Proyecto Final - Machine Learning para E-commerce
Por José Alejandro Llamas C.
El e-commerce es una realidad que ha venido creciendo durante los últimos años. El 2020 no fue la excepción, el cual logró crecer en +30% tan solo en U.S.A. (CNBC, 2020).
Entre mis aspiraciones personales y profesionales es poder montar un e-commerce a principios del 2021. Por ende consideré realizar el siguiente proyecto basado en esta industria con la finalidad de comprender un poco sobre el comportamiento de los usuarios así como algunas buenas prácticas al momento de realizarlo.
Debo aclarar que el siguiente dataset no es mío. El mismo puede ser descargado de Kaggle en el siguiente link: https://www.kaggle.com/sarthi316/ecommerce-dataset-for-begginers
1. Sobre el data set
#Carga del data set
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, uniondataset = read.csv("Ecommerce Customers.csv")
glimpse(dataset)## Rows: 500
## Columns: 8
## $ Email <fct> mstephenson@fernandez.com, hduke@hotmail.com, ...
## $ Address <fct> "835 Frank Tunnel\nWrightmouth, MI 82180-9605"...
## $ Avatar <fct> Violet, DarkGreen, Bisque, SaddleBrown, Medium...
## $ Avg..Session.Length <dbl> 34.49727, 31.92627, 33.00091, 34.30556, 33.330...
## $ Time.on.App <dbl> 12.65565, 11.10946, 11.33028, 13.71751, 12.795...
## $ Time.on.Website <dbl> 39.57767, 37.26896, 37.11060, 36.72128, 37.536...
## $ Length.of.Membership <dbl> 4.082621, 2.664034, 4.104543, 3.120179, 4.4463...
## $ Yearly.Amount.Spent <dbl> 587.9511, 392.2049, 487.5475, 581.8523, 599.40...El data set consiste en 500 registros y 8 columnas (Variables) donde las primeras 3 son nominales: email del usuario, su dirección de envío y el avatar que emplean. Las siguientes 5 son numéricas: tiempo promedio por sesión, tiempo (en minutos) del uso del App y el Sitio Web, tiempo (en años) de ser miembro, y el consumo promedio anual.
En base a las variables anteriores, nos interesará conocer el consumo promedio anual. Para ello se desecharán las variables nominales ya que se considera que no aportarán valor alguno:
#Filtro de variables nominales
library(dplyr)
dataset = dataset %>%
select(Avg..Session.Length, Time.on.App, Time.on.Website, Length.of.Membership, Yearly.Amount.Spent)
dataset## Avg..Session.Length Time.on.App Time.on.Website Length.of.Membership
## 1 34.49727 12.655651 39.57767 4.0826206
## 2 31.92627 11.109461 37.26896 2.6640342
## 3 33.00091 11.330278 37.11060 4.1045432
## 4 34.30556 13.717514 36.72128 3.1201788
## 5 33.33067 12.795189 37.53665 4.4463083
## 6 33.87104 12.026925 34.47688 5.4935072
## 7 32.02160 11.366348 36.68378 4.6850172
## 8 32.73914 12.351959 37.37336 4.4342734
## 9 33.98777 13.386235 37.53450 3.2734336
## 10 31.93655 11.814128 37.14517 3.2028061
## 11 33.99257 13.338975 37.22581 2.4826078
## 12 33.87936 11.584783 37.08793 3.7132092
## 13 29.53243 10.961298 37.42022 4.0464232
## 14 33.19033 12.959226 36.14467 3.9185418
## 15 32.38798 13.148726 36.61996 2.4945436
## 16 30.73772 12.636606 36.21376 3.3578468
## 17 32.12539 11.733862 34.89409 3.1361327
## 18 32.33890 12.013195 38.38514 2.4208062
## 19 32.18781 14.715388 38.24411 1.5165756
## 20 32.61786 13.989593 37.19050 4.0645486
## 21 32.91279 11.365492 37.60779 4.5999374
## 22 33.50309 12.877984 37.44102 1.5591519
## 23 31.53160 13.378563 38.73401 2.2451478
## 24 32.90325 11.657576 36.77260 3.9193023
## 25 34.50755 12.893670 37.63576 5.7051540
## 26 33.02933 11.765813 37.73852 2.7217360
## 27 33.54123 12.783892 36.43065 4.6481993
## 28 32.33599 13.007819 37.85178 2.9963645
## 29 33.11021 11.982045 35.29309 3.9234887
## 30 33.10544 11.965020 37.27781 4.7425775
## 31 33.24190 12.305418 36.16365 3.0623681
## 32 33.46106 10.869164 35.62244 3.4714135
## 33 32.17550 13.387492 35.69417 4.3430629
## 34 32.72836 13.104507 38.87804 2.8200972
## 35 32.82031 11.634893 35.36863 4.1245853
## 36 33.61604 11.936386 38.76864 3.6492862
## 37 31.72165 11.755024 36.76572 1.8473704
## 38 32.86533 11.984418 37.04436 3.4523886
## 39 32.74937 9.954976 37.38831 4.6504913
## 40 32.56723 12.489013 36.37148 4.2224362
## 41 32.07055 11.733106 37.53429 4.6712755
## 42 33.01955 10.634561 37.49669 4.6461200
## 43 33.79204 12.507525 37.14286 4.2144951
## 44 32.89398 11.529878 36.88809 4.6432585
## 45 32.04449 13.414935 36.11244 2.2586864
## 46 34.55577 12.170525 39.13110 3.6631055
## 47 34.56456 13.146551 37.33545 3.8768752
## 48 32.72678 12.988510 36.46200 4.1132261
## 49 33.11722 11.864126 36.58273 3.2025312
## 50 31.66105 11.398064 36.59446 3.1983993
## 51 33.25634 13.858062 37.78026 5.9767681
## 52 33.90022 10.956791 37.26688 2.9526690
## 53 34.18777 10.320116 37.45341 2.0948917
## 54 33.76207 9.984514 35.93345 3.8554717
## 55 34.39016 12.645195 38.46832 2.8745969
## 56 33.92530 11.588655 35.25224 3.3920505
## 57 32.68823 13.761533 39.25293 2.9957612
## 58 34.30187 10.568295 36.17313 3.3152248
## 59 32.84393 11.832286 36.81401 3.4719191
## 60 33.75499 12.064157 37.27122 3.9705556
## 61 33.87978 12.495592 38.05261 4.6393203
## 62 33.07654 9.607315 36.49399 5.0812101
## 63 32.22730 13.728627 37.99703 4.8026306
## 64 32.78977 11.670066 37.40875 3.4146884
## 65 32.77261 13.276313 36.60078 3.4622988
## 66 34.37426 15.126994 37.15762 5.3775936
## 67 33.07872 12.695790 35.35844 4.0017863
## 68 32.80522 11.835476 36.37507 3.4395906
## 69 32.43076 11.306232 37.68040 2.7795207
## 70 32.17910 11.187539 40.00518 3.5526498
## 71 33.15418 11.887494 36.26500 2.6022871
## 72 34.33590 12.228935 36.15719 4.6943223
## 73 32.38625 10.674653 38.00658 3.4015223
## 74 32.80870 12.817113 37.03154 3.8515788
## 75 33.87974 13.587806 38.26035 3.2581129
## 76 32.04984 12.238057 38.73086 3.1205689
## 77 33.55521 11.551821 36.62883 2.8379432
## 78 33.14208 11.433380 35.89243 4.4702826
## 79 32.59718 10.889567 38.21257 4.4420543
## 80 33.16714 11.928842 36.91463 3.1649440
## 81 31.51474 12.595671 39.60038 3.7517346
## 82 34.59402 10.947259 35.88399 3.1597544
## 83 33.50137 13.898082 37.05891 4.1305628
## 84 32.40237 10.875560 37.78114 1.9140899
## 85 34.65549 10.338073 36.15726 4.3966519
## 86 31.80930 11.634668 36.18254 5.1133195
## 87 33.87778 12.517666 37.15192 2.6699416
## 88 34.44787 10.607724 36.81910 3.3664637
## 89 31.95630 12.828893 36.95162 4.5712130
## 90 32.60558 12.068816 36.10500 3.9174511
## 91 32.49145 12.530357 37.87522 2.4761391
## 92 33.61602 13.516284 36.77312 4.1255844
## 93 33.47160 11.662263 36.05024 3.9972554
## 94 33.71065 13.664748 37.72439 1.3626741
## 95 32.19772 11.830231 36.63386 4.1933246
## 96 32.46121 13.291143 38.63363 3.8710034
## 97 33.79039 11.942341 38.06341 4.0818027
## 98 34.18382 13.349913 37.82739 4.2520061
## 99 32.28867 12.020112 39.07440 3.9117087
## 100 33.82635 12.084092 35.89036 3.0216718
## 101 32.49839 13.410759 35.99049 3.1846187
## 102 31.88541 11.281931 37.38532 2.8772249
## 103 32.42570 11.448902 37.58019 2.5869680
## 104 33.43783 12.595420 36.26203 2.9696402
## 105 31.38959 10.994224 38.07445 3.4288599
## 106 33.46870 13.085506 35.84583 2.9269402
## 107 32.29176 12.190474 36.15246 3.7818230
## 108 32.06377 10.719150 37.71251 3.0047425
## 109 33.15570 12.931550 38.16644 3.8544739
## 110 33.35687 13.452129 38.50301 3.3188223
## 111 31.85307 12.149375 37.32533 3.3618146
## 112 32.01230 12.178331 37.71599 3.7225612
## 113 32.38845 11.010482 38.41504 3.5435471
## 114 32.65318 11.602532 37.30969 2.7894615
## 115 32.93134 12.732212 35.60082 5.4859767
## 116 33.23561 11.223369 37.69230 2.5941897
## 117 33.92579 12.011022 36.70105 2.7534242
## 118 33.05926 11.725910 35.99910 5.0048206
## 119 32.40173 12.089310 38.30991 3.8733376
## 120 33.88994 13.068639 37.54052 3.7987253
## 121 34.56938 12.854990 35.00748 3.2927977
## 122 33.70161 11.564022 37.67321 4.7161050
## 123 33.26833 11.113330 37.38795 4.0187266
## 124 31.35848 12.809883 36.54967 3.6377013
## 125 33.01479 11.761172 37.57016 3.8341697
## 126 31.57613 12.579894 37.09326 4.5319866
## 127 32.65727 11.957923 36.63465 4.1060552
## 128 34.70932 10.651794 37.14601 3.2182654
## 129 34.53666 12.752077 36.71414 3.2836635
## 130 32.77172 11.540832 37.52642 2.9240207
## 131 33.70040 11.924395 37.24503 3.9052503
## 132 32.43977 12.424130 38.94883 4.9203184
## 133 34.31217 11.810587 37.41413 2.4735961
## 134 32.45518 12.759169 36.59911 4.1312766
## 135 33.54098 11.851891 37.42455 1.7677307
## 136 33.35840 12.703688 36.10091 2.7241082
## 137 32.68613 12.215252 36.59436 3.8971159
## 138 34.55829 11.281445 36.49441 2.4916715
## 