546 7.52144902 2.12074421 3.11110766 8.48147900
## New Mexico 12.60682268 12.87623881 1.79379836 6.71327724 17.75054399
## New York 8.44239678 12.89550998 0.12265318 6.06564329 16.33096303
## North Carolina 22.40177844 12.90935568 9.07474138 11.18069645 18.46762384
## North Dakota 10.22394613 2.00068487 21.28864087 7.06918142 1.10973048
## Ohio 1.32119223 3.86017452 3.28514929 0.48669039 4.67002547
## Oklahoma 2.75086636 2.30071586 3.40028454 0.28124557 3.76028167
## Oregon 4.01275463 3.90348789 4.30290039 1.38787597 6.08228793
## Pennsylvania 1.46876356 2.30185532 5.35190622 0.70776879 2.46769371
## Rhode Island 4.23988480 6.04801132 6.27891398 5.44550641 6.47890146
## South Carolina 18.08904131 11.93699647 6.84538136 8.10531922 16.82256808
## South Dakota 7.86515909 0.65129587 14.44357863 3.38992001 0.97746951
## Tennessee 9.45401067 8.54649832 3.79406253 3.27621430 11.68021486
## Texas 6.70897865 11.00393558 0.67919876 4.01431766 13.66222215
## Utah 1.14698097 4.10818703 5.18547204 1.96551040 4.70112123
## Vermont 13.84461097 3.16749661 23.64332485 8.21853263 2.99235525
## Virginia 4.19399195 2.88975830 3.46889129 0.37543145 4.71106314
## Washington 2.38792134 3.55772058 4.24894202 1.30091037 5.06377441
## West Virginia 10.77931961 2.07315085 16.93164668 5.05285785 2.32772694
## Wisconsin 2.77787893 1.46540730 12.10388410 2.82445977 0.39917991
## Wyoming 4.78883792 1.36606915 5.12731438 0.79188339 2.95657109
## Kansas Kentucky Louisiana Maine Maryland
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky 1.69525087
## Louisiana 7.44423549 5.86703556
## Maine 3.20902545 3.97039706 16.72967417
## Maryland 7.50811673 7.96903502 1.62285603 17.02311911
## Massachusetts 2.05733156 6.90872372 9.93797170 7.24701609 8.84657503
## Michigan 8.42213816 9.71163371 2.78155634 20.55118995 1.16661334
## Minnesota 0.94982027 3.73789651 13.62050882 1.68489790 13.28524413
## Mississippi 10.68226853 5.71156636 2.64676430 16.01167509 5.28643104
## Missouri 2.30818648 3.87191576 3.37169373 10.27584240 2.46670731
## Montana 0.84097447 0.72653492 8.66993669 1.76124712 9.15029570
## Nebraska 0.27868813 2.02192165 10.05291547 1.74739492 9.80257562
## Nevada 14.73924785 17.34246547 8.07166192 30.41868695 5.08562807
## New Hampshire 2.58697994 4.03751069 16.94814276 0.24959724 17.35867602
## New Jersey 2.91420212 7.24407975 7.19654672 10.58360912 6.89769103
## New Mexico 8.04083877 9.00439974 2.22357482 18.88818342 0.28664166
## New York 6.81002042 9.74274230 3.06078390 18.14411008 2.06271914
## North Carolina 11.82509412 8.29329403 3.94761968 16.50931251 4.21988369
## North Dakota 5.74599510 5.99395875 22.06918056 0.53371919 22.48943802
## Ohio 0.61105486 3.14236613 6.24848456 6.47995306 6.28088518
## Oklahoma 0.27026773 2.13846254 5.53922852 4.80917223 5.05932453
## Oregon 1.80281363 4.57475500 7.55732668 7.73583684 5.04735958
## Pennsylvania 0.29777100 2.54214242 8.08881680 3.68546728 8.75304098
## Rhode Island 4.03488407 9.27678579 12.70783246 7.46987885 11.81925689
## South Carolina 9.36931258 5.84014168 1.72972674 16.01246261 2.61326028
## South Dakota 2.78926951 2.28462927 14.03068398 0.61042821 14.43384182
## Tennessee 4.63672693 3.05898057 1.27656874 12.54609633 2.31113906
## Texas 5.00787825 6.39980673 1.77563217 15.51280350 2.38142544
## Utah 1.62603388 6.48300467 11.18299783 6.87388079 9.20394303
## Vermont 7.45201413 5.70652130 21.89859376 2.03167395 22.49659518
## Virginia 0.69755060 1.19216350 3.82362003 5.51059209 4.04992277
## Washington 1.34075972 5.12127859 8.82424005 6.91298000 6.46934722
## West Virginia 4.51336172 2.32144809 14.39991155 1.39667951 16.20188227
## Wisconsin 1.75375638 4.38911390 15.64929007 1.31924283 16.07327247
## Wyoming 0.57588794 1.14370352 5.68206261 3.12054491 5.77983837
## Massachusetts Michigan Minnesota Mississippi Missouri
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky
