library(HDclassif)
## Loading required package: MASS
library(psych)
data("wine")

#Bartlett
cortest.bartlett(wine) # Nos indica que el data.frame es propicio para realizar anĂ¡lisis de factores (p value muy bajo)
## R was not square, finding R from data
## $chisq
## [1] 1709.671
## 
## $p.value
## [1] 9.80679e-297
## 
## $df
## [1] 91
#Kaiser-Meyer-Olkin factor adequacy 
#Pregunta 8 y 9
KMO(wine) #Nos indica que el data.frame es propicio para realizar anĂ¡lisis de factores (tiene que ser mayor a 0.5)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = wine)
## Overall MSA =  0.8
## MSA for each item = 
## class    V1    V2    V3    V4    V5    V6    V7    V8    V9   V10   V11   V12 
##  0.79  0.75  0.82  0.46  0.72  0.71  0.88  0.81  0.83  0.88  0.59  0.85  0.90 
##   V13 
##  0.81
library(HDclassif)
library(psych)

#Componentes principales
pca=prcomp(wine, scale=TRUE)
pca$sdev
##  [1] 2.3528595 1.5802140 1.2025283 0.9632849 0.9367510 0.8202307 0.7441767
##  [8] 0.5916369 0.5427172 0.5121583 0.4752351 0.4108488 0.3599502 0.2404419
pca$x
##                 PC1         PC2          PC3           PC4           PC5
##   [1,] -3.513024083 -1.44901095  0.164331927 -0.0132354868  0.7352712495
##   [2,] -2.521744523  0.32909093  2.021005638 -0.4159709585 -0.2824170691
##   [3,] -2.777194851 -1.03401911 -0.980471909  0.6623639624 -0.3864747681
##   [4,] -3.911554382 -2.76042344  0.174475992  0.5634982615 -0.3234473063
##   [5,] -1.403551861 -0.86533209 -2.020130938 -0.4396655603  0.2273080377
##   [6,] -3.278880486 -2.12418306  0.627223018 -0.6036690217 -0.4084741747
##   [7,] -2.742840318 -1.17585305  0.974588274 -0.3525938619 -1.0213955679
##   [8,] -2.386135518 -1.60674987 -0.145319533 -1.2420979161  0.2068543466
##   [9,] -2.787393428 -0.92058266  1.765943961 -0.1563853889 -0.8560500287
##  [10,] -2.997142086 -0.79404427  0.980974418  0.2695328266 -0.4705179079
##  [11,] -3.668340606 -1.30883136  0.420667517  0.0020641733 -0.2591095954
##  [12,] -2.103700480 -0.61125770  1.188218133 -1.0954534601 -0.5563297061
##  [13,] -2.431597118 -0.67661466  0.863079058 -0.6569263584 -1.0846618504
##  [14,] -3.663161193 -1.13691426  1.200382567 -0.2307148420 -1.8174847430
##  [15,] -4.429081842 -2.10438296  1.258899205  0.2034302321 -0.8421767145
##  [16,] -2.601585110 -1.66173047 -0.217020571 -1.5141875503 -0.0993603741
##  [17,] -2.468465215 -2.32434003 -0.829262820 -0.8947559752  0.2104437913
##  [18,] -2.219970165 -1.62899496 -0.792322900 -1.1470164581 -0.1301127546
##  [19,] -3.731742493 -2.52129300  0.483468544 -1.0517270184 -0.7203326906
##  [20,] -2.387676152 -1.06153499  0.164248436  0.5657676657  0.5355417469
##  [21,] -3.327183368 -0.79377365  0.362828827  0.2460633165  0.9659055564
##  [22,] -1.477236883 -0.23941013 -0.933597405  0.8972332665 -0.2092843901
##  [23,] -2.820113471  0.08661323  0.311089177 -0.2063638159 -0.4862010173
##  [24,] -2.002066457  0.51416609 -0.142851007 -0.5766810317 -0.3755931522
##  [25,] -2.108687681  0.31503190 -0.887220699 -0.3306825055 -0.6221761937
##  [26,] -1.393606311 -0.93557614 -3.809097443 -1.3437600270  0.3416893362
##  [27,] -2.127486643 -0.68516927  0.087212048 -0.5743975719 -1.1272041930
##  [28,] -1.625119559  0.09092753  1.383913414 -0.6725541885 -0.3736816112
##  [29,] -2.500553765 -0.69080117 -1.390249800 -0.9842005795 -0.6296900736
##  [30,] -2.552283493 -0.19492305  1.089605707  0.1314594809 -0.5732839737
##  [31,] -2.764645791 -1.24284687 -1.382356023 -0.4453631101 -0.4093778814
##  [32,] -2.926877371 -1.47412052  0.330919192 -0.3201106169  0.0574711790
##  [33,] -1.985647144 -0.05310222  0.167342712 -0.9315926959 -0.4862800756
##  [34,] -2.239392808 -1.63007087 -1.168088719 -2.3488460169  0.3504664856
##  [35,] -1.781959583 -0.69551841 -0.477611427 -1.0973471140  0.2233640082
##  [36,] -2.221372441 -0.17878459 -0.449455981  0.2015024704 -0.2722279181
##  [37,] -1.763055105 -0.65602175 -0.456232639 -1.3829910011 -0.0000909193
##  [38,] -1.518893365 -0.11190937  0.039998863 -1.0962609938 -0.2040317644
##  [39,] -1.867098082  0.76714174  1.422805688 -0.8429806630 -0.0654146334
##  [40,] -2.789246215 -1.80372079  0.341693195  1.3400651300  0.7390136544
##  [41,] -2.832944297 -0.78395014  0.117450556  0.5997674680  0.3234324933
##  [42,] -1.102462188 -0.16541830  0.782362035  0.9753745009 -0.9692610714
##  [43,] -3.297592710 -1.16068133  0.311321750  0.4527754947 -0.4487258743
##  [44,] -0.902253275 -0.32515521  0.202014386  1.2465061207 -0.3859798701
##  [45,] -2.390093523  0.06671774  0.653643575  0.8384543292  0.2477136628
##  [46,] -1.533486566 -1.77008445 -0.027590759  0.4444440465 -0.5367447936
##  [47,] -2.982802310 -1.19425370  0.537948354  1.1630797384 -0.9194897999
##  [48,] -3.050710625 -0.65198279  1.151509681  0.9943126920 -0.2012736508
##  [49,] -2.312248880 -1.24671983  0.057136838  0.1388179196 -0.4034442457
##  [50,] -2.951147454 -1.75365679  0.640847869 -0.1453572609 -0.3404551050
##  [51,] -3.402583023 -0.17641815  1.966734122  1.2019811189 -0.1051906911
##  [52,] -3.107612066 -0.74999309 -0.004984078 -0.3655687766 -0.6349122583
##  [53,] -3.689802644 -1.61852620  0.518406089  0.0391276724 -0.4914206657
##  [54,] -2.530410292 -1.87324374 -0.338228062 -1.3272359836 -0.2757676005
##  [55,] -2.437912181 -1.01784394  0.954877345 -0.0581426554  0.8348386884
##  [56,] -2.715155381 -1.33148772 -0.512742467  0.5072379620  0.8573653468
##  [57,] -2.976919241 -1.43957671  