139 33.54775 10.735363 37.45837 3.8634254
## 140 31.95490 10.963132 37.32728 3.5786339
## 141 31.06622 11.735095 36.59937 3.9588923
## 142 31.85125 12.418962 35.97765 3.2517418
## 143 32.60928 10.537308 35.73055 3.9143847
## 144 32.11512 11.919242 39.29404 1.4435151
## 145 33.92462 11.911416 38.27470 2.9100379
## 146 33.47719 12.488067 36.51838 3.3455710
## 147 32.11640 12.380695 37.23200 3.0895278
## 148 32.25590 10.480507 37.33867 4.5141224
## 149 32.69239 12.296518 36.95156 1.8258847
## 150 32.38473 10.861604 36.58444 3.9936565
## 151 34.33873 10.716355 38.30720 2.6521583
## 152 32.88710 12.387184 37.43116 6.4012288
## 153 32.51022 10.984836 37.39650 5.3912751
## 154 31.94540 12.965761 36.96639 6.0766536
## 155 36.13966 12.050267 36.95964 3.8648607
## 156 32.44952 13.457725 37.23881 2.9414108
## 157 32.29464 12.443048 37.32785 5.0848613
## 158 34.60331 12.207298 33.91385 6.9226893
## 159 33.59852 11.586320 39.09463 3.6043986
## 160 34.56868 11.378087 38.30447 3.7849321
## 161 32.83810 12.364342 38.03911 3.3091823
## 162 33.50371 12.399436 35.01281 0.9686221
## 163 33.30188 12.542481 38.31136 3.7685620
## 164 30.87948 13.280432 36.93616 3.5851606
## 165 33.15425 11.795887 37.65862 4.5203534
## 166 32.04780 12.718039 37.66111 3.6758488
## 167 33.63080 12.039648 38.92409 2.8730075
## 168 34.04664 12.474455 35.03786 4.0557760
## 169 33.64418 13.160020 36.40775 3.0151753
## 170 32.65462 11.052324 37.63301 4.7171025
## 171 33.42875 10.636761 37.57884 2.9263964
## 172 31.86483 13.443406 36.87832 2.3610869
## 173 34.48239 13.283033 35.90730 4.9687427
## 174 32.52977 11.747732 36.93988 0.8015157
## 175 33.43223 10.859609 38.83567 3.6692256
## 176 33.30857 11.691686 37.48091 1.7157772
## 177 32.33264 11.548761 38.57652 4.7735030
## 178 34.71345 11.724002 36.81386 4.0878373
## 179 32.63588 12.178573 35.67426 4.1317550
## 180 33.07570 12.319845 37.81916 3.4427992
## 181 32.23015 11.084361 37.95968 4.7240274
## 182 34.14286 13.177775 38.85604 3.2309738
## 183 32.49720 12.832803 37.67924 2.9722714
## 184 33.12240 11.509048 37.25306 3.1823297
## 185 33.08853 11.857663 36.08693 4.8063496
## 186 32.53380 12.293366 37.06462 3.6203650
## 187 32.48426 10.933252 36.54551 3.2613247
## 188 32.54346 13.332839 37.96439 3.5974600
## 189 32.28312 10.902556 36.09424 4.7892016
## 190 32.20080 12.276982 38.23261 3.3164647
## 191 34.71332 12.038808 37.63530 4.6324609
## 192 32.71251 11.724474 37.15315 3.3084430
## 193 33.69490 11.202670 35.49396 4.0159866
## 194 31.57020 13.378063 36.33780 4.3693668
## 195 33.45948 11.388613 37.90914 2.5666398
## 196 31.82100 10.771074 37.27864 3.5190324
## 197 32.73322 11.818572 37.10203 1.5038544
## 198 32.40715 13.808799 37.42677 5.0399553
## 199 33.50609 11.659833 37.28139 4.4787126
## 200 30.83643 13.100110 35.90772 3.3616130
## 201 34.87849 13.067896 36.67822 1.9207155
## 202 34.00721 12.494323 36.04546 4.3307145
## 203 31.52575 11.340036 37.03951 3.8112482
## 204 31.04722 11.199661 38.68871 3.0887640
## 205 34.59578 11.332488 35.45986 4.5416953
## 206 34.96761 13.919494 37.95201 5.0666969
## 207 32.29525 11.031358 38.25298 3.1074687
## 208 33.32424 11.084584 36.77602 4.7469897
## 209 32.90345 10.542645 35.53386 3.0918269
## 210 32.55949 11.797796 37.77737 3.1956258
## 211 31.76562 12.442617 38.13171 3.8502796
## 212 34.08165 12.104542 36.05965 3.9745225
## 213 33.30443 12.378490 38.76430 3.8438489
## 214 34.33075 13.722454 35.77312 2.9090085
## 215 32.07895 12.725909 36.54466 1.1390935
## 216 33.60580 13.685119 34.89198 2.6852848
## 217 32.74515 10.012583 38.35496 3.1089114
## 218 32.12236 11.435534 36.22356 4.8528424
## 219 32.53083 12.354607 37.12235 2.3075524
## 220 31.73664 10.748534 35.73871 4.8355287
## 221 34.11757 11.591872 37.74362 3.6785894
## 222 33.63662 11.236507 37.67502 5.2547089
## 223 34.33486 11.109456 38.58585 3.8928915
## 224 34.81498 12.114945 36.28872 4.3894552
## 225 34.64267 11.866481 37.71777 4.0033250
## 226 32.83694 10.256549 36.14391 0.7895199
## 227 32.29965 12.168596 37.07362 4.4033698
## 228 31.94802 13.085357 37.60565 2.6485968
## 229 32.72732 13.013376 36.65128 2.3678482
## 230 33.94624 10.983977 37.95149 3.0507130
## 231 32.35148 13.105159 35.57484 3.6414972
## 232 34.17375 12.144749 37.25803 3.3973631
## 233 32.97518 13.909916 37.79224 4.2976865
## 234 32.00475 11.395209 37.33281 3.8033650
## 235 34.19706 13.033566 37.07680 2.6334200
## 236 33.17720 11.622777 35.96890 3.6340937
## 237 32.69324 12.600750 37.37012 3.4670141
## 238 31.62536 13.187911 37.06709 1.4943109
## 239 31.26065 13.266760 36.97120 2.2672511
## 240 31.72077 11.752343 38.57361 5.0239342
## 241 32.92261 11.568116 36.90938 2.4717507
## 242 32.68625 12.638572 36.09722 4.2977375
## 243 34.05095 11.388645 39.08156 2.4369589
## 244 32.45455 11.822983 36.94613 3.6569839
## 245 31.28345 12.725677 35.96567 5.0002434
## 246 32.98003 11.201160 37.68934 2.4128310
## 247 31.90963 11.347264 36.32365 5.3143541
## 248 34.40241 14.220979 37.52320 4.0777751
## 249 32.95976 11.546276 36.94795 3.2750707
## 250 33.78016 11.917636 36.84473 3.6349960
## 251 32.67294 12.276057 37.19279 3.9824715
## 252 32.72852 10.131712 34.84561 3.2877018
## 253 33.40992 12.026942 36.13389 2.3133499
## 254 31.72420 13.172287 36.19975 3.5578137
## 255 32.71112 12.326291 36.67388 3.3502793
## 256 33.13666 13.891313 39.22071 2.9070949
## 257 34.37939 12.930929 36.36025 3.7927120
## 258 35.53090 11.379257 36.63610 4.0294538
## 259 33.24727 14.069382 38.99332 4.9784758
## 260 32.09611 10.804891 37.37276 2.6995621
## 261 35.03928 14.426491 37.37418 3.9306153
## 262 32.55053 13.041245 36.65521 3.4562338
## 263 32.58249 11.739744 36.85481 2.1820170
## 264 33.29698 12.491059 38.23894 2.7095266
## 265 33.10834 12.892375 36.52739 4.5941169
## 266 33.90272 11.668867 37.34127 4.2569833
## 267 34.55528 11.777772 37.97983 3.7842731
## 268 33.73265 12.138794 36.85388 1.6234196
## 269 31.60051 12.222967 36.82275 3.4145062
## 270 34.31893 13.402332 37.29204 3.6060869
## 271 34.00649 12.956277 38.65509 3.2757337
## 272 33.54048 12.884125 36.22604 5.0072720
## 273 34.43643 13.325469 36.76860 3.3712581
## 274 33.55170 12.158585 36.57513 5.4539695
## 275 31.81862 11.226546 35.66994 3.7558694
## 276 32.36312 12.461135 37.74561 4.6642585
## 277 33.19157 9.846125 36.87631 3.8066709
## 278 32.19250 13.325412 36.89729 5.0499275
## 279 32.60790 13.677246 37.74470 2.8719475
## 280 32.26200 11.644970 37.02688 3.2367328
## 281 32.27185 13.485009 37.55088 3.0863373
## 282 33.79512 11.620997 38.41947 4.5596991
## 283 31.65481 13.014459 37.78904 3.0102098
## 284 33.07773 11.466984 35.67573 1.8092296
## 285 31.31235 11.684904 38.71708 3.5942951
## 286 32.87274 12.093966 36.62077 3.0491957
## 287 33.70815 14.325655 35.72183 3.6343402
## 288 33.90857 12.914847 39.06886 1.4823596
## 289 32.31291 9.824402 35.74278 2.9213501
## 290 34.39433 12.807752 38.55103 1.8100799
## 291 32.42330 13.058278 37.26388 3.3731047
## 292 33.53940 10.534553 37.03479 2.2147975
## 293 33.37402 11.143433 35.94640 5.4544633
## 294 33.79476 10.982806 34.81063 3.2018017
## 295 33.77090 11.153966 37.24033 4.7294845
## 296 31.30919 11.947175 36.19083 3.2055298
## 297 33.61256 11.470565 37.06169 3.8025114
## 298 33.39826 11.037850 38.61733 4.1163405
## 299 33.62259 11.167357 35.62659 5.4625008
## 300 30.49254 11.562936 35.97656 1.4816166
## 301 31.90486 12.227728 36.98591 3.7714201
## 302 33.02642 13.186813 38.06693 2.8982996
## 303 32.97519 13.394452 37.80698 3.5690465
## 304 30.81620 11.851399 36.92504 1.0845853
## 305 33.91402 12.266504 36.57503 3.0234744
## 306 33.30267 13.459222 36.33952 5.5663849
## 307 31.91208 11.792972 36.25782 2.3951681
## 308 32.40856 10.985740 37.36839 3.5048335
## 309 32.64462 12.637557 36.51709 5.2266877
## 310 34.10228 8.508152 35.46240 1.8382107
## 311 33.24851 11.656592 36.54861 3.3634114
## 312 34.72908 11.966898 36.54760 2.9574488
## 313 30.39318 11.802986 36.31576 2.0838142
## 314 33.38411 12.677401 35.62253 3.6808473
## 315 32.87847 13.032535 37.87095 4.6937321
## 316 34.50142 12.447617 37.53453 4.0083522
## 317 33.56647 12.235659 37.27757 2.5320441
## 318 32.84879 10.973162 36.60951 2.8709869
## 319 33.53186 13.665770 36.90022 3.5156883
## 320 33.41907 13.391120 37.19419 4.0699166
## 321 32.49542 12.968326 38.29611 1.2004839
## 322 33.67403 12.968893 37.33311 3.2294509
## 323 33.26463 10.732131 36.14579 4.0865663
## 324 32.76246 10.952353 37.64629 4.0194704
## 325 33.47947 12.608889 37.22939 