## Louisiana
## Maine
## Maryland
## Massachusetts
## Michigan 9.34947755
## Minnesota 2.75136684 14.43627683
## Mississippi 16.98861527 8.83446266 16.86547798
## Missouri 3.92457148 1.97932272 5.80270038 8.23285169
## Montana 5.25282682 11.12149651 1.60342316 9.00915525 4.12644338
## Nebraska 2.84387944 11.20842641 0.37007934 12.43942222 3.86193175
## Nevada 14.86568907 1.58997401 21.52135471 16.86317230 5.51733243
## New Hampshire 6.03858077 19.93280673 0.86104433 17.55269491 9.53927066
## New Jersey 0.63642765 6.59382282 4.95247236 15.12768401 2.91711193
## New Mexico 9.16557542 0.33437010 13.97090623 7.05292839 2.12548917
## New York 5.05325081 1.66344295 11.82781864 10.66402702 2.33624013
## North Carolina 16.62470243 9.13975089 17.82496458 1.39875350 9.13541486
## North Dakota 11.18695298 26.18567330 3.26370639 20.02837994 14.29692398
## Ohio 1.33817699 5.98284529 2.31535568 11.66153346 1.28310556
## Oklahoma 1.79110916 5.92277037 2.01595534 9.28185692 1.19413618
## Oregon 3.50036112 4.67695720 3.71336738 12.27365305 0.99484090
## Pennsylvania 1.28547593 9.64011931 1.02143624 12.23023026 3.16611074
## Rhode Island 0.89131353 13.92819815 4.12520152 19.25015710 7.54875763
## South Carolina 14.67688662 5.39789163 15.59035972 0.61868820 5.68631756
## South Dakota 8.36663493 17.42622012 2.24709607 12.49989199 8.33040932
## Tennessee 8.80833741 2.55047150 9.62441307 3.33777169 1.54104270
## Texas 5.10487854 1.66116548 9.88364417 8.08363073 1.35819703
## Utah 0.81284812 8.66797295 2.00991494 18.12304796 3.05512270
## Vermont 15.42731858 26.26642254 5.76956751 17.67921601 15.05703387
## Virginia 3.42390423 5.03551681 3.21564976 6.44299359 0.95791432
## Washington 1.81521558 6.10841843 2.54575379 14.54690406 1.56318816
## West Virginia 11.41274347 19.95261145 4.32295006 11.07633557 10.58724291
## Wisconsin 3.56556516 17.66885220 0.24411820 18.47965902 7.93635363
## Wyoming 3.31297531 8.02281441 2.20402750 7.18951936 2.58368988
## Montana Nebraska Nevada New Hampshire New Jersey
## 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 0.54611152
## Nevada 18.69966728 18.17224511
## New Hampshire 1.77675677 1.27706268 29.02130660
## New Jersey 6.71454089 4.51408534 11.19853602 9.16224324
## New Mexico 10.18622848 10.55865777 2.97039667 18.80159747 6.86863818
## New York 10.66849454 9.56376651 4.69768691 17.29429939 2.67150641
## North Carolina 10.37436884 13.32263556 17.45020020 18.62536291 15.53843682
## North Dakota 3.34566441 3.62473636 36.62603176 0.85227873 15.33991605
## Ohio 2.70153151 1.60136636 10.84431791 5.33401871 1.23206075
## Oklahoma 1.49458332 0.93601923 11.63403150 4.28369861 2.16418915
## Oregon 3.25608376 2.47367139 8.16889579 6.95756193 3.89622373
## Pennsylvania 1.75468314 0.71962275 16.31569768 2.82980876 2.02096318
## Rhode Island 7.22995543 4.53859248 21.33084709 6.66321240 2.15161305
## South Carolina 8.42410114 11.23404454 11.85266577 17.30303273 12.83554289
## South Dakota 0.78449080 1.58543833 26.43684464 0.97507942 11.10103940
## Tennessee 5.05981058 6.51619229 7.11089831 12.45979177 6.93780191
## Texas 8.00832900 7.60036039 5.18276782 14.57579392 2.63300107
## Utah 4.39169383 2.12372682 12.86583362 5.43117088 1.72708040
## Vermont 3.70999623 5.26807477 36.52733134 2.79428918 19.36476679
## Virginia 1.33556897 1.55557312 10.89122085 5.23406772 3.33266975
## Washington 3.40132841 1.92099188 9.96715739 5.86365595 2.48363073
## West Virginia 1.62771492 3.28255887 30.20952623 2.14590987 13.98918631
## Wisconsin 2.22497950 0.94476001 25.75738752 0.51203017 6.08668685
## Wyoming 0.66423665 0.85899577 15.36852949 3.22229569 4.15023576
## New Mexico New York North Carolina North Dakota Ohio
## 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 1.77531525
## North Carolina 6.42538035 10.34522795
## North Dakota 24.45353876 24.32984439 21.01011081
## Ohio 6.23046747 4.17589027 13.10852182 9.88994245
## Oklahoma 5.48789273 4.56553323 9.83866030 7.97875506 0.42041000
## Oregon 4.64537433 