0.610072535  0.3314729598  0.3934957803
##  [58,] -2.481147879 -1.21207339 -0.260757766 -0.6786912183 -0.5660882366
##  [59,] -3.341859666 -1.73570661  0.283934186  0.3148888067  0.1126734748
##  [60,]  0.872463924  3.06906636  4.572747016 -0.9563997544  0.6275758550
##  [61,]  1.410681395  1.38604434  0.874005360 -3.0912998406 -0.2744946030
##  [62,]  1.709058108  0.83649642  1.602551167 -1.5174852564  0.0470183441
##  [63,] -0.012262270  1.25914400  1.779585217 -1.2505752226 -0.0611418366
##  [64,] -1.827944810  1.90800383  0.005293848  0.8946565543  0.0366697373
##  [65,]  0.572919811  1.90577501 -0.676769930 -2.1054805416  0.4774320067
##  [66,] -0.789244791  0.75659127 -0.572580565 -0.5541012381  0.2292950887
##  [67,] -2.014349238  1.86686522  2.023991089  1.4233673830 -0.7164993234
##  [68,] -0.142877938  2.41893339  1.066506203  0.0393480459 -0.4761304712
##  [69,]  0.749393715  0.22457552  0.706161729 -2.5840378504  0.0231580473
##  [70,] -1.735430290  1.38709532  1.232125446  0.0429697814  4.4364724920
##  [71,]  1.472147656  0.88973874  0.628170741 -0.9767367476  1.1131030281
##  [72,] -1.487780934  0.94526061 -1.948340937  0.0977860970 -0.6012808281
##  [73,]  0.692014768  1.06386229 -0.079639585 -0.1550748596 -0.2033526420
##  [74,] -2.292988910 -0.27358675 -3.367318406 -0.2951990697  2.3365157106
##  [75,] -1.629534655  1.27379658 -0.458893645  0.5571709203  1.0990547206
##  [76,]  0.826667392  2.44082053  1.559305570 -0.6612385100  0.8440438939
##  [77,] -0.299586657  2.14501373  2.441851283 -0.0049350335  0.2551069248
##  [78,]  1.357349276  1.38643530  0.227660494 -0.5636538362  0.9770814485
##  [79,] -1.092965398  0.76049755  1.179046816 -0.1108679886  2.9193995414
##  [80,] -0.318321791  1.02188781 -1.789772178  0.8905992971 -0.4187367854
##  [81,] -0.669369362  3.36104386  0.355699086 -0.2904468514  0.0829047192
##  [82,] -0.921511435  1.44104161  0.361149182  0.2892456616 -0.2669378978
##  [83,]  0.466177014  2.37706017 -1.331385398 -1.2403044957 -0.6944024953
##  [84,]  2.345799530  0.09985828 -0.470925908  0.3011720470 -1.4601432075
##  [85,] -0.716202927  1.46398422 -0.609624740  0.8858952722  0.8528328270
##  [86,] -0.696331774  2.01654573  0.253347696 -0.6526096061  0.5329081241
##  [87,]  0.762423688  2.23121016 -0.770097379 -1.0504000997 -0.0129179547
##  [88,]  0.526763293  2.36901453 -2.300558102 -1.1289412214 -0.2076102023
##  [89,]  1.034935645  1.80278255 -0.955565596 -0.5559240661 -0.6826831004
##  [90,]  0.519957513  2.65290035 -0.846122506 -0.3342281562 -1.2758223296
##  [91,]  1.249832965  2.11877956  0.048664596 -0.7154600389 -0.7806202456
##  [92,]  1.456600366  1.85446817 -0.777742334 -0.7494541293 -0.3732225821
##  [93,]  1.786207616  1.56474926  0.090606491 -0.8470575623 -1.0369338318
##  [94,] -0.651466573  2.30189958 -0.115233376  1.2876361057 -0.0542681006
##  [95,] -0.833793070  2.21131104 -0.143248503  0.5972760582  0.8929325984
##  [96,] -2.254248359 -0.18376798 -0.789480800  0.1107719397  4.0663648536
##  [97,]  0.553910314  0.36908618 -1.305556225 -0.4963563021  3.3841378308
##  [98,] -0.912422670  2.55243922  1.082317859  0.3189957414 -0.0981641925
##  [99,] -2.015298555  1.41622541  0.227409987  1.0617973221 -0.1452220471
## [100,] -1.261867189  2.15241081 -0.748018962  1.0980510341 -0.8215622229
## [101,] -0.699459195  2.36554300  1.562836762  0.1625605281  0.6465004756
## [102,]  0.529376478  2.28889834  1.494953851 -0.2444700318  0.3501542988
## [103,]  0.175661199  1.16151354 -1.000937507  0.6641368609  0.0448806635
## [104,]  0.640933972  2.67474439  0.762854448  0.4879971317  0.0251332267
## [105,] -0.336756194  2.09049963  0.470161381  0.3716630303 -0.3721102369
## [106,]  1.632606159  1.72150808 -0.942839902 -0.1129215983 -1.1715785634
## [107,]  0.357763434  2.16471222  0.480162069  0.2664561545 -0.5471626790
## [108,]  1.508862423  1.35952123 -0.285205159 -0.2225251768 -0.5973127479
## [109,] -0.030011598  2.29802529  0.461615311  1.0126145072  0.2047521677
## [110,] -1.405437791  1.44902406 -1.776215153  0.8067413279  0.3142213345
## [111,] -1.214817581  1.40423165 -0.141470234  3.9709574525  1.3886533397
## [112,]  0.287503606  1.92579398 -0.078534098  0.9184270265 -0.0503862244
## [113,]  1.192733062  0.76827541 -1.992431363 -1.9505827082 -0.4048226953
## [114,]  0.450347812  2.26461884 -1.058193872 -0.8227905444  0.0084270389
## [115,]  0.470511600  1.93592019 -1.319756633 -0.2720226700 -0.7938730928
## [116,] -0.422208091  3.85811034 -1.340820048 -0.9791292285 -0.4907136803
## [117,]  0.263632851  2.81397819  0.301622915  0.5286856804  0.2322549091
## [118,]  0.137071803  1.92302889 -0.688550173  0.0008419067  1.0905968925
## [119,]  2.244146166  1.26575475  1.899538915  0.5186917999 -0.9440158700
## [120,]  0.529252028  2.21815964  0.355418409  1.2772205306 -0.2719341234
## [121,] -0.639483447  1.40036246 -1.123135333  1.3102893198  0.1558250277
## [122,] -1.181035347 -0.26022334 -5.331659333  0.4232295913  0.3503147235
## [123,]  1.103828179  0.66761374 -3.000997182  1.0463971104 -0.2082659651
## [124,]  0.457357792  0.61814477 -0.482109421  3.3300635245 -1.0124024926
## [125,] -0.843727170  1.43506066 -1.478597872  3.8010786747 -0.4672855010
## [126,]  0.116208906  2.10396851 -0.433730192  0.9370399364 -0.5706199849
## [127,]  0.007066766  1.26195130 -0.686109852  1.2117517948 -0.5507040746
## [128,]  1.491102408  1.21225981 -3.350613092 -0.4045531092 -0.5827758165