4.2059039
## 326 33.78521 13.039511 36.31273 2.0181946
## 327 33.21719 10.999684 38.44277 4.2438128
## 328 31.12809 13.278956 37.38718 4.6260753
## 329 33.36952 10.627949 38.04031 3.0029570
## 330 32.83789 13.185181 35.92160 1.8235952
## 331 30.57436 11.351049 37.08885 4.0783080
## 332 32.27459 12.954811 37.10882 3.6899166
## 333 33.14423 11.737041 37.93519 2.1901322
## 334 33.48552 11.887345 35.86245 3.2067567
## 335 31.97648 10.757131 36.59587 1.9770071
## 336 32.13386 11.612651 39.24880 3.3492454
## 337 32.30255 11.979061 38.26906 3.5328616
## 338 31.82798 12.461147 37.42900 2.9747368
## 339 32.01807 10.079463 38.07066 2.6181653
## 340 32.99746 12.589241 37.33224 2.8040137
## 341 31.81643 14.288015 36.77386 2.9644979
## 342 34.46151 11.917116 37.76669 4.3508878
## 343 32.34280 11.409645 35.77778 3.8724320
## 344 32.30275 12.815393 37.95781 4.6154263
## 345 33.06644 11.673229 37.84066 2.7272095
## 346 33.89464 10.610537 37.97739 3.5371239
## 347 32.76566 12.506548 35.82347 3.1265095
## 348 33.76981 11.304462 37.83397 5.1378167
## 349 31.81248 10.886921 34.89783 3.1286389
## 350 32.00850 12.095889 36.37751 3.1789524
## 351 33.30434 12.692661 37.33359 3.8273759
## 352 32.18984 11.386776 38.19748 4.8083204
## 353 34.93561 10.728419 36.88119 4.0485101
## 354 33.55165 11.936895 35.90025 4.5433324
## 355 32.38697 12.717995 35.12882 3.4810621
## 356 33.34451 10.969803 35.97458 2.6276250
## 357 33.67276 13.420546 37.76369 4.7943123
## 358 34.00207 11.854682 37.49189 2.7618619
## 359 32.65540 11.918860 35.71627 2.1596760
## 360 32.05426 13.149670 37.65040 4.1956144
## 361 33.22877 12.685394 36.04899 2.1394030
## 362 32.07759 10.347877 39.04516 3.4345597
## 363 33.98101 9.316289 36.91495 2.8684282
## 364 34.17952 12.581548 35.44426 3.1370690
## 365 32.60274 11.764448 37.92270 3.5258064
## 366 32.03055 12.644202 38.00183 5.0381075
## 367 33.10036 11.832112 36.84149 3.6122392
## 368 32.99060 10.441235 35.93896 2.8950752
## 369 34.38582 12.729720 36.23211 5.7059407
## 370 34.35720 9.477778 37.90601 5.0470226
## 371 33.70511 10.163179 37.76304 4.7789736
## 372 32.40430 11.608998 38.11046 2.9665589
## 373 31.82935 11.268259 36.95697 2.6689198
## 374 31.36621 11.163160 37.08832 3.6203546
## 375 31.44745 10.101632 38.04345 4.2382962
## 376 33.58295 12.761531 36.90819 2.4793398
## 377 32.39742 12.055340 37.68547 3.5069676
## 378 35.03745 11.935935 35.78392 3.3101503
## 379 32.78494 12.451200 36.66579 3.5358025
## 380 33.97172 12.284467 38.29573 1.1304770
## 381 33.38599 12.782172 35.55077 3.2287177
## 382 33.55656 12.960307 37.95195 3.3459223
## 383 33.58737 9.953995 37.34574 3.2156668
## 384 34.18818 13.130022 35.42933 3.7905521
## 385 33.59396 11.520567 36.18913 3.5612153
## 386 33.23627 10.972554 34.57403 2.9316195
## 387 33.20892 13.531913 38.95246 3.0465406
## 388 33.63781 12.039502 34.48718 2.7392005
## 389 33.59049 10.942070 36.17049 2.7839631
## 390 34.19551 12.664193 37.02715 4.3304074
## 391 35.86024 11.730661 36.88215 3.4162100
## 392 33.48193 11.918670 37.31770 3.3363394
## 393 33.25824 11.514949 37.12804 4.6628453
## 394 32.31986 12.418113 36.15534 3.2220808
## 395 32.43084 13.887275 38.38196 3.7729690
## 396 31.44597 12.846499 37.86922 3.4201495
## 397 35.74267 10.889828 35.56544 6.1151989
## 398 34.01262 12.914570 36.04620 3.4880300
## 399 34.14039 11.568527 38.91875 4.0828553
## 400 32.37799 11.971751 37.19937 2.8296996
## 401 33.17233 13.078692 37.32982 5.4054065
## 402 33.24732 11.956426 36.51735 3.4517507
## 403 33.59891 13.252737 37.30596 2.9355773
## 404 33.08530 13.093537 38.31565 4.7503601
## 405 32.27844 12.527472 36.68837 3.5314023
## 406 33.44155 11.235969 37.05262 3.9044794
## 407 32.86530 12.074830 35.56917 2.3990798
## 408 31.52620 12.045332 38.50588 2.8477090
## 409 33.00085 11.230743 36.99529 3.7817036
## 410 32.08838 11.907844 35.18912 4.3497784
## 411 33.26544 13.052210 38.77567 4.5742877
## 412 32.99257 13.004362 36.98504 4.6204164
## 413 33.86319 11.523523 35.93805 3.0130325
## 414 32.59209 10.314718 36.72903 4.7911087
## 415 32.38103 12.433129 37.62691 4.3340014
## 416 31.51712 10.745189 38.79123 1.4288239
## 417 33.45430 11.016756 37.63731 4.1370004
## 418 32.21553 12.216855 36.95396 2.9105308
## 419 31.67392 12.329147 37.07437 3.9824623
## 420 33.71755 10.806966 36.01232 3.7012292
## 421 33.21547 12.135101 37.14209 5.8405059
## 422 31.57414 12.941556 36.72528 4.5603961
## 423 33.89457 13.300299 36.39368 4.4900021
## 424 33.12869 10.398458 36.68339 3.8598180
## 425 34.37033 11.887800 37.86145 3.0466202
## 426 34.08026 11.591440 36.45690 4.6528544
## 427 31.42523 13.271475 37.23985 4.0221029
## 428 33.62531 12.988221 39.67259 3.9694178
## 429 31.86274 14.039867 37.02227 3.7382252
## 430 33.29259 11.906508 38.42287 3.3766875
## 431 33.74923 11.137140 38.40137 4.5955227
## 432 34.14497 12.902665 36.61120 2.2239935
## 433 31.12397 12.386516 35.63211 4.2884868
## 434 34.27825 11.822722 36.30855 2.1173825
## 435 33.66662 10.985764 36.35250 0.9364976
## 436 32.25997 14.132893 37.02348 3.7620704
## 437 35.43317 11.912210 36.08964 4.0009636
## 438 31.96732 11.481587 39.24096 3.5325172
## 439 32.14906 10.047315 37.18145 3.5350884
## 440 33.91884 12.428737 37.30536 4.1582147
## 441 33.20062 11.965980 36.83154 3.5490361
## 442 32.53677 11.121366 36.97937 4.1292547
## 443 34.08366 8.668350 35.90676 2.2524460
## 444 33.02502 12.504220 37.64584 4.0513825
## 445 31.26810 12.132509 35.45680 3.0720761
## 446 32.21292 11.732991 35.63395 4.3318630
## 447 33.49951 11.946591 36.48633 3.9378626
## 448 32.90485 12.556108 37.80551 0.2699011
## 449 32.20465 12.480702 37.68029 3.2794663
## 450 32.67515 12.594194 37.68388 2.5717778
## 451 32.99839 10.946842 37.64781 3.8260306
## 452 33.94312 11.484199 36.83937 2.4024538
## 453 33.55211 11.120871 36.80838 4.0278138
## 454 33.67683 10.971392 37.72237 3.6293399
## 455 32.64195 11.588949 36.32214 3.1896099
## 456 33.42121 10.706642 35.76615 3.3939750
## 457 32.76708 11.076259 34.77975 2.5749485
## 458 33.11995 12.953263 37.03428 3.4720214
## 459 35.37188 10.572467 36.86218 4.1983491
## 460 33.97608 11.658037 37.42528 2.0863481
## 461 34.03416 13.592513 36.83866 3.6059339
## 462 32.77049 11.371767 35.26150 4.0343861
## 463 33.50381 11.233415 37.21115 2.3205502
## 464 31.87455 10.290351 36.92976 3.4910933
## 465 32.53324 14.121784 38.40633 5.3200939
## 466 34.85131 12.415542 37.67232 3.1305385
## 467 34.21146 10.770249 34.64980 4.9852050
## 468 33.45962 12.664391 36.36684 1.7269620
## 469 34.20054 12.667809 37.48705 3.7016223
## 470 31.16951 13.970181 36.67395 1.7851739
## 471 32.51820 11.509253 36.59929 3.0226758
## 472 34.52302 11.405770 36.37827 4.0412450
## 473 33.66599 12.263718 38.86023 3.1395269
## 474 31.60984 12.710701 36.16646 2.5628188
## 475 33.70089 13.471578 37.07164 2.3790765
## 476 33.81173 11.186809 36.29889 4.3019965
## 477 34.33668 11.246813 38.68258 2.0947617
## 478 31.06133 12.357638 36.16604 4.0893308
## 479 33.06977 11.764326 36.87503 3.5160510
## 480 34.60624 11.761884 38.12652 1.8208106
## 481 34.23824 11.550300 35.76933 4.1831437
## 482 32.04781 12.482670 35.53602 3.3939028
## 483 30.97168 11.731364 36.07455 4.4263641
## 484 33.60685 12.214074 37.19843 2.9052384
## 485 33.44813 11.903757 36.87454 2.7827578
## 486 33.36938 12.222484 36.35523 3.4470178
## 487 33.45230 12.005916 36.53410 4.7122336
## 488 32.90469 11.913745 36.05865 1.2281124
## 489 35.63085 12.125402 38.18776 4.0190514
## 490 32.24635 11.305551 37.13313 1.7073897
## 491 34.69559 11.608997 37.68488 3.1630919
## 492 34.34392 11.693058 36.81293 3.4470929
## 493 33.68094 11.201570 37.83545 2.2088137
## 494 32.06091 12.625433 35.53914 5.4123578
## 495 33.43110 13.350632 37.96597 2.7688519
## 496 33.23766 13.566160 36.41798 3.7465730
## 497 34.70253 11.695736 37.19027 3.5765259
## 498 32.64678 11.499409 38.33258 4.9582645
## 499 33.32250 12.391423 36.84009 2.3364847
## 500 33.71598 12.418808 35.77102 2.7351596
## Yearly.Amount.Spent
## 1 587.9511
## 2 392.2049
## 3 487.5475
## 4 581.8523
## 5 599.4061
## 6 637.1024
## 7 521.5722
## 8 549.9041
## 9 570.2004
## 10 427.1994
## 11 492.6060
## 12 522.3374
## 13 408.6404
## 14 573.4159
## 15 470.4527
## 16 461.7807
## 17 457.8477
## 18 407.7045
## 19 452.3157
## 20 605.0610
## 21 534.7057
## 22 419.9388
## 23 436.5156
## 24 519.3410
## 25 700.9171
## 26 423.1800
## 27 619.8956
## 28 486.8389
## 29 529.5377
## 30 554.7221
## 31 497.5867
## 32 447.6879
## 33 588.7126
## 34 491.0732