5.16549156 12.31672445 10.79915712 1.53948704
## Pennsylvania 9.37579177 6.73370021 13.54531184 6.53065040 0.60548603
## Rhode Island 12.98374651 7.66323173 17.79640789 11.58878201 3.86505637
## South Carolina 3.84016655 7.70375205 1.09753128 20.34386320 9.79056869
## South Dakota 15.97561960 16.91240404 13.65700621 1.06604462 5.95079431
## Tennessee 2.41128232 4.34636244 5.46374409 16.50240219 4.06740325
## Texas 2.07885671 0.71532645 9.52181377 20.93009633 2.79274563
## Utah 8.90652167 6.16379144 18.21652638 10.07314108 1.03108243
## Vermont 24.42022638 26.73382392 19.25457345 0.96527811 12.12840457
## Virginia 4.55462257 4.59639579 7.57214052 8.66917419 0.95538670
## Washington 6.14844421 5.17469914 14.48235119 10.06533325 0.94575873
## West Virginia 18.21695490 19.60683686 12.94420646 1.61717215 8.20843742
## Wisconsin 17.07983618 14.20315445 19.73976543 2.62969665 3.47815074
## Wyoming 6.90991748 6.70314952 7.56312758 5.84225475 1.71255957
## Oklahoma Oregon Pennsylvania Rhode Island South 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
## New Mexico
## New York
## North Carolina
## North Dakota
## Ohio
## Oklahoma
## Oregon 1.15220513
## Pennsylvania 0.66916008 2.99073183
## Rhode Island 3.89932107 7.08697374 2.67952517
## South Carolina 7.54652030 9.08085251 11.17540941 17.52370125
## South Dakota 4.13735377 6.24443631 3.91672364 9.77357160 12.40165106
## Tennessee 3.42260964 4.12364431 5.92587190 12.77623630 2.06644070
## Texas 3.35353317 4.43228795 5.04483272 8.27022360 6.01832571
## Utah 1.53089038 1.64484513 1.56977787 3.08558905 15.14168381
## Vermont 9.61639102 11.73938689 9.16307553 16.89552415 18.20641622
## Virginia 0.31880185 1.60387778 1.38514914 5.91955374 5.12412866
## Washington 0.91901465 0.35228302 1.95813100 4.72780874 11.42596446
## West Virginia 6.06722404 9.21113720 5.66405621 12.53220774 12.00738896
## Wisconsin 3.21012760 5.80265478 1.48953685 4.31788699 17.80078206
## Wyoming 0.54264812 2.56416650 1.14160775 4.72054126 6.27956291
## South Dakota Tennessee Texas Utah Vermont
## 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 9.35744330
## Texas 13.76487084 2.16467664
## Utah 7.19493825 8.22434163 5.77913639
## Vermont 1.17865202 15.48951472 22.50976330 13.35613043
## Virginia 4.12776320 1.82641456 2.86341401 3.10184851 9.38707664
## Washington 6.29198248 5.66896306 4.68087805 0.48172861 12.11340609
## West Virginia 0.50535205 10.05362413 15.67097415 10.67991506 1.07755896
## Wisconsin 2.38312536 11.73554965 11.92978072 3.26968915 5.53126287
## Wyoming 2.44759295 3.72438609 5.09165889 3.44178057 6.91655040
## 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
## Virginia
## Washington 1.90696640
## West Virginia 5.45372431 9.51509813
## Wisconsin 4.52263896 4.25919728 4.12451010
## Wyoming 0.49537795 2.53750448 3.54252609 3.04375685b## Alabama Alaska Arizona Arkansas California
## Alaska 0.7138307819
## Arizona 1.4465947843 0.8307245898
## Arkansas 0.0877416809 0.3672785641 1.1766554172
## California 1.8659223310 0.8137128067 0.2949017541 1.5863126412
## Colorado 1.6872310193 0.5155556175 0.5983808782 1.3709254337 0.1146234010
## Connecticut 1.7135870980 1.8617870018 0.7759582405 1.8986422868 0.6631595707
## Delaware 1.1428182422 1.4788738310 0.3411540927 1.1920258659 0.8973252909
## Florida 0.1049203486 0.7861031722 1.0409926090 0.1421425885 1.7009808084
## Georgia 0.1162516972 0.7367030469 1.7839695560 0.2511757376 1.8595181408
## Hawaii 1.8059006680 1.5764752423 1.1458813737 1.9369776851 0.5651593270
## Idaho 1.4792354141 0.7916559296 0.0025732601 1.1919825459 0.2520373794
## Illinois 1.3090956230 1.8653950071 0.6962514485 1.5310645251 0.9943388791
## Indiana 1.4749888379 1.1435786713 1.5288959172 1.5522560010 0.7788542333
## Iowa 1.8953868930 1.6097240352 0.9237936588 1.9927501530 0.4446590775
## Kansas 1.7692452854 1.6312115837 1.1868843924 1.9304960880 0.6286302776
## Kentucky 0.2262067640 0.8211189668 