## [129,]  0.477255414  1.93482045 -1.292892678  0.6692306399 -0.1918360272
## [130,]  1.659463471  1.15593073 -0.779240086  1.1203010811 -1.1076570698
## [131,]  1.773941467 -0.17183005  1.175553358 -0.8066887624  2.6710636154
## [132,]  2.734206054 -0.36981404  0.721605538  0.0090219131  1.3148085834
## [133,]  3.245142808 -0.25683895  0.167311462 -0.1349493514  1.1336306922
## [134,]  2.523248571 -0.36495915  0.451519908  0.4463207772  1.5845266541
## [135,]  2.705392785  0.46256928  1.098523718 -0.9732550533 -0.6214219049
## [136,]  3.339568060 -0.34459011  1.096809718 -0.8707710846 -0.4653633175
## [137,]  4.105585600 -0.14157372 -0.219600186 -0.2617053616 -0.5717873043
## [138,]  4.132471237 -0.64539266 -1.705885922  0.2423082453 -0.8599124042
## [139,]  3.356457341 -0.33945309  1.024956287 -0.3781338207 -1.0568608727
## [140,]  2.705046169 -0.28665576 -1.238069126 -0.8170712107 -0.1988655388
## [141,]  3.063004861 -0.27901886 -0.607095387 -1.0343148309 -0.3775463093
## [142,]  2.618758258 -0.36719705  0.969247208 -0.4623116185 -0.2649908488
## [143,]  3.251225399 -0.47973752 -0.943208733 -1.2210394810 -0.4088805064
## [144,]  2.696440656 -0.47611678  0.252649495  0.4100798642 -0.9009926235
## [145,]  2.583559833 -1.15424388  1.241122061  0.7074794712  1.4999146288
## [146,]  2.945701626 -0.55628229  0.853732986  0.3764587661  0.4772543183
## [147,]  4.447404469 -0.63369144  1.455803574  0.7936772470 -0.9177679323
## [148,]  3.818478101 -1.25877875  0.111535135  0.7844840132 -0.8996515477
## [149,]  3.124835228 -1.56024487  0.471405998  0.5711314663 -0.3545820071
## [150,]  3.225615029 -2.02959917  0.494455986  0.7943659978  1.2372108549
## [151,]  2.704934424 -2.34725826 -0.437160957  0.5260405066  2.1799516027
## [152,]  2.922695870 -2.03623954  0.310676967  0.8992601375  1.7741733763
## [153,]  2.244243506 -1.52365809 -1.359923625  0.3763904736  1.9010819150
## [154,]  3.088807178 -2.12748039  0.961988851  0.6150367169 -0.4799689521
## [155,]  3.068400079 -0.40365232  1.186977880 -0.4202871571  0.7767855032
## [156,]  3.845311076 -1.78704838  0.094754987  1.0014256800 -0.9929652397
## [157,]  3.199363404 -1.91343033  0.780424797  1.1448242335 -0.8605794321
## [158,]  3.648203029 -1.29891673 -1.596585827 -0.6226842135 -0.4871611758
## [159,]  1.548613374 -3.50919410 -1.158329264  1.0054843213 -0.6143268621
## [160,]  2.052494053 -2.40077381 -0.548025852  0.7489594810 -0.7405670611
## [161,]  3.428876889 -0.72848827  0.091211835  0.8394013061 -0.6362868496
## [162,]  2.577218124 -1.16803350  0.101493698 -1.2012463379  0.0178686047
## [163,]  3.135612031 -0.54749143 -0.801213829 -0.9623182516 -0.0609850333
## [164,]  2.917065291 -0.69070844  0.882697528 -0.1303817871  0.7208687878
## [165,]  3.252651435 -1.54423447  0.981033103 -0.0392067762 -0.2891452141
## [166,]  3.766961021 -0.86985778  0.465819479  0.3126326238 -0.8957322714
## [167,]  2.766834344 -2.58142276 -0.427200494 -0.0081609314  0.5630765673
## [168,]  3.233494876 -1.26428151  1.210301113  0.2395309073 -0.2911058026
## [169,]  2.556532083 -2.06907266 -0.761927237 -0.2060270681  0.5619280216
## [170,]  2.740997451 -2.57781035 -1.414277551  0.8070590823  0.8625966388
## [171,]  3.481375653  0.25873035  0.845357270 -0.1243268311  0.5474030675
## [172,]  3.918081965 -0.83503051  1.336577475 -0.2311936957 -0.3968441849
## [173,]  2.807376194 -2.18317766  0.916342551 -0.0809192597 -0.5584224011
## [174,]  3.617790848 -2.20040992  0.342700950  0.7495901505 -1.0012845827
## [175,]  2.934451479 -1.74733418 -0.206896115  0.3982573193  0.1537892027
## [176,]  3.018756881 -2.74828765  0.938156609  0.6060488662  1.1249629591
## [177,]  2.747471377 -2.28733179  0.548925224 -0.3904689551  1.0640813934
## [178,]  3.486500654 -2.75284255 -1.010301210  0.3486468140 -1.0023088794
##                 PC6          PC7          PC8          PC9         PC10
##   [1,] -0.299870285  0.572261286 -0.055480771 -0.457474579  1.062572157
##   [2,] -0.881821897 -0.029632889 -1.007529774  0.218190602 -0.020125260
##   [3,]  0.467522784  0.486931824  0.268200489  1.219329902 -0.105950252
##   [4,]  0.261877693 -0.397243535 -0.617102916 -0.114335795  0.107368253
##   [5,] -0.592091911  0.446615701 -0.433713850 -0.260812021  0.112118049
##   [6,]  0.257549435  0.377511025 -0.365793608  0.044785952 -0.217353076
##   [7,] -0.461318788 -0.024690576  0.349679028  0.591076796  0.776935402
##   [8,] -1.385078298 -0.100285359 -0.212688006 -0.060780781  0.622593999
##   [9,]  0.014200394  0.084395484  0.526326337 -0.531269228  0.327330764
##  [10,]  0.296824392 -0.861406406 -0.159662457 -0.171674223  0.241558013
##  [11,] -0.039608393  0.188595988  1.225008970  0.449282832 -0.377774162
##  [12,] -0.402839920 -0.492162831  0.952768897  0.563402415  0.148380877
##  [13,] -0.019228886 -0.283919623  0.439162759  0.830010491 -0.304196708
##  [14,]  1.007162809  1.453011942  0.439585290 -0.099983560 -0.314810258
##  [15,]  0.999317750  0.996343630  0.438403302  0.635605691 -0.669856197
##  [16,] -0.242466994 -0.247455297 -0.046570534  0.182063406 -0.894553695
##  [17,] -0.058218077  0.103759439  0.386446567  0.004404340  0.099593022
##  [18,]  0.416688871  0.119269231 -0.108343550 -0.385808700 -0.200898637
##  [19,]  0.628974362 -0.073847345  0.089121714  0.181315477 -0.946945281
##  [20,] -1.539171921 -0.192752218 -0.563881465 -0.111290263 -0.122468282
##  [21,] -0.209642356  0.259951993 -0.146381463 -1.194804578  0.666103870
##  [22,] -1.428156526  0.236704365  0.070224246  0.588239544 -0.146026814
##  [23,] -0.902334794 -0.232102279  0.087016816 -0.005507423  0.723118875
##  [24,] -0.718269083 -0.719862872 -0.239715487  0.749834806  0.269907782
##  [25,] -0.794752935 -0.697934878  0.323603338  0.060240223  0.666198811
##  [26,] -0.402163166  0.489990098 -0.138639518  0.062332499  0.566423687
##  [27,] -0.422939777 -0.506795823 -0.939145103  0.731707565  0.182778638
##  [28,] -0.602774581 -0.392270162  0.176860964  0.820291496  0.159014454
##  [29,] -0.431454399  0.031381896  0.124065944 -0.492584270  0.040062530
##  [30,] -0.277472234 -0.189244445  0.447606181  0.045794331  0.791702150
##  [31,]  0.713866790 -0.377166887  1.021001240  0.558666432 -0.335855112
##  [32,]  0.240108848 -0.518865768  0.491799407  0.766010043 -0.354709984
##  [33,] -0.057690245  0.964875254  0.492352381 -0.040736907  0.248663860
##  [34,] -0.284540201  0.927744034 -0.458168965 -0.734559984  0.197296382
##  [35,] -0.735179399 -0.269822758  0.187373550  0.478502945  0.163724167
##  [36,] -0.168560672 -0.650042123  0.315747552 -0.039767477  0.467137963
##  [37,] -0.605385994 -0.111631358 -0.964782601  0.224498853 -0.251669302
##  [38,] -0.391546036 -0.421949027 -0.020009462  0.823976189 -0.413793805
##  [39,] -0.422070033 -0.051264914  0.009292604  0.259222982 -0.267618584
##  [40,] -1.820501661  0.854134222 -0.708090247 -0.767926504  0.142661063
##  [41,]  0.557519813  0.635870786 -0.716917056 -0.682317590  0.567804171
##  [42,] -1.462007047 -0.046930500  0.290852577  0.350428554 -0.029398059
##  [43,] -0.648223001 -1.086440075 -0.915741480  0.148875618  0.067211121
##  [44,] -1.353471972  0.547714763 -0.593041703 -0.209475363  0.132207438
##  [45,]  0.179614653  0.099556554 -0.673239795 -0.136071784  0.563641065
##  [46,] -2.002738367  0.026135568 -0.223449007 -0.520419519  0.292636123
##  [47,] -0.986220329  0.622210040  0.311099018 -0.521350067 -0.078922870
##  [48,]  0.282434224 -0.433255121 -0.161210010 -0.292929087  0.393963317
##  [49,]  0.491698285  0.282145637  0.764686971  0.014928583  0.140983927
##  [50,]  0.804611992  0.059801284  0.245886837 -0.167586320 -0.174955285
##  [51,]  1.152980538  0.377938496  0.402199838  1.159493377 -0.752534627
##  [52,]  0.002237947 -0.398147944  1.041942571  0.991105135 -0.128895270
##  [53,]  0.346676846  0.128751812 -1.343395872 -0.632756760 -0.456314587
##  [54,] -0.147123569  0.419644572 -0.380338536  0.214333251 -0.226437007
##  [55,] -0.493709673 -0.402382255 -0.325472170 -0.122744339  0.570035104
##  [56,]  0.391682959 -0.267737225  0.468863523  0.298031375  0.252272895
##  [57,]  0.055297521 -0.017590387 -0.339556051 -0.814501457  0.572953596
##  [58,] -0.136972484 -0.249822377 -0.616864231  0.668092680 -0.662061472
##  [59,]  0.417084706 -0.802469065 -0.649233835  0.351605489 -0.283781567
##  [60,] -0.426045638 -0.116133214 -0.643777735 -0.480556957 -0.327747691
##  [61,]  0.152434953  1.025111713 -1.012077489 -0.479649414 -0.559187147
##  [62,]  0.617836491  0.335287324 -0.973965627 -0.914826561 -0.200843029
##  [63,] -0.346688437 -0.672415707  0.711002121 -1.245394687 -0.046255859
##  [64,]  1.047242469 -1.064026946 -0.191200705 -0.962492718 -1.286082765
##  [65,] -0.099139879  0.451292302  0.058149576 -0.555664285 -0.921260198
##  [66,]  1.122951649  0.250557967 -0.082908981  0.403961376 -0.803744786
##  [67,]  1.566971920 -0.294076237  0.247879885 -0.909421176 -0.239356872
##  [68,]  0.162764044 -1.376565218  0.241298141 -0.370764405  0.173796801
##  [69,] -0.154940168  0.303996953 -1.166920857 -1.073582349  0.226555951
##  [70,] -0.020812920  1.529314796  1.038548787 -0.238237571  0.480829796
##  [71,] -0.007906407  0.241511226  0.580060343  1.362172495  0.563274763
##  [72,]  0.167019457 -1.605779104  1.653139371 -1.291988690 -0.465249897
##  [73,] -0.400096324 -1.635415547  1.041424925 -0.666541885  0.692742514
##  [74,] -0.221683253 -0.524455802  1.235259839 -1.178266466 -0.015495355
##  [75,]  0.210301280 -1.380794933 -0.501109797  0.249796261 -0.512163143
##  [76,] -0.037841594  0.452135774 -0.064278270  0.079934270 -0.853522616
##  [77,]  0.659979492 -0.614030618  0.765678291 -0.763203373 -0.173822324
##  [78,] -1.119885983  0.906745294 -0.864196412  0.046133721  0.068471141
##  [79,]  1.124975428  2.183742024  0.115854270  0.323982050  0.563229856
##  [80,] -0.666877766  1.091382416  0.441837126 -0.972414783 -0.465118774
##  [81,]  0.441263880 -0.441492971  0.315798032 -0.819602858 -0.517733728
##  [82,]  0.092873799 -0.505754397  0.630263080  0.213160864 -0.235705459
##  [83,]  0.367243804 -0.667302164  0.936287817  0.510881363 -0.250567980
##  [84,] -0.007745477  1.204077032  0.446704255  0.003628677  0.387227503
##  [85,]  0.778548754 -0.711556746 -0.671630405  1.349153086  0.529074145
##  [86,] -0.019103207 -0.316900461  0.198166934 -0.541885368  0.164452986
##  [87,]  0.383781568  0.275456599  1.050911630  0.066088474 -0.380674145
##  [88,] -0.074222932 -0.531932890  0.862114993  0.389886741 -0.240088486
##  [89,]  0.069969911  0.104734033 -0.367706999  0.929707234  0.074021188
##  [90,]  0.269446742 -0.773912538  0.401670401  0.470067392  0.524591106
##  [91,]  0.458952715  0.805663875  0.066725425  0.693779124  0.112172586
##  [92,]  0.657109729  0.232103869  0.348562110  0.655799223  0.610101624
##  [93,]  0.852424202  0.640588107  0.452065413  0.441032036  0.851110778