## 35 507.4418
## 36 521.8836
## 37 347.7769
## 38 490.7386
## 39 478.1703
## 40 537.8462
## 41 532.7518
## 42 501.8744
## 43 591.1972
## 44 547.2443
## 45 448.2298
## 46 549.8606
## 47 593.9150
## 48 563.6729
## 49 479.7319
## 50 416.3584
## 51 725.5848
## 52 442.6673
## 53 384.6266
## 54 451.4574
## 55 522.4041
## 56 483.6733
## 57 520.8988
## 58 453.1695
## 59 496.6507
## 60 547.3651
## 61 616.8515
## 62 507.2126
## 63 613.5993
## 64 483.1597
## 65 540.2634
## 66 765.5185
## 67 553.6015
## 68 469.3109
## 69 408.6202
## 70 451.5757
## 71 444.9666
## 72 595.8228
## 73 418.1501
## 74 534.7772
## 75 578.2416
## 76 478.7194
## 77 444.2859
## 78 544.7799
## 79 488.7861
## 80 475.7591
## 81 489.8125
## 82 462.8976
## 83 596.4302
## 84 338.3199
## 85 533.5149
## 86 536.7719
## 87 487.3793
## 88 473.7290
## 89 547.1259
## 90 505.1133
## 91 449.0703
## 92 611.0000
## 93 515.8288
## 94 439.0748
## 95 514.0890
## 96 543.3402
## 97 521.1430
## 98 614.7153
## 99 507.3901
## 100 495.2994
## 101 518.0646
## 102 390.1033
## 103 420.7377
## 104 492.1051
## 105 410.0696
## 106 497.5137
## 107 494.5519
## 108 378.3309
## 109 570.4517
## 110 549.0082
## 111 459.2851
## 112 492.9451
## 113 424.7626
## 114 422.4268
## 115 642.1016
## 116 413.3718
## 117 479.2311
## 118 593.0772
## 119 506.5473
## 120 571.3075
## 121 576.3112
## 122 576.8025
## 123 514.2395
## 124 495.1760
## 125 514.3366
## 126 541.2266
## 127 516.8316
## 128 468.4457
## 129 548.2803
## 130 431.6177
## 131 552.9403
## 132 573.3062
## 133 452.6273
## 134 542.7116
## 135 407.8040
## 136 482.3536
## 137 529.2301
## 138 433.0488
## 139 476.1914
## 140 439.9979
## 141 448.9333
## 142 472.9922
## 143 463.9235
## 144 350.0582
## 145 460.0613
## 146 505.7711
## 147 463.4850
## 148 479.7319
## 149 424.1855
## 150 465.8893
## 151 426.7752
## 152 684.1634
## 153 555.8926
## 154 657.0199
## 155 595.8038
## 156 503.9784
## 157 586.1559
## 158 744.2219
## 159 512.8254
## 160 528.2238
## 161 468.9135
## 162 357.5914
## 163 536.4231
## 164 490.2066
## 165 550.0476
## 166 513.4506
## 167 497.8119
## 168 578.9863
## 169 506.5364
## 170 501.7492
## 171 421.9668
## 172 439.8913
## 173 666.1256
## 174 298.7620
## 175 465.1766
## 176 373.8857
## 177 532.7175
## 178 554.9008
## 179 537.7732
## 180 501.1002
## 181 517.1651
## 182 557.5293
## 183 493.7192
## 184 452.1226
## 185 577.2735
## 186 485.9231
## 187 425.7451
## 188 537.2151
## 189 524.6380
## 190 478.8854
## 191 612.3852
## 192 476.7667
## 193 505.1196
## 194 545.9455
## 195 434.0217
## 196 424.6753
## 197 352.5501
## 198 662.9611
## 199 560.5602
## 200 467.5019
## 201 504.8704
## 202 590.5627
## 203 443.9656
## 204 392.4974
## 205 568.7176
## 206 712.3963
## 207 413.2960
## 208 562.0820
## 209 412.0129
## 210 468.6685
## 211 496.5541
## 212 548.5185
## 213 536.1309
## 214 558.4273
## 215 357.8637
## 216 529.0567
## 217 387.3571
## 218 528.9336
## 219 420.9162
## 220 496.9334
## 221 519.3730
## 222 591.4377
## 223 502.4098
## 224 604.3348
## 225 555.0684
## 226 256.6706
## 227 547.1110
## 228 461.9209
## 229 458.3769
## 230 436.2835
## 231 532.9352
## 232 512.5525
## 233 630.4228
## 234 463.7460
## 235 493.1802
## 236 501.2092
## 237 501.9283
## 238 376.3369
## 239 421.3266
## 240 538.7749
## 241 398.1635
## 242 571.4710
## 243 451.6286
## 244 490.6004
## 245 591.7811
## 246 409.0705
## 247 563.4460
## 248 647.6195
## 249 448.3404
## 250 518.7865
## 251 523.6339
## 252 393.8574
## 253 426.1545
## 254 503.3879
## 255 482.6025
## 256 524.7976
## 257 574.6548
## 258 574.7472
## 259 660.4252
## 260 375.3985
## 261 640.1877
## 262 514.0098
## 263 376.4968
## 264 484.5198
## 265 614.7296
## 266 567.4750
## 267 554.0031
## 268 399.9839
## 269 479.1729
## 270 585.9318
## 271 540.9957
## 272 628.0478
## 273 582.4919
## 274 640.7862
## 275 446.4187
## 276 570.6301
## 277 423.3083
## 278 616.6603
## 279 530.3625
## 280 442.3631
## 281 511.9799
## 282 560.4438
## 283 475.2634
## 284 374.2697
## 285 463.5914
## 286 471.6029
## 287 626.0187
## 288 432.4721
## 289 356.6156
## 290 467.4278
## 291 503.2174
## 292 378.4736
## 293 584.2183
## 294 451.7279
## 295 557.6341
## 296 432.7207
## 297 506.4239
## 298 510.1598
## 299 587.5748
## 300 282.4712
## 301 473.9499
## 302 489.9081
## 303 541.9722
## 304 266.0863
## 305 494.6872
## 306 689.7876
## 307 387.5347
## 308 441.8966
## 309 604.8413
## 310 302.1895
## 311 479.6148
## 312 506.1323
## 313 319.9289
## 314 528.3092
## 315 610.1280
## 316 584.1059
## 317 466.4212
## 318 404.8245
## 319 564.7910
## 320 596.5167
## 321 368.6548
## 322 542.4125
## 323 478.2621
## 324 473.3605
## 325 559.1990
## 326 447.1876
## 327 505.2301
## 328 557.2527
## 329 422.3687
## 330 445.0622
## 331 442.0644
## 332 533.0401
## 333 424.2028
## 334 498.6356
## 335 330.5944
## 336 443.4419
## 337 478.6009
## 338 440.0027
## 339 357.7831
## 340 476.1392
## 341 501.1225
## 342 592.6885
## 343 486.0834
## 344 576.0252
## 345 442.7229
## 346 461.7910
## 347 488.3875
## 348 593.1564
## 349 392.8103
## 350 443.1972
## 351 535.4808
## 352 533.3966
## 353 532.1274
## 354 558.9481
## 355 508.7719
## 356 403.7669
## 357 640.5841
## 358 461.6283
## 359 382.4161
## 360 561.8747
## 361 444.5761
## 362 401.0331
## 363 384.3261
## 364 527.7830
## 365 482.1450
## 366 594.2745
## 367 502.0925
## 368 407.6572
## 369 708.9352
## 370 531.9616
## 371 521.2408
## 372 447.3690
## 373 385.1523
## 374 430.5889
## 375 418.6027
## 376 478.9514
## 377 483.7965
## 378 538.9420
## 379 486.1638
## 380 385.0950
## 381 527.7838
## 382 547.1907
## 383 410.6029
## 384 583.9778
## 385 474.5323
## 386 414.9351
## 387 550.8134
## 388 458.7811
## 389 407.5422
## 390 581.3089
## 391 546.5567
## 392 503.1751
## 393 549.1316
## 394 482.8310
## 395 557.6083
## 396 484.8770
## 397 669.9871
## 398 547.7100
## 399 537.8253
## 400 408.2169
## 401 663.0748
## 402 506.3759
## 403 528.4193
## 404 632.1236
## 405 488.2703
## 406 508.7357
## 407 411.1870
## 408 409.0945
## 409 467.8009
## 410 512.1659
## 411 608.2718
## 412 589.0265
## 413 444.0538
## 414 493.1813
## 415 532.7248
## 416 275.9184
## 417 511.0388
## 418 438.4177
## 419 475.7251
## 420 483.5432
## 421 663.8037
## 422 544.4093
## 423 630.1567
## 424 461.1122
## 425 491.9115
## 426 574.4157
## 427 530.7667
## 428 581.7988
## 429 556.2981
## 430 502.1328
## 431 556.1864
## 432 475.0716
## 433 486.9471
## 434 434.1442
## 435 304.1356
## 436 571.2160
## 437 583.0796
## 438 445.7498
## 439 392.9923
## 440 565.9944
## 441 499.1402
## 442 510.5394
## 443 308.5277
## 444 561.5165
## 445 423.4705
## 446 513.1531
## 447 529.1945
## 448 314.4385
## 449 478.5843
## 450 444.5822
## 451 475.0154
## 452 436.7206
## 453 521.1953
## 454 478.1831
## 455 432.4812
## 456 438.3037
## 457 388.9405
## 458 534.7715
## 459 537.9158
## 460 407.8764
## 461 618.8460
## 462 502.7711
## 463 397.4206
## 464 392.2852
## 465 689.2357
## 466 543.1326
## 467 577.7360
## 468 436.5807
## 469 553.9947
## 470 427.3565
## 471 424.7288
## 472 541.0498
## 473 469.3831
## 474 444.5455
## 475 492.5568
## 476 535.3216
## 477 408.9583
## 478 487.5555
## 479 487.6462
## 480 402.1671
## 481 551.0230
## 482 497.3896
## 483 494.6386
## 484 479.2474
## 485 462.6565
## 486 515.5025
## 487 576.4776
## 488 357.8580
## 489 597.7399
## 490 327.3780
## 491 510.4014
## 492 510.5015
## 493 403.8195
## 494 627.6033
## 495 510.6618
## 496 573.8474
## 497 529.0490
## 498 551.6201
## 499 456.4695
## 500 497.7786Ya con esto daremos inicio a la etapa de anális.
2. Análisis
Lo siguiente será hacer un resumen rápido acerca de la composición estadística de las variables:
summary(dataset)## Avg..Session.Length Time.on.App Time.on.Website Length.of.Membership
## Min. :29.53 Min. : 8.508 Min. :33.91 Min. :0.2699
## 1st Qu.:32.34 1st Qu.:11.388 1st Qu.:36.35 1st Qu.:2.9304
## Median :33.08 Median :11.983 Median :37.07 Median :3.5340
## Mean :33.05 Mean :12.052 Mean :37.06 Mean :3.5335
## 3rd Qu.:33.71 3rd Qu.:12.754 3rd Qu.:37.72 3rd Qu.:4.1265
## Max. :36.14 Max. :15.127 Max. :40.01 Max. :6.9227
## Yearly.Amount.Spent
## Min. :256.7
## 1st Qu.:445.0
## Median :498.9
## Mean :499.3
## 3rd Qu.:549.3
## Max. :765.5A grosso modo, el comportamiento de las variables parecen obedecer una distribución normal. Eso lo podemos saber por el simple hecho que la media y mediana están bastante cercanas. Esto a lo largo de las 5 variables.
Lo siguiente a realizar será un pequeño análisis por variables para confirmar lo anterior.