1.8896787427 0.3945142447 1.8241158706
## Louisiana 0.0416804313 0.9708133042 1.6141501191 0.2417304309 1.9726883264
## Maine 1.2447409234 1.7558367789 0.5636322340 1.4147766173 0.9736656266
## Maryland 0.3068186638 0.4639642310 0.6726108873 0.1481740524 1.3073045972
## Massachusetts 1.7894923852 1.7874177991 0.6759197083 1.9234913599 0.5431469651
## Michigan 0.7852281487 0.0160233723 0.9351396709 0.4522302697 0.7845906291
## Minnesota 1.9380385065 1.5554053936 0.8202405883 1.9948508668 0.3603658226
## Mississippi 0.0001410904 0.6988312003 1.4366445350 0.0809945041 1.8574210543
## Missouri 1.4280619231 0.4597251487 1.0825496071 1.1987780947 0.4392700914
## Montana 0.3613201986 0.4043314953 1.6866753522 0.3341386073 1.4929667476
## Nebraska 1.9552044704 1.4469332669 0.8259917570 1.9724706420 0.3045480232
## Nevada 1.3546910596 0.2635366264 0.8480253841 1.0278904693 0.3667780030
## New Hampshire 1.8052455037 1.7834106100 0.9335432054 1.9763608584 0.5930225147
## New Jersey 1.7034480814 1.8819483401 0.9259932394 1.9203821726 0.7177102454
## New Mexico 0.4866250619 0.1544579029 0.6233621173 0.1892735525 1.0182846624
## New York 1.4405383983 1.9111958371 0.7494785897 1.6714293586 0.9119916203
## North Carolina 0.1005419555 0.6815996338 1.0190868258 0.0978489483 1.6583662185
## North Dakota 1.8325523371 0.9297233018 0.1500384685 1.5752656513 0.0376465024
## Ohio 1.7629487564 1.6040313401 1.2086276023 1.9187361114 0.6289392120
## Oklahoma 1.9163174185 1.6423424756 0.7596105442 1.9969853196 0.3978409346
## Oregon 1.6997566344 0.5157436131 0.4662059483 1.3612944186 0.0704774712
## Pennsylvania 1.5772254713 1.8951088612 1.2252417444 1.8607800842 0.9076276018
## Rhode Island 1.5485337745 1.8603206882 0.6465916089 1.7324209040 0.7726884642
## South Carolina 0.0291288261 0.5217321656 1.2706656015 0.0177942668 1.7211633716
## South Dakota 0.2970145365 0.1388506123 1.2490997809 0.1148539078 1.3342480484
## Tennessee 0.2041030039 0.4628624009 1.6851841442 0.2161213362 1.6514791316
## Texas 0.9358083387 1.6985755420 1.8148596616 1.3185998185 1.5345413026
## Utah 1.9936607906 1.3916603633 0.5992137279 1.9512088364 0.1923868967
## Vermont 0.4044726325 0.0833334212 1.1898013199 0.1805657123 1.2046037022
## Virginia 0.3445471205 0.8152198710 1.9274904038 0.5026132238 1.7289903339
## Washington 1.9568457805 0.9983021047 0.4482645444 1.7558264095 0.0322727276
## West Virginia 0.0384036580 0.6152466715 1.6034021040 0.1112667168 1.8337534041
## Wisconsin 1.7930675184 1.7768919032 0.9950200526 1.9729672358 0.6165352255
## Wyoming 0.3432852855 1.3277086920 1.0167123371 0.5400904982 1.7004642321
## Colorado Connecticut Delaware Florida Georgia
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut 1.0185123544
## Delaware 1.3582485780 0.4608111033
## Florida 1.7129152223 1.5460029888 0.7181523250
## Georgia 1.5295690153 1.7039265274 1.5418713236 0.4170422475
## Hawaii 0.6324566539 0.2432644035 1.1318870533 1.9136686462 1.4965738366
## Idaho 0.5341813172 0.7928419016 0.3939093803 1.0897845135 1.7939763287
## Illinois 1.4383840525 0.1530107077 0.1489267035 1.0203976420 1.5144605369
## Indiana 0.5474764400 0.7794305428 1.7009930816 1.8152555713 1.0081816430
## Iowa 0.6095631090 0.1429784233 0.9223844015 1.8958223096 1.6786397073
## Kansas 0.7054066822 0.2232956426 1.1096940357 1.8797225866 1.4629520300
## Kentucky 1.4687209001 1.6106288136 1.6449136460 0.5858134248 0.0210269564
## Louisiana 1.8213148508 1.5262510539 1.1317428594 0.1874542948 0.0962874713
## Maine 1.4385240677 0.2420976543 0.0636718795 0.8972729389 1.5300602864
## Maryland 1.3200251263 1.6479985362 0.7081470504 0.1161020758 0.6777247923
## Massachusetts 0.9013147940 0.0087811793 0.4591556130 1.5998373785 1.7894552886
## Michigan 0.4386452325 1.8370934575 1.6148352274 0.9230258769 0.7229795857
## Minnesota 0.5421367089 0.1496278955 0.8821567640 1.9037641259 1.7506853022
## Mississippi 1.6768722831 1.7234165763 1.1447218887 