##  [94,] -0.510850111  0.142241999  0.253232245 -0.250147883 -0.437058214
##  [95,] -0.332802174 -0.802314932 -0.816945619 -0.468894752 -1.296102741
##  [96,]  0.804762977  2.772275622  0.528726175 -0.055577697  0.495578068
##  [97,] -1.162363604 -0.322166694  0.026384920  1.064893447 -0.076546291
##  [98,]  0.539790016  0.007780287  0.027061409 -0.382463504 -0.711865891
##  [99,]  1.295585625 -0.827816132 -0.688090349 -0.525616367 -0.948048335
## [100,]  0.664255581  2.062594865  0.700720753 -0.462845962 -1.224916825
## [101,] -0.272607347  0.229776298  0.440103887 -0.286942278 -0.634176934
## [102,] -0.188111924 -0.404477048  0.747974521  0.270073269  0.694974056
## [103,] -0.694597119 -0.534942282 -0.955953573 -0.268342879  0.574269296
## [104,]  0.349604671  0.017960924 -0.460198881 -0.205381272  0.004814913
## [105,] -0.128247770 -0.491282837  0.401936874 -0.060042242  0.664299512
## [106,] -0.021463123  1.110390043 -0.456212863 -0.407054197  1.589832136
## [107,]  0.217931676 -0.213531952  0.231676566  0.502014428  0.578995987
## [108,]  0.490118164  0.013878010  0.581196831  0.424261266  1.063344598
## [109,]  0.953622220  0.337111953 -0.350922915 -0.313886097  0.968973936
## [110,]  0.833678846 -0.216250262 -0.660806174  1.188738667 -0.106671906
## [111,]  0.869876391  1.867223487 -0.092144183  0.556548663 -0.254149371
## [112,] -0.675978350 -0.890760418 -0.262327201 -0.607569727 -0.014582555
## [113,] -0.459360014  1.070483542 -0.820079232  0.484157400 -0.705740071
## [114,]  1.068671694 -0.409195560 -0.768158284  0.323004255 -0.539649835
## [115,]  0.139582202 -0.985294012 -0.955376154 -0.335970418  0.395022008
## [116,]  1.134455209  1.408743898  0.764301338 -0.228687345 -1.374550261
## [117,] -0.017594189 -0.533075504  0.082267433  0.363978399  0.783405519
## [118,] -0.107969633  0.014165692  0.350202500 -0.620542951  0.701332231
## [119,] -1.012182232  0.221346552 -0.673651627 -0.022500113  0.303550184
## [120,] -0.779585278  0.935880029  0.166660018  0.554142375  0.302178047
## [121,]  0.035005832 -0.177116743 -1.409976218  0.550246418 -0.065026486
## [122,]  0.867563096 -0.531938184 -1.753871961 -0.528495879 -0.176094268
## [123,] -1.386416372  0.537495188  0.255101783 -0.212147143  0.267127899
## [124,] -1.741196003  0.649253551  0.296058820 -0.508958482 -0.111050166
## [125,] -0.325140690  0.198072312 -0.128872301  0.744106290 -0.197302108
## [126,] -0.078218996 -0.532475389 -0.835107239 -0.405988737  0.355282140
## [127,]  0.971757715 -0.702172430 -1.022395294 -0.362895746  0.624395259
## [128,]  0.780342449  0.247529576  0.032374300  0.349237454  0.348050849
## [129,]  0.615942328 -0.319954619  0.240216948 -0.150546589  0.812259133
## [130,] -1.145360337  0.268484127 -0.288260927  0.699614475 -0.218797244
## [131,] -0.233296306 -0.822748941 -0.270825240  0.117696562 -0.111673138
## [132,] -0.769022312 -0.972457196  0.145402606  0.259088952 -0.520070917
## [133,] -0.135433308 -1.566956914  0.509433557  0.460080354  0.043463075
## [134,] -1.098983957 -1.081482886  0.321728269  0.177571812 -1.118543135
## [135,]  1.587356834  0.431605353 -0.856516337  0.279475653  0.163671354
## [136,]  0.871611928  0.774390337 -0.750111358  0.072210540  0.095646352
## [137,] -1.196250812  0.797349605 -0.194230793  0.981976224 -0.797400673
## [138,] -0.992752769  1.372691931  0.120990630 -0.121299166 -0.648765982
## [139,] -0.266348943  0.694251343  0.211352502 -0.570347789  0.146048547
## [140,] -0.238758684 -0.013262033 -0.239908574 -0.699259803 -0.147972278
## [141,] -0.578637031 -0.084018697 -0.406255917  0.140658407  0.488483743
## [142,] -0.688126304 -1.069068234  0.160626257  0.297424568  0.652937067
## [143,] -1.003947423 -0.383306845  0.395058462 -0.550807850  0.230617343
## [144,] -1.421013697  0.766178113  0.518021704 -0.785319300 -0.581294054
## [145,] -0.559885466  0.014992359 -0.311997654  0.878194826 -0.489331282
## [146,] -0.588365612  0.546828758  0.378555713  0.431583939  0.579176676
## [147,] -1.672581796 -0.200195932  0.773904817 -0.054542092  0.052310558
## [148,] -0.611576644 -0.228231175 -0.422021386  0.334420759 -0.285750708
## [149,]  0.572200837 -0.393357764 -0.137425098 -0.024729789  0.040293356
## [150,] -0.059912699 -0.327684836 -0.069577718 -0.104808630 -0.421599891
## [151,] -0.129099827 -1.209609951  0.433764201 -0.231316034 -0.156971573
## [152,]  0.762767169 -1.463279229 -0.350782349  0.218685543 -0.244777971
## [153,]  0.885728019 -1.417611318  0.050191863 -0.317062571 -0.091888033
## [154,]  1.678664535  1.180954925 -0.407803539  0.069876758  0.134034753
## [155,]  1.740914151  0.222921889 -0.483352271  0.252721846  0.876427229
## [156,]  0.031439163  1.436428765  0.198319025  0.141832818 -0.212170004
## [157,]  0.417062662  0.251330066  0.148947138 -0.344385868 -0.029132190
## [158,]  0.828456056  0.168790648 -0.150173681  0.481753622  0.176008617
## [159,]  3.463744672 -0.383205926  0.493062002 -0.740431949  0.627922147
## [160,]  3.080319213 -0.470653621 -0.181713746 -0.108836896  0.168212900
## [161,]  0.371598265 -0.028728410 -1.079109928 -0.027816576 -0.663704783
## [162,] -0.615301793  0.404570107  0.247608396 -0.749011318 -0.296705226
## [163,] -0.250060137  0.810385176 -0.198921228 -0.370047265  0.182906892
## [164,] -0.807706928  0.214306214 -0.249062536  0.289121877  0.040938532
## [165,]  0.604592347 -0.942596523  0.768419955 -0.248050153  0.176581424
## [166,] -0.448054067  