2.1. Duración promedio por sesión
#Histograma - Avg..Session.Length
hist(dataset$Avg..Session.Length,
col = "orange2",
xlab = "Tiempo (minutos)",
ylab = "Frecuencia",
main = "Duración promedio por sesión")
La duración promedio de los usuarios es ronda por los 30 minutos. Se concentra más ahí por los 33 minutos y pico.
2.2. Tiempo en el App
#Histograma - Time.on.App
hist(dataset$Time.on.App,
col = "green2",
xlab = "Tiempo (minutos)",
ylab = "Frecuencia",
main = "Tiempo promedio en el App")
##### La duración promedio de navegación vía App ronda entre los 12 y 13 minutos. Vemos que, a comparación de las sesiones, estas son más cortas –poco más del doble –, por lo que se puede decir que los usuarios aprovecharían a utilizarla únicamente si algo les llamó la atención. Es decir que son búsquedas efímeras que pudieron ser: para matar el tiempo o bien porque vieron algún anuncio que los redireccionó al software.
Será interesante ver lo que es su complementaria: la Web.
2.3. Tiempo en el Sitio Web
#Histograma - Time.on.Website
hist(dataset$Time.on.Website,
col = "yellow2",
xlab = "Tiempo (minutos)",
ylab = "Frecuencia",
main = "Tiempo promedio en el Sitio Web")
2.4. Longevidad de la membresía
#Histograma - Length.of.Membership
hist(dataset$Length.of.Membership,
col = "pink2",
xlab = "Tiempo (años)",
ylab = "Frecuencia",
main = "Longevidad de la membresía")
##### Actualmente la mayor concentración de membresías oscilan entre los 3 y 4 años de longevidad. De igual manera se observa que el comportamiento del mismo es normal, por lo que existen membresías tanto más antiguas (7 años) como más recientes (algunos meses).
2.5. Consumo promedio anual
#Histograma - Yearly.Amount.Spent
hist(dataset$Yearly.Amount.Spent,
col = "red2",
xlab = "Gasto (en USD)",
ylab = "Frecuencia",
main = "Consumo promedio anual")
sd(dataset$Yearly.Amount.Spent)## [1] 79.31478Como se puede observar, el ticket promedio anual del e-commerce oscila entre los USD500, con una desviación estándar de +-USD80. Así mismo obedece un comportamiento normal.
2.6.Boxplot
#Normalización de los datos
library(scales)
base.escalada = scale(dataset[,], center = T, scale = T)
boxplot(base.escalada)
##### A través de una rescalación de las variables nos percatamos que el comportamiento es bastante similar entre ellas: cuartiles y mediana muy parecidos –difiere levemente el uso del App (segunda caja)–. Lo que los diferencia visualmente son los outliers que exceden mucho en las dos últimas cajas. Será interesante ver su comportamiento en el análisis por correlación.
2.7. Análisis de correlación
library(corrplot)## corrplot 0.84 loadedplot(dataset)
numeric.var= cor(dataset)
corrplot(numeric.var, method="number", type="upper")
##### Es interesante observar que, a través de los elementos visuales, las variables que guardan mayor relación con el consumo promedio anual es prácticamente la longevidad de la membresía en un alto índice, seguido por el tiempo de navegación en el App.
3. Variable de clasificación
#Creación de la variable Categoria.Cliente
dataset$Categoria.Cliente = ifelse(dataset$Yearly.Amount.Spent >= 600,"Oro",ifelse(dataset$Yearly.Amount.Spent >= 400,"Platino","Bronce"))
dataset## Avg..Session.Length Time.on.App Time.on.Website Length.of.Membership
## 1 34.49727 12.655651 39.57767 4.0826206
## 2 31.92627 11.109461 37.26896 2.6640342
## 3 33.00091 11.330278 37.11060 4.1045432
## 4 34.30556 13.717514 36.72128 3.1201788
## 5 33.33067 12.795189 37.53665 4.4463083
## 6 33.87104 12.026925 34.47688 5.4935072
## 7 32.02160 11.366348 36.68378 4.6850172
## 8 32.73914 12.351959 37.37336 4.4342734
## 9 33.98777 13.386235 37.53450 3.2734336
## 10 31.93655 11.814128 37.14517 3.2028061
## 11 33.99257 13.338975 37.22581 2.4826078
## 12 33.87936 11.584783 37.08793 3.7132092
## 13 29.53243 10.961298 37.42022 4.0464232
## 14 33.19033 12.959226 36.14467 3.9185418
## 15 32.38798 13.148726 36.61996 2.4945436
## 16 30.73772 12.636606 36.21376 3.3578468
## 17 32.12539 11.733862 34.89409 3.1361327
## 18 32.33890 12.013195 38.38514 2.4208062
## 19 32.18781 14.715388 38.24411 1.5165756
## 20 32.61786 13.989593 37.19050 4.0645486
## 21 32.91279 11.365492 37.60779 4.5999374
## 22 33.50309 12.877984 37.44102 1.5591519
## 23 31.53160 13.378563 38.73401 2.2451478
## 24 32.90325 11.657576 36.77260 3.9193023
## 25 34.50755 12.893670 37.63576 5.7051540
## 26 33.02933 11.765813 37.73852 2.7217360
## 27 33.54123 12.783892 36.43065 4.6481993
## 28 32.33599 13.007819 37.85178 2.9963645
## 29 33.11021 11.982045 35.29309 3.9234887
## 30 33.10544 11.965020 37.27781 4.7425775
## 31 33.24190 12.305418 36.16365 3.0623681
## 32 33.46106 10.869164 35.62244 3.4714135
## 33 32.17550 13.387492 35.69417 4.3430629
## 34 32.72836 13.104507 38.87804 2.8200972
## 35 32.82031 11.634893 35.36863 4.1245853
## 36 33.61604 11.936386 38.76864 3.6492862
## 37 31.72165 11.755024 36.76572 1.8473704
## 38 32.86533 11.984418 37.04436 3.4523886
## 39 32.74937 9.954976 37.38831 4.6504913
## 40 32.56723 12.489013 36.37148 4.2224362
## 41 32.07055 11.733106 37.53429 4.6712755
## 42 33.01955 10.634561 37.49669 4.6461200
## 43 33.79204 12.507525 37.14286 4.2144951
## 44 32.89398 11.529878 36.88809 4.6432585
## 45 32.04449 13.414935 36.11244 2.2586864
## 46 34.55577 12.170525 39.13110 3.6631055
## 47 34.56456 13.146551 37.33545 3.8768752
## 48 32.72678 12.988510 36.46200 4.1132261
## 49 33.11722 11.864126 36.58273 3.2025312
## 50 31.66105 11.398064 36.59446 3.1983993
## 51 33.25634 13.858062 37.78026 5.9767681
## 52 33.90022 10.956791 37.26688 2.9526690
## 53 34.18777 10.320116 37.45341 2.0948917
## 54 33.76207 9.984514 35.93345 3.8554717
## 55 34.39016 12.645195 38.46832 2.8745969
## 56 33.92530 11.588655 35.25224 3.3920505
## 57 32.68823 13.761533 39.25293 2.9957612
## 58 34.30187 10.568295 36.17313 3.3152248
## 59 32.84393 11.832286 36.81401 3.4719191
## 60 33.75499 12.064157 37.27122 3.9705556
## 61 33.87978 12.495592 38.05261 4.6393203
## 62 33.07654 9.607315 36.49399 5.0812101
## 63 32.22730 13.728627 37.99703 4.8026306
## 64 32.78977 11.670066 37.40875 3.4146884
## 65 32.77261 13.276313 36.60078 3.4622988
## 66 34.37426 15.126994 37.15762 5.3775936
## 67 33.07872 12.695790 35.35844 4.0017863
## 68 32.80522 11.835476 36.37507 3.4395906
## 69 32.43076 11.306232 37.68040 2.7795207
## 70 32.17910 11.187539 40.00518 3.5526498
## 71 33.15418 11.887494 36.26500 2.6022871
## 72 34.33590 12.228935 36.15719 4.6943223
## 73 32.38625 10.674653 38.00658 3.4015223
## 74 32.80870 12.817113 37.03154 3.8515788
## 75 33.87974 13.587806 38.26035 3.2581129
## 76 32.04984 12.238057 38.73086 3.1205689
## 77 33.55521 11.551821 36.62883 2.8379432
## 78 33.14208 11.433380 35.89243 4.4702826
## 79 32.59718 10.889567 38.21257 4.4420543
## 80 33.16714 11.928842 36.91463 3.1649440
## 81 31.51474 12.595671 39.60038 3.7517346
## 82 34.59402 10.947259 35.88399 3.1597544
## 83 33.50137 13.898082 37.05891 4.1305628
## 84 32.40237 10.875560 37.78114 1.9140899
## 85 34.65549 10.338073 36.15726 4.3966519
## 86 31.80930 11.634668 36.18254 5.1133195
## 87 33.87778 12.517666 37.15192 2.6699416
## 88 34.44787 10.607724 36.81910 3.3664637
## 89 31.95630 12.828893 36.95162 4.5712130
## 90 32.60558 12.068816 36.10500 3.9174511
## 91 32.49145 12.530357 37.87522 2.4761391
## 92 33.61602 13.516284 36.77312 4.1255844
## 93 33.47160 11.662263 36.05024 3.9972554
## 94 33.71065 13.664748 37.72439 1.3626741
## 95 32.19772 11.830231 36.63386 4.1933246
## 96 32.46121 13.291143 38.63363 3.8710034
## 97 33.79039 11.942341 38.06341 4.0818027
## 98 34.18382 13.349913 37.82739 4.2520061
## 99 32.28867 12.020112 39.07440 3.9117087
## 100 33.82635 12.084092 35.89036 3.0216718
## 101 32.49839 13.410759 35.99049 3.1846187
## 102 31.88541 11.281931 37.38532 2.8772249
## 103 32.42570 11.448902 37.58019 2.5869680
## 104 33.43783 12.595420 36.26203 2.9696402
## 105 31.38959 10.994224 38.07445 3.4288599
## 106 33.46870 13.085506 35.84583 2.9269402
## 107 32.29176 12.190474 36.15246 3.7818230
## 108 32.06377 10.719150 37.71251 3.0047425
## 109 33.15570 12.931550 38.16644 3.8544739
## 110 33.35687 13.452129 38.50301 3.3188223
## 111 31.85307 12.149375 37.32533 3.3618146
## 112 32.01230 12.178331 37.71599 3.7225612
## 113 32.38845 11.010482 38.41504 3.5435471
## 114 32.65318 11.602532 37.30969 2.7894615
## 115 32.93134 12.732212 35.60082 5.4859767
## 116 33.23561 11.223369 37.69230 2.5941897
## 117 33.92579 12.011022 36.70105 2.7534242
## 118 33.05926 11.725910 35.99910 5.0048206
## 119 32.40173 12.089310 38.30991 3.8733376
## 120 33.88994 