0.1030843838 0.1190046803
## Missouri 0.1270352066 1.2511104277 1.7656621709 1.6717365956 1.0986787646
## Montana 1.0371431493 1.8412147980 1.8478283803 0.7301993195 0.1326503438
## Nebraska 0.4372841195 0.2269913177 0.9862057604 1.9508364344 1.7366422587
## Nevada 0.0850658323 1.3936267318 1.6394405167 1.5027837765 1.1492466894
## New Hampshire 0.8364591781 0.0484850390 0.7406686936 1.7557057927 1.6542207500
## New Jersey 1.0179595210 0.0138671533 0.5956434120 1.6088477225 1.6182796640
## New Mexico 0.9022934338 1.8030190487 1.0093153099 0.3718183417 0.7501278679
## New York 1.3346274313 0.0716783704 0.2405499199 1.1954467959 1.5698015171
## North Carolina 1.6376229111 1.6246802788 0.7780225601 0.0058800900 0.4066814869
## North Dakota 0.2664591169 0.5634348110 0.6325884541 1.5593899587 1.9431513897
## Ohio 0.6860637020 0.2505176081 1.1510907482 1.8896044569 1.4419702702
## Oklahoma 0.6440972507 0.0815588033 0.7357293514 1.8269177319 1.7885487360
## Oregon 0.0112610188 0.9909631670 1.2268326777 1.6579431786 1.6105452936
## Pennsylvania 1.1007741760 0.1066979873 0.8275177418 1.6135748630 1.3807940318
## Rhode Island 1.2047706713 0.0484596718 0.2346510620 1.2809684478 1.6800323905
## South Carolina 1.5360150109 1.8199134790 1.1317094997 0.0883713273 0.1943872899
## South Dakota 0.9669701935 1.9992774379 1.5707904560 0.4797572639 0.2883765233
## Tennessee 1.2407565041 1.8616146897 1.7108604023 0.5290963708 0.0535222009
## Texas 1.4771065310 0.6252472586 1.2468021394 1.2025497890 0.6424671557
## Utah 0.3952580801 0.2154653086 0.8155301702 1.8888326485 1.8747589639
## Vermont 0.8261595348 1.9871700490 1.6139688377 0.5886898330 0.3731091961
## Virginia 1.3394222476 1.5720254303 1.7552683347 0.7483007177 0.0674516539
## Washington 0.1443213664 0.5086289742 0.9579044238 1.8504888961 1.8621468964
## West Virginia 1.5421860929 1.7997828180 1.4086435375 0.2550494908 0.0322204217
## Wisconsin 0.8324040739 0.0689103714 0.8034949135 1.7750903478 1.6116405473
## Wyoming 1.9129645619 1.0249404824 0.3839982882 0.1540326117 0.6726365889
## Hawaii Idaho Illinois Indiana Iowa
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho 1.1194637192
## Illinois 0.6914531794 0.7465587060
## Indiana 0.2013613293 1.4793914393 1.2840194438
## Iowa 0.0282225069 0.9034570743 0.5480239849 0.3523302067
## Kansas 0.0029975967 1.1649380722 0.6496748393 0.2145303950 0.0348817924
## Kentucky 1.3110295308 1.8924747942 1.5171894830 0.8111626802 1.5188948361
## Louisiana 1.6202379913 1.6533727507 1.1521202197 1.3410960799 1.7319619872
## Maine 0.8513847169 0.6173772594 0.0189375246 1.4536026973 0.6799165640
## Maryland 1.9809006430 0.7020143344 1.1875458869 1.8853274782 1.9074566364
## Massachusetts 0.2378864446 0.6868917486 0.1901128578 0.7809217595 0.1224235643
## Michigan 1.4435858401 0.8870923265 1.9286084543 0.9653039349 1.5065738607
## Minnesota 0.0541245177 0.7979379705 0.5538445586 0.3986556827 0.0061350369
## Mississippi 1.8142598556 1.4687214214 1.3188066041 1.4803110344 1.9025429436
## Missouri 0.6317248457 1.0108902036 1.7176157354 0.2903752822 0.7268623875
## Montana 1.3710765709 1.6608269229 1.8636395079 0.7458418733 1.5718759316
## Nebraska 0.0549854976 0.7948162656 0.6741582764 0.3389140713 0.0195338128
## Nevada 0.8746092973 0.7793340325 1.7638460774 0.5474904019 0.9225815521
## New Hampshire 0.0788727931 0.9310950364 0.3507917748 0.4931429210 0.0321473524
## New Jersey 0.1655594681 0.9379933225 0.2183672402 0.6393231759 0.1021636020
## New Mexico 1.8892976931 0.6209766683 1.5249749381 1.6479179073 1.8415117997
## New York 0.5213352450 0.7908364720 0.0171515854 1.1069439752 0.3947126025
## North Carolina 1.9507527897 1.0621327220 1.1147797397 1.8081850272 1.9366596466
## North Dakota 0.6568052017 0.1242187891 0.7797410414 1.0037593052 0.4857325583
## Ohio 0.0024548531 1.1842842571 0.6891693557 0.1892748734 0.0422265760
## Oklahoma 0.0927185454 0.7476089769 0.4222362362 0.5135359785 