0.465340370  1.102160861 -0.420916454  0.171364472
## [167,]  0.552434551  0.074718730  0.701278607 -0.287352068 -0.737215297
## [168,]  0.438950275 -0.606983692 -0.011848436  0.379678521 -0.670451615
## [169,]  0.689037383 -0.699519890  0.895002792  0.212978726  0.218715724
## [170,] -1.014221257 -1.005322879  0.336287067 -0.164991988 -0.706859139
## [171,] -0.495041075 -0.296548339 -0.612000878  0.572127062 -0.022182487
## [172,]  0.893632156 -0.919905217 -0.724722902  0.038781204  0.067470540
## [173,]  0.863023729 -0.786661504  0.292329710 -0.244013326  0.340934411
## [174,] -1.139939246  0.841082264  0.206044724 -0.125065905 -0.391514872
## [175,] -0.062289046  0.139553613  0.563996559  0.055185648 -0.235602201
## [176,]  0.005275476  0.730964144 -0.052396746 -0.027802925 -0.212150899
## [177,]  1.009714032  0.753298285 -0.425312224  0.048646933  0.478443539
## [178,]  0.376162259  0.015263586  0.324087919 -0.717958122  0.079682974
##                PC11         PC12         PC13          PC14
##   [1,] -0.419311078 -0.551372411 -0.302125915 -2.002924e-01
##   [2,] -0.129653891 -0.393860128 -0.146232803 -1.260468e-01
##   [3,] -0.278289088 -0.001892654  0.021218163  5.559469e-02
##   [4,]  0.771688951  0.230279641 -0.499866743 -1.984687e-02
##   [5,] -0.536418018  0.226048523  0.273337857  5.160422e-01
##   [6,]  0.406638322  0.375655765 -0.017393570 -2.388884e-01
##   [7,] -0.401144507 -0.159682213 -0.573752772 -1.571678e-01
##   [8,]  0.319654339 -0.389910627 -0.307340232 -1.162721e-01
##   [9,] -0.506734442  0.634450713  0.101395098 -7.208372e-02
##  [10,]  0.015045667 -0.548060428  0.021433151  1.047683e-01
##  [11,]  0.730295547  0.078689862 -0.034377295 -2.540316e-01
##  [12,]  0.047574990  0.162718688  0.125702870 -7.859019e-03
##  [13,]  0.057200416  0.087292083 -0.045667483 -4.573412e-03
##  [14,] -1.227597359  0.764258779 -0.081607879 -4.556787e-01
##  [15,] -0.309962009  0.131286792 -0.394273611 -3.591457e-01
##  [16,]  0.083663937 -0.492127392  0.052444968  1.335718e-01
##  [17,]  0.073015643  0.506466363  0.375842629 -3.878994e-02
##  [18,]  0.285640056  0.279678569  0.724870242  2.425497e-06
##  [19,]  0.899795909 -0.160189018  0.313333365 -4.932805e-01
##  [20,] -0.837910776 -0.284449852  0.126957345  9.719401e-02
##  [21,] -0.457918747 -0.470738666  0.040820927  9.170078e-02
##  [22,] -0.659972141 -0.677887989 -0.013051006  5.296748e-01
##  [23,] -0.059141553 -0.493242752 -0.304846085 -2.229935e-01
##  [24,] -0.012858421 -0.490548192 -0.321335240  2.417081e-01
##  [25,] -0.359108507 -0.319646123 -0.223217249  1.703698e-01
##  [26,] -0.431750853  0.112615461  0.139230799  3.619403e-01
##  [27,] -0.011872668  0.199844720 -0.168952586 -1.024942e-01
##  [28,]  0.871493026  0.377734736  0.100082464  2.019070e-01
##  [29,] -0.535327145 -0.052133061 -0.170344007  1.219043e-01
##  [30,] -0.097574341 -0.145303795 -0.434683405  2.525539e-01
##  [31,]  0.362800416  0.615221055  0.237118399  1.577463e-01
##  [32,]  1.065540864  0.003289926  0.301468243 -5.452623e-02
##  [33,] -0.220080286  0.208330577  0.288215349  2.020110e-02
##  [34,]  0.623281390 -0.107013907  0.072545643  2.574100e-02
##  [35,] -0.171299383  0.221919526  0.182702397  1.351032e-01
##  [36,]  0.199199423 -0.225959650  0.286488201  1.880307e-01
##  [37,] -1.100732106  0.148237214  0.042613416  2.120576e-01
##  [38,] -0.006331597  0.408361693  0.229178312  3.305682e-01
##  [39,]  0.270281671  0.189274912  0.459414350  9.112164e-02
##  [40,] -1.189357198 -0.171110587 -0.144559855  1.339277e-01
##  [41,] -0.282244193 -0.190271797  0.233366862  1.918090e-01
##  [42,]  0.814467408  0.087220201  0.641617258  1.756224e-01
##  [43,] -0.426057495  0.176358945 -0.252737574 -2.239559e-01
##  [44,] -0.085928789  0.065307529  0.590079867  4.745373e-01
##  [45,]  0.472678263 -0.049496470  0.272167229  2.622616e-01
##  [46,]  0.593112800 -0.042583331  0.174619061  1.756565e-01
##  [47,]  0.047420763  0.199562466 -0.179865338  2.124277e-02
##  [48,]  0.122841972  0.089854603  0.249221674  2.914183e-02
##  [49,] -0.113865530  0.327373033  0.365849328  2.690395e-01
##  [50,]  0.528660258 -0.725444392  0.643750457 -1.105953e-01
##  [51,] -0.381210855 -0.403046087  0.226595035  1.322432e-01
##  [52,] -0.535677231 -0.323372039 -0.208294720 -1.343351e-01
##  [53,]  0.284457857  0.086582358 -0.196510172 -7.133751e-02
##  [54,]  0.311878507 -0.003982141 -0.180983459  6.228677e-02
##  [55,]  0.177275244 -0.172555036  0.355557584  2.725616e-02
##  [56,]  0.328030058  0.175971344  0.078939025  5.076298e-01
##  [57,] -0.040280424  0.055246235 -0.024195628  2.467617e-01
##  [58,]  0.076562562  0.127011403  0.103432656 -2.505831e-02
##  [59,]  0.254164895  0.559169145  0.156378044 -5.582207e-02
##  [60,]  0.350305311  0.603278404 -0.206599427  5.056228e-01
##  [61,]  0.132177226  0.305758267  0.020830388  1.761041e-01
##  [62,]  0.116293816  0.105863349  0.749899516  3.904870e-01
##  [63,]  0.237305764  0.145212476  0.151569112 -1.452982e-01
##  [64,] -0.030018263  0.234195918 -0.236102848  1.325675e-01
##  [65,] -0.911150675 -0.281427947  0.199054287  1.158830e-01
##  [66,] -0.819279698  0.203763724  0.022064127 -2.289588e-01
##  [67,] -0.164709679 -0.180129323 -0.054108573 -3.779094e-01
##  [68,]  0.480054364 -1.096825023 -0.021278088 -4.375724e-02
##  [69,]  0.236190868  0.992214650 -0.327381959  6.819688e-02
##  [70,]  0.242606717 -0.728809158 -0.473888191  1.538005e-01
##  [71,]  0.241618888  0.458603326  0.427684364  4.179757e-02
##  [72,] -0.756048843  0.459445913 -0.368138728 -5.723547e-02
##  [73,]  0.095261942  0.183845273  0.356476811  3.109822e-02
##  [74,]  1.772533874  0.101315890 -0.399317651 -2.306761e-01
##  [75,]  1.077114936  0.446710474 -1.038428157  2.730546e-01
##  [76,] -0.205554469 -0.581635924  0.559317234  1.952610e-01
##  [77,] -0.406809164 -0.209575849  0.402879583  1.198674e-02
##  [78,]  0.061699007 -0.339973712  0.206429593  1.115953e-01
##  [79,] -0.367792564  0.182633641 -0.024246874 -1.886460e-01
##  [80,]  0.247070609 -0.011953181 -0.069752730 -6.539942e-02
##  [81,] -0.142499750 -0.481884016 -0.062903982  3.674748e-02
##  [82,] -0.128074378 -0.366161160 -0.114945228 -4.351062e-01
##  [83,]  0.127560537  0.038184161 -0.268338423  1.662357e-01
##  [84,]  0.024478939  0.213787961  0.844659732  1.690583e-01
##  [85,] -1.221059381  0.194746144 -0.558334380 -6.963697e-02
##  [86,] -0.591859496 -0.278389371 -0.424158370 -1.083328e-01
##  [87,] -0.041538759  0.100032604  0.349361065  1.566881e-01
##  [88,]  0.315997649 -0.791118721 -0.220476254  2.012243e-01
##  [89,]  0.333722517 -0.155749721 -0.054712430 -1.068537e-02
##  [90,]  0.641759217  0.062202450 -0.465277123  8.114360e-02
##  [91,] -0.662568071  0.180643104  0.141211259  3.219185e-02
##  [92,] -0.395682822 -0.441060093  0.144818263  2.666972e-01
##  [93,] -0.423495435  0.466207546  0.547647968 -1.724250e-02
##  [94,] -0.799089293 -0.262314160 -0.395862677  3.350125e-02
##  [95,] -0.202275478 -0.215710790 -0.439524441  3.985851e-01
##  [96,]  0.256542532  0.444304565 -0.355866473 -2.898951e-01
##  [97,] -0.672506479  0.213466367 -0.246594462  5.217980e-01
##  [98,] -0.410326780  0.067145619 -0.071397273 -1.339747e-01
##  [99,]  0.472993931  0.586894835  0.121222927 -4.529788e-01
## [100,] -0.643817539  0.082434301 -0.103521757 -2.431198e-01
## [101,]  0.952397591 -0.635434538  0.121534194 -2.221077e-01
## [102,] -0.015203004 -0.123583738  0.073240988 -5.586943e-02
## [103,] -0.004511193 -0.057417032 -0.337865213 -1.067782e-02
## [104,]  0.664312646  0.572003354  0.036576730  4.051316e-01
## [105,]  0.744810915 -0.521831614 -0.348668065 -2.053581e-01
## [106,]  0.044183639 -0.550362863  0.395095961 -2.728733e-01
## [107,] -0.258031047 -0.607801899  0.154653855 -2.980685e-01
## [108,] -0.245221885  0.236884290  0.666432356 -1.363482e-01
## [109,] -0.047971051  0.178652303 -0.012168260  8.601325e-02
## [110,] -0.568930079  0.214709604 -0.590549693 -3.752495e-01
## [111,]  0.735615066  0.623412010 -0.154137403  3.482463e-01
## [112,]  0.078660746  0.598382620  0.152477935  6.570078e-02
## [113,] -0.693680931 -0.706261547  0.247088968 -2.809547e-01
## [114,] -0.171999945  0.331719258  0.010882339  3.163300e-01
## [115,]  0.120499348 -0.021791075 -0.076245495 -4.318472e-02
## [116,]  0.258367532 -0.715929944 -0.097430826  1.623530e-01
## [117,]  0.496016154 -0.299920813 -0.226550067  7.692405e-02
## [118,]  0.006120640  0.015076562  0.317284786 -8.426638e-02
## [119,] -0.329134323  0.312377117  0.495320883  2.009219e-01
## [120,]  0.330767282  0.009152936 -0.199298377 -2.696511e-02
## [121,]  0.395898115 -0.150339289 -0.294362366 -2.394172e-01
## [122,]  0.133515816 -0.833373649  1.103369349 -1.132066e+00
## [123,] -0.026994082  0.005120869  0.205420551  5.730117e-02
## [124,]  0.189287442  0.364380598  0.322083196 -1.155165e-01
## [125,] -0.445389974 -0.036775275 -0.284518432 -8.953603e-02
## [126,]  0.393234211 -0.048844594  0.185347209 -2.304369e-01
## [127,] -0.015737509  0.574121421  0.557519936 -3.105152e-01
## [128,]  0.345844581  0.376844646  0.641545633  9.614070e-02
## [129,]  0.065074821  0.618061190  0.473370891 -1.030181e-01
## [130,]  0.416131234  0.262613021  0.204047808  1.432466e-01
## [131,] -0.535316955  1.017342492 -0.004143416 -5.768163e-01
## [132,] -0.561186334  0.397360179  0.310359004 -4.120753e-01
## [133,] -0.011876987  0.528773370  0.562615365 -2.920870e-01
## [134,]  0.031734286  0.694492749  0.188310957 -1.690039e-01
## [135,]  0.004553365  0.650194749 -0.678551873 -7.366263e-02
## [136,]  0.408949326 -0.171512710 -0.078553918 -2.142815e-01
## [137,]  0.193057550  0.571426289 -0.125759587 -1.806482e-01
## [138,]  0.426123667  0.071986575 -0.081820525  1.182596e-01
## [139,]  0.134417253  0.075983746 -0.313578833 -1.817526e-01
## [140,]  0.549011788  0.205129315 -0.849500737  1.019443e-01
## [141,] -0.379269652 -0.075808581 -0.803960373 -3.239036e-01
## [142,]  0.120758130 -0.260617991 -0.762385024 -4.431325e-01
## [143,] -0.335743473  0.231976084 -0.537088182 -2.253459e-01
## [144,] -0.078675173  0.268366949 -0.618158741 -2.223151e-01
## [145,]  0.498856957 -0.994842346 -0.089162844 -2.074232e-01
## [146,]  0.667585040  0.850996345 -0.308153976 -3.699405e-01
## [147,] -0.598613712  0.661897895  0.257795257 -1.194931e-01
## [148,]  0.222071461 -0.282816688 -0.149241323  5.824272e-02
## [149,]  0.178160518  0.156668455 -0.170975177  1.358834e-01
## [150,] -0.104942033 -0.332520457  0.877982107 -1.824441e-01
## [151,] -0.606316553  0.194454835  0.823806727 -2.312916e-01
## [152,] -0.437330170 -0.572723334  0.722739448  8.394095e-02
## [153,] -0.474682514  1.004743309 -0.004154291  2.747870e-01
## [154,] -0.120632383 -0.441409476  0.012539614  8.146901e-02
## [155,]  0.377347554  0.010717956  0.052854085 -3.828702e-02
## [156,]  0.571687574  0.006605533  0.065051116  7.556944e-02