13.068639 37.54052 3.7987253
## 121 34.56938 12.854990 35.00748 3.2927977
## 122 33.70161 11.564022 37.67321 4.7161050
## 123 33.26833 11.113330 37.38795 4.0187266
## 124 31.35848 12.809883 36.54967 3.6377013
## 125 33.01479 11.761172 37.57016 3.8341697
## 126 31.57613 12.579894 37.09326 4.5319866
## 127 32.65727 11.957923 36.63465 4.1060552
## 128 34.70932 10.651794 37.14601 3.2182654
## 129 34.53666 12.752077 36.71414 3.2836635
## 130 32.77172 11.540832 37.52642 2.9240207
## 131 33.70040 11.924395 37.24503 3.9052503
## 132 32.43977 12.424130 38.94883 4.9203184
## 133 34.31217 11.810587 37.41413 2.4735961
## 134 32.45518 12.759169 36.59911 4.1312766
## 135 33.54098 11.851891 37.42455 1.7677307
## 136 33.35840 12.703688 36.10091 2.7241082
## 137 32.68613 12.215252 36.59436 3.8971159
## 138 34.55829 11.281445 36.49441 2.4916715
## 139 33.54775 10.735363 37.45837 3.8634254
## 140 31.95490 10.963132 37.32728 3.5786339
## 141 31.06622 11.735095 36.59937 3.9588923
## 142 31.85125 12.418962 35.97765 3.2517418
## 143 32.60928 10.537308 35.73055 3.9143847
## 144 32.11512 11.919242 39.29404 1.4435151
## 145 33.92462 11.911416 38.27470 2.9100379
## 146 33.47719 12.488067 36.51838 3.3455710
## 147 32.11640 12.380695 37.23200 3.0895278
## 148 32.25590 10.480507 37.33867 4.5141224
## 149 32.69239 12.296518 36.95156 1.8258847
## 150 32.38473 10.861604 36.58444 3.9936565
## 151 34.33873 10.716355 38.30720 2.6521583
## 152 32.88710 12.387184 37.43116 6.4012288
## 153 32.51022 10.984836 37.39650 5.3912751
## 154 31.94540 12.965761 36.96639 6.0766536
## 155 36.13966 12.050267 36.95964 3.8648607
## 156 32.44952 13.457725 37.23881 2.9414108
## 157 32.29464 12.443048 37.32785 5.0848613
## 158 34.60331 12.207298 33.91385 6.9226893
## 159 33.59852 11.586320 39.09463 3.6043986
## 160 34.56868 11.378087 38.30447 3.7849321
## 161 32.83810 12.364342 38.03911 3.3091823
## 162 33.50371 12.399436 35.01281 0.9686221
## 163 33.30188 12.542481 38.31136 3.7685620
## 164 30.87948 13.280432 36.93616 3.5851606
## 165 33.15425 11.795887 37.65862 4.5203534
## 166 32.04780 12.718039 37.66111 3.6758488
## 167 33.63080 12.039648 38.92409 2.8730075
## 168 34.04664 12.474455 35.03786 4.0557760
## 169 33.64418 13.160020 36.40775 3.0151753
## 170 32.65462 11.052324 37.63301 4.7171025
## 171 33.42875 10.636761 37.57884 2.9263964
## 172 31.86483 13.443406 36.87832 2.3610869
## 173 34.48239 13.283033 35.90730 4.9687427
## 174 32.52977 11.747732 36.93988 0.8015157
## 175 33.43223 10.859609 38.83567 3.6692256
## 176 33.30857 11.691686 37.48091 1.7157772
## 177 32.33264 11.548761 38.57652 4.7735030
## 178 34.71345 11.724002 36.81386 4.0878373
## 179 32.63588 12.178573 35.67426 4.1317550
## 180 33.07570 12.319845 37.81916 3.4427992
## 181 32.23015 11.084361 37.95968 4.7240274
## 182 34.14286 13.177775 38.85604 3.2309738
## 183 32.49720 12.832803 37.67924 2.9722714
## 184 33.12240 11.509048 37.25306 3.1823297
## 185 33.08853 11.857663 36.08693 4.8063496
## 186 32.53380 12.293366 37.06462 3.6203650
## 187 32.48426 10.933252 36.54551 3.2613247
## 188 32.54346 13.332839 37.96439 3.5974600
## 189 32.28312 10.902556 36.09424 4.7892016
## 190 32.20080 12.276982 38.23261 3.3164647
## 191 34.71332 12.038808 37.63530 4.6324609
## 192 32.71251 11.724474 37.15315 3.3084430
## 193 33.69490 11.202670 35.49396 4.0159866
## 194 31.57020 13.378063 36.33780 4.3693668
## 195 33.45948 11.388613 37.90914 2.5666398
## 196 31.82100 10.771074 37.27864 3.5190324
## 197 32.73322 11.818572 37.10203 1.5038544
## 198 32.40715 13.808799 37.42677 5.0399553
## 199 33.50609 11.659833 37.28139 4.4787126
## 200 30.83643 13.100110 35.90772 3.3616130
## 201 34.87849 13.067896 36.67822 1.9207155
## 202 34.00721 12.494323 36.04546 4.3307145
## 203 31.52575 11.340036 37.03951 3.8112482
## 204 31.04722 11.199661 38.68871 3.0887640
## 205 34.59578 11.332488 35.45986 4.5416953
## 206 34.96761 13.919494 37.95201 5.0666969
## 207 32.29525 11.031358 38.25298 3.1074687
## 208 33.32424 11.084584 36.77602 4.7469897
## 209 32.90345 10.542645 35.53386 3.0918269
## 210 32.55949 11.797796 37.77737 3.1956258
## 211 31.76562 12.442617 38.13171 3.8502796
## 212 34.08165 12.104542 36.05965 3.9745225
## 213 33.30443 12.378490 38.76430 3.8438489
## 214 34.33075 13.722454 35.77312 2.9090085
## 215 32.07895 12.725909 36.54466 1.1390935
## 216 33.60580 13.685119 34.89198 2.6852848
## 217 32.74515 10.012583 38.35496 3.1089114
## 218 32.12236 11.435534 36.22356 4.8528424
## 219 32.53083 12.354607 37.12235 2.3075524
## 220 31.73664 10.748534 35.73871 4.8355287
## 221 34.11757 11.591872 37.74362 3.6785894
## 222 33.63662 11.236507 37.67502 5.2547089
## 223 34.33486 11.109456 38.58585 3.8928915
## 224 34.81498 12.114945 36.28872 4.3894552
## 225 34.64267 11.866481 37.71777 4.0033250
## 226 32.83694 10.256549 36.14391 0.7895199
## 227 32.29965 12.168596 37.07362 4.4033698
## 228 31.94802 13.085357 37.60565 2.6485968
## 229 32.72732 13.013376 36.65128 2.3678482
## 230 33.94624 10.983977 37.95149 3.0507130
## 231 32.35148 13.105159 35.57484 3.6414972
## 232 34.17375 12.144749 37.25803 3.3973631
## 233 32.97518 13.909916 37.79224 4.2976865
## 234 32.00475 11.395209 37.33281 3.8033650
## 235 34.19706 13.033566 37.07680 2.6334200
## 236 33.17720 11.622777 35.96890 3.6340937
## 237 32.69324 12.600750 37.37012 3.4670141
## 238 31.62536 13.187911 37.06709 1.4943109
## 239 31.26065 13.266760 36.97120 2.2672511
## 240 31.72077 11.752343 38.57361 5.0239342
## 241 32.92261 11.568116 36.90938 2.4717507
## 242 32.68625 12.638572 36.09722 4.2977375
## 243 34.05095 11.388645 39.08156 2.4369589
## 244 32.45455 11.822983 36.94613 3.6569839
## 245 31.28345 12.725677 35.96567 5.0002434
## 246 32.98003 11.201160 37.68934 2.4128310
## 247 31.90963 11.347264 36.32365 5.3143541
## 248 34.40241 14.220979 37.52320 4.0777751
## 249 32.95976 11.546276 36.94795 3.2750707
## 250 33.78016 11.917636 36.84473 3.6349960
## 251 32.67294 12.276057 37.19279 3.9824715
## 252 32.72852 10.131712 34.84561 3.2877018
## 253 33.40992 12.026942 36.13389 2.3133499
## 254 31.72420 13.172287 36.19975 3.5578137
## 255 32.71112 12.326291 36.67388 3.3502793
## 256 33.13666 13.891313 39.22071 2.9070949
## 257 34.37939 12.930929 36.36025 3.7927120
## 258 35.53090 11.379257 36.63610 4.0294538
## 259 33.24727 14.069382 38.99332 4.9784758
## 260 32.09611 10.804891 37.37276 2.6995621
## 261 35.03928 14.426491 37.37418 3.9306153
## 262 32.55053 13.041245 36.65521 3.4562338
## 263 32.58249 11.739744 36.85481 2.1820170
## 264 33.29698 12.491059 38.23894 2.7095266
## 265 33.10834 12.892375 36.52739 4.5941169
## 266 33.90272 11.668867 37.34127 4.2569833
## 267 34.55528 11.777772 37.97983 3.7842731
## 268 33.73265 12.138794 36.85388 1.6234196
## 269 31.60051 12.222967 36.82275 3.4145062
## 270 34.31893 13.402332 37.29204 3.6060869
## 271 34.00649 12.956277 38.65509 3.2757337
## 272 33.54048 12.884125 36.22604 5.0072720
## 273 34.43643 13.325469 36.76860 3.3712581
## 274 33.55170 12.158585 36.57513 5.4539695
## 275 31.81862 11.226546 35.66994 3.7558694
## 276 32.36312 12.461135 37.74561 4.6642585
## 277 33.19157 9.846125 36.87631 3.8066709
## 278 32.19250 13.325412 36.89729 5.0499275
## 279 32.60790 13.677246 37.74470 2.8719475
## 280 32.26200 11.644970 37.02688 3.2367328
## 281 32.27185 13.485009 37.55088 3.0863373
## 282 33.79512 11.620997 38.41947 4.5596991
## 283 31.65481 13.014459 37.78904 3.0102098
## 284 33.07773 11.466984 35.67573 1.8092296
## 285 31.31235 11.684904 38.71708 3.5942951
## 286 32.87274 12.093966 36.62077 3.0491957
## 287 33.70815 14.325655 35.72183 3.6343402
## 288 33.90857 12.914847 39.06886 1.4823596
## 289 32.31291 9.824402 35.74278 2.9213501
## 290 34.39433 12.807752 38.55103 1.8100799
## 291 32.42330 13.058278 37.26388 3.3731047
## 292 33.53940 10.534553 37.03479 2.2147975
## 293 33.37402 11.143433 35.94640 5.4544633
## 294 33.79476 10.982806 34.81063 3.2018017
## 295 33.77090 11.153966 37.24033 4.7294845
## 296 31.30919 11.947175 36.19083 3.2055298
## 297 33.61256 11.470565 37.06169 3.8025114
## 298 33.39826 11.037850 38.61733 4.1163405
## 299 33.62259 11.167357 35.62659 5.4625008
## 300 30.49254 11.562936 35.97656 1.4816166
## 301 31.90486 12.227728 36.98591 3.7714201
## 302 33.02642 13.186813 38.06693 2.8982996
## 303 32.97519 13.394452 37.80698 3.5690465
## 304 30.81620 11.851399 36.92504 1.0845853
## 305 33.91402 12.266504 36.57503 3.0234744
## 306 33.30267 13.459222 36.33952 5.5663849
## 307 31.91208 11.792972 36.25782 2.3951681
## 308 32.40856 10.985740 37.36839 3.5048335
## 309 32.64462 12.637557 36.51709 