0.0195685768
## Oregon 0.6938055995 0.4072638253 1.3630857867 0.6731154411 0.6369366915
## Pennsylvania 0.1218279259 1.2333890666 0.3500496379 0.4609426946 0.1287849470
## Rhode Island 0.4808735307 0.6814258072 0.0362817055 1.0858894086 0.3378788928
## South Carolina 1.9127627993 1.2963552424 1.4116417088 1.5656382261 1.9756124256
## South Dakota 1.7320021389 1.2303197685 1.8638402260 1.1835050738 1.8393697570
## Tennessee 1.5176048483 1.6748264034 1.7623384622 0.9299519728 1.7040434728
## Texas 0.4717715849 1.8289408291 0.7412902397 0.4434643356 0.6167798742
## Utah 0.1541697506 0.5720533433 0.6069461768 0.5184719237 0.0665213145
## Vermont 1.6686135300 1.1621915322 1.9134622503 1.1157721485 1.7714347203
## Virginia 1.1727496872 1.9195043682 1.5755631320 0.6467402868 1.3974859251
## Washington 0.3523820515 0.4041477984 0.9165183156 0.5847754624 0.2598098819
## West Virginia 1.6991330263 1.6192564786 1.5139502191 1.2381033254 1.8409717107
## Wisconsin 0.0579469122 0.9901532458 0.3908860240 0.4391707809 0.0272786223
## Wyoming 1.5829463662 1.0859923304 0.5040705614 1.7725351795 1.5212227682
## Kansas Kentucky Louisiana Maine Maryland
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky 1.2769869476
## Louisiana 1.5671655737 0.1666374285
## Maine 0.8143828375 1.5708956778 1.1347819452
## Maryland 1.9821235619 0.8765575743 0.5059016414 1.0106304327
## Massachusetts 0.2277022005 1.7002032521 1.6299578502 0.2679847940 1.6390192621
## Michigan 1.5005628044 0.7728802563 1.0195154196 1.8489898544 0.6150082648
## Minnesota 0.0673887259 1.6023967656 1.8001473208 0.6700882699 1.8653760357
## Mississippi 1.7787032838 0.2307929344 0.0465917420 1.2520280757 0.2976238695
## Missouri 0.6920571260 0.9944204833 1.5130565286 1.7707556534 1.4186673280
## Montana 1.3743202082 0.1221136254 0.4169708548 1.8817092914 0.8062347963
## Nebraska 0.0766833137 1.5832122171 1.8392595313 0.7896306497 1.8731089707
## Nevada 0.9457530653 1.1043225410 1.5214576814 1.7554477567 1.1456075438
## New Hampshire 0.0685318801 1.5114611931 1.6067550329 0.4788920208 1.8471321619
## New Jersey 0.1428893334 1.4977856935 1.4894347169 0.3349330489 1.7528642471
## New Mexico 1.9220152639 0.9211102866 0.7521270863 1.3514751901 0.1026385722
## New York 0.4832462132 1.5362466083 1.2593194566 0.0658178933 1.3635339873
## North Carolina 1.9239337577 0.5800226666 0.2093686710 0.9829108486 0.0822455043
## North Dakota 0.7111361480 1.9433442437 1.9375995064 0.7318710437 1.1802334153
## Ohio 0.0008935177 1.2528560274 1.5637871555 0.8560339620 1.9887584301
## Oklahoma 0.0990717118 1.6569136357 1.7697115639 0.5275210878 1.8093139913
## Oregon 0.7680844013 1.5730414633 1.8532631357 1.3402045079 1.2334575070
## Pennsylvania 0.0898935464 1.2269824824 1.3208890394 0.5058662614 1.8534931631
## Rhode Island 0.4526942781 1.6448300708 1.3889194427 0.0785015366 1.3871954150
## South Carolina 1.8919058548 0.3318660820 0.1379721449 1.3109064705 0.1798307688
## South Dakota 1.7523766779 0.3746721665 0.4799104973 1.7809199909 0.3813680915
## Tennessee 1.5082578283 0.0748635158 0.2546363442 1.7608737943 0.6565209615
## Texas 0.4157088181 0.4998564380 0.6630374235 0.9120786613 1.6343534163
## Utah 0.1829280349 1.7576986240 1.9223507859 0.6830908113 1.7344374675
## Vermont 1.6989726818 0.4493189605 0.6033963743 1.8320021142 0.4365675289
## Virginia 1.1453515261 0.0154710865 0.2749515567 1.6523181429 1.0215192876
## Washington 0.4072060469 1.7797189100 1.9958533418 0.9441436823 1.5355199270
## West Virginia 1.6706212924 0.1033420753 0.0759578361 1.4803915776 0.4500151060
## Wisconsin 0.0470896154 1.4592503680 1.5872433001 0.5285754991 1.8802894951
## Wyoming 1.5244615169 0.8017745127 0.3003023924 0.4299878625 0.4022482853
## Massachusetts Michigan Minnesota Mississippi
## Alaska
## Arizona
## Arkansas
## California
## Colorado
## Connecticut
## Delaware
## Florida
## Georgia
## Hawaii
## Idaho
## Illinois
## Indiana