## [157,] -0.665944154 -0.041839100 -0.093559981  1.227862e-01
## [158,]  1.326308401 -0.024421607 -0.198830040  1.073614e-01
## [159,] -0.278215538 -0.093309590 -0.585735387  4.790010e-01
## [160,] -0.364882734 -0.091226683 -0.588880011  4.926426e-01
## [161,]  0.449840196  0.115592440 -0.131176801  2.853592e-01
## [162,] -0.217844295  0.088372011 -0.658024359 -1.833743e-01
## [163,]  0.021446906 -0.327255509 -0.438853089 -1.887735e-01
## [164,] -0.196476193  0.158350184 -0.244613942 -3.790340e-01
## [165,] -0.080275816 -0.470908999  0.192106698  2.510633e-02
## [166,] -0.009415628 -0.117955601  0.088198638 -4.672457e-02
## [167,] -0.125549749 -0.788480062  0.131882983  1.760682e-01
## [168,]  0.060332382 -1.072554369  0.028098695  1.359398e-01
## [169,] -0.217910235 -0.156844681 -0.195987742 -3.888823e-02
## [170,] -0.169193338 -0.250893595 -0.263014837  2.081887e-01
## [171,] -0.187930939 -0.250201682 -0.138953326 -1.125676e-01
## [172,] -0.135547013 -0.795321881  0.226878455  2.174743e-01
## [173,] -0.598772128 -0.104632309 -0.306587295  7.278809e-03
## [174,]  0.136398554 -0.174315544 -0.198243688 -9.368622e-02
## [175,]  0.253570543  0.276738278 -0.184543121  2.420908e-02
## [176,]  0.501226372 -0.691386023  0.166565798  3.160658e-02
## [177,]  0.312903079 -0.343151836 -0.109206813 -1.025339e-01
## [178,] -0.237612114  0.189332048 -0.163628435  2.641713e-01
pca$rotation #Pregunta 14
##                PC1          PC2          PC3         PC4         PC5
## class  0.393669533 -0.005690412 -0.001217953  0.12246373  0.15758395
## V1    -0.136325011 -0.484160868  0.207400812 -0.08191848 -0.25089415
## V2     0.222676383 -0.223590947 -0.088796064  0.46988824 -0.18860015
## V3    -0.002257932 -0.315855884 -0.626102363 -0.24984122 -0.09352360
## V4     0.224298489  0.011615737 -0.611989600  0.07199322  0.04656750
## V5    -0.124630159 -0.300551432 -0.130984580 -0.16321412  0.77833048
## V6    -0.359264042 -0.067119829 -0.146507749  0.19098521 -0.14466563
## V7    -0.390711715  0.001313454 -0.150962746  0.14461667 -0.11200553
## V8     0.267001203 -0.026988703 -0.169975512 -0.32801272 -0.43257916
## V9    -0.279062504 -0.041222563 -0.149879586  0.46275771  0.09158820
## V10    0.089318293 -0.529782740  0.137266298  0.07211248 -0.04626960
## V11   -0.276822650  0.277907354 -0.085328539 -0.43466618 -0.02986657
## V12   -0.350526181  0.162776250 -0.166204360  0.15672341 -0.14419358
## V13   -0.269515252 -0.366058862  0.126686846 -0.25579490 -0.08440794
##               PC6         PC7         PC8          PC9        PC10        PC11
## class  0.20033864 -0.05938234  0.07179553 -0.162368819 -0.19899373  0.01444169
## V1    -0.13517139 -0.09269887  0.42154435 -0.450190708  0.31127983 -0.22154641
## V2    -0.59841948  0.37436980  0.08757556 -0.006025687 -0.32592413  0.06839251
## V3    -0.10799983 -0.16708856 -0.17208034  0.262494455 -0.12452347 -0.49452428
## V4     0.08811224 -0.26872469  0.41324857 -0.118633417  0.15716811  0.47461722
## V5    -0.14483831  0.32957951 -0.14881189 -0.252536278  0.12773363  0.07119731
## V6     0.14809748 -0.03789829 -0.36343884 -0.406373544 -0.30772263  0.29740957
## V7     0.06247252 -0.06773223 -0.17540500 -0.090919334 -0.14044000 -0.03219187
## V8     0.25868639  0.61111195 -0.23075135 -0.159122818  0.24054263  0.12200984
## V9     0.46627764  0.42292282  0.34373920  0.265786794  0.10869629 -0.23292405
## V10    0.42525454 -0.18613617 -0.04069617 -0.075264592 -0.21704255  0.01972448
## V11   -0.01565089  0.19204101  0.48362564 -0.212416815 -0.50966073 -0.06140493
## V12   -0.21770365 -0.07850980 -0.06865116 -0.084264837  0.45570504  0.06646166
## V13   -0.06656550  0.05420370  0.11146671  0.544905394 -0.04620802  0.55130818
##              PC12        PC13         PC14
## class -0.01575769 -0.49224318 -0.669045280
## V1     0.26411262 -0.05610645 -0.090626055
## V2    -0.11921210  0.06675544  0.025225306
## V3     0.04502305 -0.19201787  0.001635816
## V4     0.06131271  0.20007784  0.095361066
## V5    -0.06116074  0.05829909 -0.022300745
## V6     0.30087591 -0.35952714  0.253037788
## V7     0.05001396  0.59834288 -0.601909165
## V8    -0.04266558  0.06403952 -0.082230935
## V9     0.09334264 -0.11013538  0.058641979
## V10   -0.59795428  0.15917751  0.178821145
## V11   -0.25774292 -0.04923091  0.022582562
## V12   -0.61109218 -0.32941979 -0.135092159
## V13    0.07268036 -0.17322892 -0.216043617
#ProporciĂ³n de la varianza
prop_varianza=pca$sdev^2/sum(pca$sdev^2)
prop_varianza # Pregunta 13
##  [1] 0.395424860 0.178362589 0.103291016 0.066279845 0.062678751 0.048055596
##  [7] 0.039557068 0.025002441 0.021038710 0.018736150 0.016132030 0.012056908
## [13] 0.009254584 0.004129451
library(NbClust)
cluster=NbClust::NbClust(wine, distance = "euclidean", min.nc = 2,max.nc=6, method = "complete", index = "all") #Pregunta 16 y 20

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 9 proposed 2 as the best number of clusters 
## * 8 proposed 3 as the best number of clusters 
## * 1 proposed 4 as the best number of clusters 
## * 3 proposed 6 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  2 
##  
##  
## *******************************************************************
#NĂºmeros de cluster optimo
euc_dist<- dist(wine, method = "euclidean") 
hc <- hclust(euc_dist, method = "complete")
complete_clusters <- cutree(hc, 2)
table(complete_clusters) #Pregunta 17
## complete_clusters
##   1   2 
##  43 135