5.2266877
## 310 34.10228 8.508152 35.46240 1.8382107
## 311 33.24851 11.656592 36.54861 3.3634114
## 312 34.72908 11.966898 36.54760 2.9574488
## 313 30.39318 11.802986 36.31576 2.0838142
## 314 33.38411 12.677401 35.62253 3.6808473
## 315 32.87847 13.032535 37.87095 4.6937321
## 316 34.50142 12.447617 37.53453 4.0083522
## 317 33.56647 12.235659 37.27757 2.5320441
## 318 32.84879 10.973162 36.60951 2.8709869
## 319 33.53186 13.665770 36.90022 3.5156883
## 320 33.41907 13.391120 37.19419 4.0699166
## 321 32.49542 12.968326 38.29611 1.2004839
## 322 33.67403 12.968893 37.33311 3.2294509
## 323 33.26463 10.732131 36.14579 4.0865663
## 324 32.76246 10.952353 37.64629 4.0194704
## 325 33.47947 12.608889 37.22939 4.2059039
## 326 33.78521 13.039511 36.31273 2.0181946
## 327 33.21719 10.999684 38.44277 4.2438128
## 328 31.12809 13.278956 37.38718 4.6260753
## 329 33.36952 10.627949 38.04031 3.0029570
## 330 32.83789 13.185181 35.92160 1.8235952
## 331 30.57436 11.351049 37.08885 4.0783080
## 332 32.27459 12.954811 37.10882 3.6899166
## 333 33.14423 11.737041 37.93519 2.1901322
## 334 33.48552 11.887345 35.86245 3.2067567
## 335 31.97648 10.757131 36.59587 1.9770071
## 336 32.13386 11.612651 39.24880 3.3492454
## 337 32.30255 11.979061 38.26906 3.5328616
## 338 31.82798 12.461147 37.42900 2.9747368
## 339 32.01807 10.079463 38.07066 2.6181653
## 340 32.99746 12.589241 37.33224 2.8040137
## 341 31.81643 14.288015 36.77386 2.9644979
## 342 34.46151 11.917116 37.76669 4.3508878
## 343 32.34280 11.409645 35.77778 3.8724320
## 344 32.30275 12.815393 37.95781 4.6154263
## 345 33.06644 11.673229 37.84066 2.7272095
## 346 33.89464 10.610537 37.97739 3.5371239
## 347 32.76566 12.506548 35.82347 3.1265095
## 348 33.76981 11.304462 37.83397 5.1378167
## 349 31.81248 10.886921 34.89783 3.1286389
## 350 32.00850 12.095889 36.37751 3.1789524
## 351 33.30434 12.692661 37.33359 3.8273759
## 352 32.18984 11.386776 38.19748 4.8083204
## 353 34.93561 10.728419 36.88119 4.0485101
## 354 33.55165 11.936895 35.90025 4.5433324
## 355 32.38697 12.717995 35.12882 3.4810621
## 356 33.34451 10.969803 35.97458 2.6276250
## 357 33.67276 13.420546 37.76369 4.7943123
## 358 34.00207 11.854682 37.49189 2.7618619
## 359 32.65540 11.918860 35.71627 2.1596760
## 360 32.05426 13.149670 37.65040 4.1956144
## 361 33.22877 12.685394 36.04899 2.1394030
## 362 32.07759 10.347877 39.04516 3.4345597
## 363 33.98101 9.316289 36.91495 2.8684282
## 364 34.17952 12.581548 35.44426 3.1370690
## 365 32.60274 11.764448 37.92270 3.5258064
## 366 32.03055 12.644202 38.00183 5.0381075
## 367 33.10036 11.832112 36.84149 3.6122392
## 368 32.99060 10.441235 35.93896 2.8950752
## 369 34.38582 12.729720 36.23211 5.7059407
## 370 34.35720 9.477778 37.90601 5.0470226
## 371 33.70511 10.163179 37.76304 4.7789736
## 372 32.40430 11.608998 38.11046 2.9665589
## 373 31.82935 11.268259 36.95697 2.6689198
## 374 31.36621 11.163160 37.08832 3.6203546
## 375 31.44745 10.101632 38.04345 4.2382962
## 376 33.58295 12.761531 36.90819 2.4793398
## 377 32.39742 12.055340 37.68547 3.5069676
## 378 35.03745 11.935935 35.78392 3.3101503
## 379 32.78494 12.451200 36.66579 3.5358025
## 380 33.97172 12.284467 38.29573 1.1304770
## 381 33.38599 12.782172 35.55077 3.2287177
## 382 33.55656 12.960307 37.95195 3.3459223
## 383 33.58737 9.953995 37.34574 3.2156668
## 384 34.18818 13.130022 35.42933 3.7905521
## 385 33.59396 11.520567 36.18913 3.5612153
## 386 33.23627 10.972554 34.57403 2.9316195
## 387 33.20892 13.531913 38.95246 3.0465406
## 388 33.63781 12.039502 34.48718 2.7392005
## 389 33.59049 10.942070 36.17049 2.7839631
## 390 34.19551 12.664193 37.02715 4.3304074
## 391 35.86024 11.730661 36.88215 3.4162100
## 392 33.48193 11.918670 37.31770 3.3363394
## 393 33.25824 11.514949 37.12804 4.6628453
## 394 32.31986 12.418113 36.15534 3.2220808
## 395 32.43084 13.887275 38.38196 3.7729690
## 396 31.44597 12.846499 37.86922 3.4201495
## 397 35.74267 10.889828 35.56544 6.1151989
## 398 34.01262 12.914570 36.04620 3.4880300
## 399 34.14039 11.568527 38.91875 4.0828553
## 400 32.37799 11.971751 37.19937 2.8296996
## 401 33.17233 13.078692 37.32982 5.4054065
## 402 33.24732 11.956426 36.51735 3.4517507
## 403 33.59891 13.252737 37.30596 2.9355773
## 404 33.08530 13.093537 38.31565 4.7503601
## 405 32.27844 12.527472 36.68837 3.5314023
## 406 33.44155 11.235969 37.05262 3.9044794
## 407 32.86530 12.074830 35.56917 2.3990798
## 408 31.52620 12.045332 38.50588 2.8477090
## 409 33.00085 11.230743 36.99529 3.7817036
## 410 32.08838 11.907844 35.18912 4.3497784
## 411 33.26544 13.052210 38.77567 4.5742877
## 412 32.99257 13.004362 36.98504 4.6204164
## 413 33.86319 11.523523 35.93805 3.0130325
## 414 32.59209 10.314718 36.72903 4.7911087
## 415 32.38103 12.433129 37.62691 4.3340014
## 416 31.51712 10.745189 38.79123 1.4288239
## 417 33.45430 11.016756 37.63731 4.1370004
## 418 32.21553 12.216855 36.95396 2.9105308
## 419 31.67392 12.329147 37.07437 3.9824623
## 420 33.71755 10.806966 36.01232 3.7012292
## 421 33.21547 12.135101 37.14209 5.8405059
## 422 31.57414 12.941556 36.72528 4.5603961
## 423 33.89457 13.300299 36.39368 4.4900021
## 424 33.12869 10.398458 36.68339 3.8598180
## 425 34.37033 11.887800 37.86145 3.0466202
## 426 34.08026 11.591440 36.45690 4.6528544
## 427 31.42523 13.271475 37.23985 4.0221029
## 428 33.62531 12.988221 39.67259 3.9694178
## 429 31.86274 14.039867 37.02227 3.7382252
## 430 33.29259 11.906508 38.42287 3.3766875
## 431 33.74923 11.137140 38.40137 4.5955227
## 432 34.14497 12.902665 36.61120 2.2239935
## 433 31.12397 12.386516 35.63211 4.2884868
## 434 34.27825 11.822722 36.30855 2.1173825
## 435 33.66662 10.985764 36.35250 0.9364976
## 436 32.25997 14.132893 37.02348 3.7620704
## 437 35.43317 11.912210 36.08964 4.0009636
## 438 31.96732 11.481587 39.24096 3.5325172
## 439 32.14906 10.047315 37.18145 3.5350884
## 440 33.91884 12.428737 37.30536 4.1582147
## 441 33.20062 11.965980 36.83154 3.5490361
## 442 32.53677 11.121366 36.97937 4.1292547
## 443 34.08366 8.668350 35.90676 2.2524460
## 444 33.02502 12.504220 37.64584 4.0513825
## 445 31.26810 12.132509 35.45680 3.0720761
## 446 32.21292 11.732991 35.63395 4.3318630
## 447 33.49951 11.946591 36.48633 3.9378626
## 448 32.90485 12.556108 37.80551 0.2699011
## 449 32.20465 12.480702 37.68029 3.2794663
## 450 32.67515 12.594194 37.68388 2.5717778
## 451 32.99839 10.946842 37.64781 3.8260306
## 452 33.94312 11.484199 36.83937 2.4024538
## 453 33.55211 11.120871 36.80838 4.0278138
## 454 33.67683 10.971392 37.72237 3.6293399
## 455 32.64195 11.588949 36.32214 3.1896099
## 456 33.42121 10.706642 35.76615 3.3939750
## 457 32.76708 11.076259 34.77975 2.5749485
## 458 33.11995 12.953263 37.03428 3.4720214
## 459 35.37188 10.572467 36.86218 4.1983491
## 460 33.97608 11.658037 37.42528 2.0863481
## 461 34.03416 13.592513 36.83866 3.6059339
## 462 32.77049 11.371767 35.26150 4.0343861
## 463 33.50381 11.233415 37.21115 2.3205502
## 464 31.87455 10.290351 36.92976 3.4910933
## 465 32.53324 14.121784 38.40633 5.3200939
## 466 34.85131 12.415542 37.67232 3.1305385
## 467 34.21146 10.770249 34.64980 4.9852050
## 468 33.45962 12.664391 36.36684 1.7269620
## 469 34.20054 12.667809 37.48705 3.7016223
## 470 31.16951 13.970181 36.67395 1.7851739
## 471 32.51820 11.509253 36.59929 3.0226758
## 472 34.52302 11.405770 36.37827 4.0412450
## 473 33.66599 12.263718 38.86023 3.1395269
## 474 31.60984 12.710701 36.16646 2.5628188
## 475 33.70089 13.471578 37.07164 2.3790765
## 476 33.81173 11.186809 36.29889 4.3019965
## 477 34.33668 11.246813 38.68258 2.0947617
## 478 31.06133 12.357638 36.16604 4.0893308
## 479 33.06977 11.764326 36.87503 3.5160510
## 480 34.60624 11.761884 38.12652 1.8208106
## 481 34.23824 11.550300 35.76933 4.1831437
## 482 32.04781 12.482670 35.53602 3.3939028
## 483 30.97168 11.731364 36.07455 4.4263641
## 484 33.60685 12.214074 37.19843 2.9052384
## 485 33.44813 11.903757 36.87454 2.7827578
## 486 33.36938 12.222484 36.35523 3.4470178
## 487 33.45230 12.005916 36.53410 4.7122336
## 488 32.90469 11.913745 36.05865 1.2281124
## 489 35.63085 12.125402 38.18776 4.0190514
## 490 32.24635 11.305551 37.13313 1.7073897
## 491 34.69559 11.608997 37.68488 3.1630919
## 492 34.34392 11.693058 36.81293 3.4470929
## 493 33.68094 11.201570 37.83545 2.2088137
## 494 32.06091 12.625433 35.53914 5.4123578
## 495 33.43110 13.350632 37.96597 2.7688519
## 496 33.23766 13.566160 36.41798 3.7465730
## 497 34.70253 11.695736 37.19027 3.5765259
## 498 32.64678 11.499409 38.33258 4.9582645
## 499 