## Iowa
## Kansas
## Kentucky
## Louisiana
## Maine
## Maryland
## Massachusetts
## Michigan 1.7636956971
## Minnesota 0.1157396102 1.4612041342
## Mississippi 1.7974872506 0.7711279050 1.9436498986
## Missouri 1.1735391052 0.3305334603 0.7042272760 1.4206237200
## Montana 1.8730991836 0.3433380776 1.6170350389 0.3584598904
## Nebraska 0.1824258831 1.3411654388 0.0089307360 1.9593131552
## Nevada 1.2928106546 0.1799187457 0.8715526902 1.3428922638
## New Hampshire 0.0509214002 1.7062389241 0.0480827529 1.8150046016
## New Jersey 0.0326997869 1.8310994222 0.1232585125 1.7146406808
## New Mexico 1.7499684754 0.2620238564 1.7788262138 0.4725455920
## New York 0.1050970275 1.9436978329 0.4052902860 1.4511438066
## North Carolina 1.6685156442 0.8164723416 1.9381605386 0.0970832642
## North Dakota 0.4491264156 0.9427670048 0.3940440918 1.8246843513
## Ohio 0.2540963869 1.4684033389 0.0755899327 1.7721853651
## Oklahoma 0.0540700850 1.5697834149 0.0121268718 1.9227417583
## Oregon 0.8662163263 0.4624564817 0.5575111879 1.6884461405
## Pennsylvania 0.1515599083 1.8091395300 0.1791232178 1.5908606017
## Rhode Island 0.0637188788 1.8902319776 0.3354040132 1.5575833130
## South Carolina 1.8677509035 0.6092607189 1.9937310600 0.0252834548
## South Dakota 1.9909615767 0.1567991577 1.8348274254 0.2873621766
## Tennessee 1.9110334834 0.4341594478 1.7540036170 0.2022109158
## Texas 0.7327297983 1.5982444923 0.7210151568 0.9515120290
## Utah 0.1516827453 1.3196166264 0.0326533416 1.9953372574
## Vermont 1.9624947204 0.0899487427 1.7575429666 0.3935102643
## Virginia 1.6536061860 0.7380994391 1.4823152089 0.3492030759
## Washington 0.4054086920 0.9355572949 0.1958827615 1.9519460641
## West Virginia 1.8717236676 0.6424320814 1.8927685307 0.0382369041
## Wisconsin 0.0747904671 1.6894267804 0.0486114956 1.8031850365
## Wyoming 1.1066952366 1.4637686881 1.5469507120 0.3486644824
## 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
## Montana 0.6045316904
## Nebraska 0.5803039260 1.5389484912
## Nevada 0.0508888152 0.6388466674 0.7422331627
## New Hampshire 0.9753270942 1.6762160610 0.0944258198 1.1740787998
## New Jersey 1.1764327210 1.7402593530 0.1938250919 1.3638772833
## New Mexico 0.9786622378 0.6464394712 1.7283779674 0.6941197972
## New York 1.5915268979 1.8682669904 0.5165855203 1.6816349620
## North Carolina 1.5924581459 0.6737159453 1.9718775908 1.4063365826
## North Dakota 0.6830710674 1.6803315621 0.3685595897 0.5721775917
## Ohio 0.6576215264 1.3382688581 0.0799277409 0.9141278109
## Oklahoma 0.8504004103 1.7213697970 0.0400813081 1.0038690131
## Oregon 0.2061823801 1.1389256129 0.4609496709 0.1269683518
## Pennsylvania 1.1087728289 1.5094403567 0.2418010391 1.3642063363
## Rhode Island 1.5058012553 1.9218780747 0.4367512096 1.5797984267
## South Carolina 1.3388614631 0.3642685539 1.9926190787 1.2000626101
## South Dakota 0.7214375288 0.1412606043 1.7548117796 0.5883807964
## Tennessee 0.8194671802 0.0260503959 1.6988835050 0.8305488553
## Texas 1.1609617032 0.8604839970 0.7712377545 1.4587503116
## Utah 0.6463927063 1.6766182529 0.0282609326 0.7422426424
## Vermont 0.6016542016 0.1584814585 1.6638475230 0.4649848933
## Virginia 0.8433111101 0.1011766981 1.4488244017 0.9852602218
## Washington 0.4159543628 1.5139937403 0.1479398762 0.4230425992
## West Virginia 1.1873957397 0.1775088901 1.8808474690 1.1585425398
## Wisconsin 0.9388344464 1.6237643420 0.0907331230 1.1531610665
## Wyoming 1.9606476936 1.1492687297 1.6534450382 1.8782873229
## New Hampshire New Jersey New Mexico New York
## 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 0.0203728912
## New Mexico 1.8957741979 1.8898013836
## New York 0.2222963805 0.1167466764 1.6576106697
## North Carolina 1.8198707129 1.6882031327 0.2961511702 1.2898437488
## North Dakota 0.5767658153 0.6537637867 0.9886387711 0.7317483654
## Ohio 0.0844858459 0.1653658184 1.9141075942 0.5195838485
## Oklahoma 0.0257607594 0.0723185219 1.7843815492 0.2912931360
## Oregon 0.8487673525 1.0152130104 0.8384753777 1.2771795023
## Pennsylvania 0.0555306843 0.0458419220 1.9848712613 0.2293760187
## Rhode Island 0.1891617632 0.1022025050 1.6356190421 0.0100380185
## South Carolina 1.9184134692 1.8343221684 0.2961797316 1.5562559201
## South Dakota 1.9394642587 1.9795876396 0.2170833923 1.9390582991
## Tennessee 1.7575234093 1.7770806331 0.5877749579 1.8030281330
## Texas 0.5300029920 0.4979806053 1.8114475771 0.6573595425
## Utah 0.1338905442 0.2212266249 1.5962259834 0.4740991019
## Vermont 1.9022004740 1.9674825759 0.2155586374 1.9727487501
## Virginia 1.4233295694 1.4410928294 1.0074305682 1.5633590655
## Washington 0.4011662888 0.5321616975 1.2625519956 0.7986747615
## West Virginia 1.8063579661 1.7517474666 0.5358830622 1.6088350316
## Wisconsin 0.0023869041 0.0295769366 1.9179607226 0.2551727018
## Wyoming 1.2901545938 1.0922252594 0.8161265668 0.6545829567
## North Carolina North Dakota Ohio Oklahoma
## 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 1.5334660335
## Ohio 1.9305660879 0.7224273197
## Oklahoma 1.8730569173 0.3894724849 0.1135825137
## Oregon 1.5840246033 0.1874986867 0.7535614934 0.6421908533
## Pennsylvania 1.6948438658 0.8972866596 0.1041933456 0.1528087139
## Rhode Island 1.3670234039 0.5992124162 0.4885377431 0.2280287820
## South Carolina 0.0629087954 1.6882794009 1.8840309592 1.9789921433
## South Dakota 0.4004425720 1.4433502477 1.7239773779 1.9077298547
## Tennessee 0.4849926609 1.7895126804 1.4781317108 1.8294151211
## Texas 1.2753845397 1.5920099336 0.4137677415 0.7259247856
## Utah 1.9051389528 0.2132190165 0.1918326612 0.0445269026
## Vermont 0.4999187795 1.3338138932 1.6682254904 1.8439010025
## Virginia 0.7371528881 1.8870575997 1.1168773891 1.5582034780
## Washington 1.8241715155 0.0918509747 0.4069737096 0.2395915914
## West Virginia 0.2356779973 1.8762239882 1.6534685677 1.9128679762
## Wisconsin 1.8380878909 0.6165079814 0.0606859470 0.0344655601
## Wyoming 0.2151566980 1.4818868846 1.5516658256 1.4171228531
## Oregon Pennsylvania Rhode Island South 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
## New Mexico
## New York
## North Carolina
## North Dakota
## Ohio
## Oklahoma
## Oregon
## Pennsylvania 1.1402152025
## Rhode Island 1.1406450586 0.2419360239
## South Carolina 1.5299656498 1.7541267394 1.6393268340
## South Dakota 0.9998229194 1.8783760662 1.9621421149 0.1941116530
## Tennessee 1.3261513949 1.5547510403 1.8786284310 0.2195857744
## Texas 1.5792856110 0.2728562511 0.7503357874 1.1713485991
## Utah 0.3846795223 0.3382295113 0.3766769616 1.9892920549
## Vermont 0.8603052484 1.8791156203 1.9772079214 0.2819179152
## Virginia 1.4605553633 1.1540094022 1.6597640598 0.4524906907
## Washington 0.1250356268 0.6790861261 0.6693868115 1.8639160485
## West Virginia 1.5911289550 1.5687910119 1.7113045304 0.0716453706
## Wisconsin 0.8550107222 0.0449914095 0.2253652497 1.9138657713
## Wyoming 1.8441095424 1.1245036904 0.7536875801 0.4132556859
## South Dakota Tennessee Texas Utah Vermont
## 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 0.1273627621
## Texas 1.3532551592 0.8523188788
## Utah 1.7739220612 1.8219725457 0.9734951576
## Vermont 0.0100223889 0.1736851072 1.4144547921 1.6770332905
## Virginia 0.4074246189 0.0924766016 0.4570537882 1.6435425977 0.4631778030
## Washington 1.4820379795 1.6902263278 1.3043144506 0.0818347191 1.3541598701
## West Virginia 0.2010383453 0.0699588182 0.8590835241 1.9658528281 0.2891370076
## Wisconsin 1.9166857823 1.7120146536 0.4867300251 0.1456776132 1.8791013765
## Wyoming 1.0026095155 0.9216589901 0.9040447147 1.5974824356 1.1320832930
## 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
## Virginia
## Washington 1.6597348538
## West Virginia 0.1816146555 1.8976998489
## Wisconsin 1.3640483557 0.4147626496 1.7773345725
## Wyoming 0.9669925767 1.7609179290 0.5618676063 1.3197538043