33.32250 12.391423 36.84009 2.3364847
## 500 33.71598 12.418808 35.77102 2.7351596
## Yearly.Amount.Spent Categoria.Cliente
## 1 587.9511 Platino
## 2 392.2049 Bronce
## 3 487.5475 Platino
## 4 581.8523 Platino
## 5 599.4061 Platino
## 6 637.1024 Oro
## 7 521.5722 Platino
## 8 549.9041 Platino
## 9 570.2004 Platino
## 10 427.1994 Platino
## 11 492.6060 Platino
## 12 522.3374 Platino
## 13 408.6404 Platino
## 14 573.4159 Platino
## 15 470.4527 Platino
## 16 461.7807 Platino
## 17 457.8477 Platino
## 18 407.7045 Platino
## 19 452.3157 Platino
## 20 605.0610 Oro
## 21 534.7057 Platino
## 22 419.9388 Platino
## 23 436.5156 Platino
## 24 519.3410 Platino
## 25 700.9171 Oro
## 26 423.1800 Platino
## 27 619.8956 Oro
## 28 486.8389 Platino
## 29 529.5377 Platino
## 30 554.7221 Platino
## 31 497.5867 Platino
## 32 447.6879 Platino
## 33 588.7126 Platino
## 34 491.0732 Platino
## 35 507.4418 Platino
## 36 521.8836 Platino
## 37 347.7769 Bronce
## 38 490.7386 Platino
## 39 478.1703 Platino
## 40 537.8462 Platino
## 41 532.7518 Platino
## 42 501.8744 Platino
## 43 591.1972 Platino
## 44 547.2443 Platino
## 45 448.2298 Platino
## 46 549.8606 Platino
## 47 593.9150 Platino
## 48 563.6729 Platino
## 49 479.7319 Platino
## 50 416.3584 Platino
## 51 725.5848 Oro
## 52 442.6673 Platino
## 53 384.6266 Bronce
## 54 451.4574 Platino
## 55 522.4041 Platino
## 56 483.6733 Platino
## 57 520.8988 Platino
## 58 453.1695 Platino
## 59 496.6507 Platino
## 60 547.3651 Platino
## 61 616.8515 Oro
## 62 507.2126 Platino
## 63 613.5993 Oro
## 64 483.1597 Platino
## 65 540.2634 Platino
## 66 765.5185 Oro
## 67 553.6015 Platino
## 68 469.3109 Platino
## 69 408.6202 Platino
## 70 451.5757 Platino
## 71 444.9666 Platino
## 72 595.8228 Platino
## 73 418.1501 Platino
## 74 534.7772 Platino
## 75 578.2416 Platino
## 76 478.7194 Platino
## 77 444.2859 Platino
## 78 544.7799 Platino
## 79 488.7861 Platino
## 80 475.7591 Platino
## 81 489.8125 Platino
## 82 462.8976 Platino
## 83 596.4302 Platino
## 84 338.3199 Bronce
## 85 533.5149 Platino
## 86 536.7719 Platino
## 87 487.3793 Platino
## 88 473.7290 Platino
## 89 547.1259 Platino
## 90 505.1133 Platino
## 91 449.0703 Platino
## 92 611.0000 Oro
## 93 515.8288 Platino
## 94 439.0748 Platino
## 95 514.0890 Platino
## 96 543.3402 Platino
## 97 521.1430 Platino
## 98 614.7153 Oro
## 99 507.3901 Platino
## 100 495.2994 Platino
## 101 518.0646 Platino
## 102 390.1033 Bronce
## 103 420.7377 Platino
## 104 492.1051 Platino
## 105 410.0696 Platino
## 106 497.5137 Platino
## 107 494.5519 Platino
## 108 378.3309 Bronce
## 109 570.4517 Platino
## 110 549.0082 Platino
## 111 459.2851 Platino
## 112 492.9451 Platino
## 113 424.7626 Platino
## 114 422.4268 Platino
## 115 642.1016 Oro
## 116 413.3718 Platino
## 117 479.2311 Platino
## 118 593.0772 Platino
## 119 506.5473 Platino
## 120 571.3075 Platino
## 121 576.3112 Platino
## 122 576.8025 Platino
## 123 514.2395 Platino
## 124 495.1760 Platino
## 125 514.3366 Platino
## 126 541.2266 Platino
## 127 516.8316 Platino
## 128 468.4457 Platino
## 129 548.2803 Platino
## 130 431.6177 Platino
## 131 552.9403 Platino
## 132 573.3062 Platino
## 133 452.6273 Platino
## 134 542.7116 Platino
## 135 407.8040 Platino
## 136 482.3536 Platino
## 137 529.2301 Platino
## 138 433.0488 Platino
## 139 476.1914 Platino
## 140 439.9979 Platino
## 141 448.9333 Platino
## 142 472.9922 Platino
## 143 463.9235 Platino
## 144 350.0582 Bronce
## 145 460.0613 Platino
## 146 505.7711 Platino
## 147 463.4850 Platino
## 148 479.7319 Platino
## 149 424.1855 Platino
## 150 465.8893 Platino
## 151 426.7752 Platino
## 152 684.1634 Oro
## 153 555.8926 Platino
## 154 657.0199 Oro
## 155 595.8038 Platino
## 156 503.9784 Platino
## 157 586.1559 Platino
## 158 744.2219 Oro
## 159 512.8254 Platino
## 160 528.2238 Platino
## 161 468.9135 Platino
## 162 357.5914 Bronce
## 163 536.4231 Platino
## 164 490.2066 Platino
## 165 550.0476 Platino
## 166 513.4506 Platino
## 167 497.8119 Platino
## 168 578.9863 Platino
## 169 506.5364 Platino
## 170 501.7492 Platino
## 171 421.9668 Platino
## 172 439.8913 Platino
## 173 666.1256 Oro
## 174 298.7620 Bronce
## 175 465.1766 Platino
## 176 373.8857 Bronce
## 177 532.7175 Platino
## 178 554.9008 Platino
## 179 537.7732 Platino
## 180 501.1002 Platino
## 181 517.1651 Platino
## 182 557.5293 Platino
## 183 493.7192 Platino
## 184 452.1226 Platino
## 185 577.2735 Platino
## 186 485.9231 Platino
## 187 425.7451 Platino
## 188 537.2151 Platino
## 189 524.6380 Platino
## 190 478.8854 Platino
## 191 612.3852 Oro
## 192 476.7667 Platino
## 193 505.1196 Platino
## 194 545.9455 Platino
## 195 434.0217 Platino
## 196 424.6753 Platino
## 197 352.5501 Bronce
## 198 662.9611 Oro
## 199 560.5602 Platino
## 200 467.5019 Platino
## 201 504.8704 Platino
## 202 590.5627 Platino
## 203 443.9656 Platino
## 204 392.4974 Bronce
## 205 568.7176 Platino
## 206 712.3963 Oro
## 207 413.2960 Platino
## 208 562.0820 Platino
## 209 412.0129 Platino
## 210 468.6685 Platino
## 211 496.5541 Platino
## 212 548.5185 Platino
## 213 536.1309 Platino
## 214 558.4273 Platino
## 215 357.8637 Bronce
## 216 529.0567 Platino
## 217 387.3571 Bronce
## 218 528.9336 Platino
## 219 420.9162 Platino
## 220 496.9334 Platino
## 221 519.3730 Platino
## 222 591.4377 Platino
## 223 502.4098 Platino
## 224 604.3348 Oro
## 225 555.0684 Platino
## 226 256.6706 Bronce
## 227 547.1110 Platino
## 228 461.9209 Platino
## 229 458.3769 Platino
## 230 436.2835 Platino
## 231 532.9352 Platino
## 232 512.5525 Platino
## 233 630.4228 Oro
## 234 463.7460 Platino
## 235 493.1802 Platino
## 236 501.2092 Platino
## 237 501.9283 Platino
## 238 376.3369 Bronce
## 239 421.3266 Platino
## 240 538.7749 Platino
## 241 398.1635 Bronce
## 242 571.4710 Platino
## 243 451.6286 Platino
## 244 490.6004 Platino
## 245 591.7811 Platino
## 246 409.0705 Platino
## 247 563.4460 Platino
## 248 647.6195 Oro
## 249 448.3404 Platino
## 250 518.7865 Platino
## 251 523.6339 Platino
## 252 393.8574 Bronce
## 253 426.1545 Platino
## 254 503.3879 Platino
## 255 482.6025 Platino
## 256 524.7976 Platino
## 257 574.6548 Platino
## 258 574.7472 Platino
## 259 660.4252 Oro
## 260 375.3985 Bronce
## 261 640.1877 Oro
## 262 514.0098 Platino
## 263 376.4968 Bronce
## 264 484.5198 Platino
## 265 614.7296 Oro
## 266 567.4750 Platino
## 267 554.0031 Platino
## 268 399.9839 Bronce
## 269 479.1729 Platino
## 270 585.9318 Platino
## 271 540.9957 Platino
## 272 628.0478 Oro
## 273 582.4919 Platino
## 274 640.7862 Oro
## 275 446.4187 Platino
## 276 570.6301 Platino
## 277 423.3083 Platino
## 278 616.6603 Oro
## 279 530.3625 Platino
## 280 442.3631 Platino
## 281 511.9799 Platino
## 282 560.4438 Platino
## 283 475.2634 Platino
## 284 374.2697 Bronce
## 285 463.5914 Platino
## 286 471.6029 Platino
## 287 626.0187 Oro
## 288 432.4721 Platino
## 289 356.6156 Bronce
## 290 467.4278 Platino
## 291 503.2174 Platino
## 292 378.4736 Bronce
## 293 584.2183 Platino
## 294 451.7279 Platino
## 295 557.6341 Platino
## 296 432.7207 Platino
## 297 506.4239 Platino
## 298 510.1598 Platino
## 299 587.5748 Platino
## 300 282.4712 Bronce
## 301 473.9499 Platino
## 302 489.9081 Platino
## 303 541.9722 Platino
## 304 266.0863 Bronce
## 305 494.6872 Platino
## 306 689.7876 Oro
## 307 387.5347 Bronce
## 308 441.8966 Platino
## 309 604.8413 Oro
## 310 302.1895 Bronce
## 311 479.6148 Platino
## 312 506.1323 Platino
## 313 319.9289 Bronce
## 314 528.3092 Platino
## 315 610.1280 Oro
## 316 584.1059 Platino
## 317 466.4212 Platino
## 318 404.8245 Platino
## 319 564.7910 Platino
## 320 596.5167 Platino
## 321 368.6548 Bronce
## 322 542.4125 Platino
## 323 478.2621 Platino
## 324 473.3605 Platino
## 325 559.1990 Platino
## 326 447.1876 Platino
## 327 505.2301 Platino
## 328 557.2527 Platino
## 329 422.3687 Platino
## 330 445.0622 Platino
## 331 442.0644 Platino
## 332 533.0401 Platino
## 333 424.2028 Platino
## 334 498.6356 Platino
## 335 330.5944 Bronce
## 336 443.4419 Platino
## 337 478.6009 Platino
## 338 440.0027 Platino
## 339 357.7831 Bronce
## 340 476.1392 Platino
## 341 501.1225 Platino
## 342 592.6885 Platino
## 343 486.0834 Platino
## 344 576.0252 Platino
## 345 442.7229 Platino
## 346 461.7910 Platino
## 347 488.3875 Platino
## 348 593.1564 Platino
## 349 392.8103 Bronce
## 350 443.1972 Platino
## 351 535.4808 Platino
## 352 533.3966 Platino
## 353 532.1274 Platino
## 354 558.9481 Platino
## 355 508.7719 Platino
## 356 403.7669 Platino
## 357 640.5841 Oro
## 358 461.6283 Platino
## 359 382.4161 Bronce
## 360 561.8747 Platino
## 361 444.5761 Platino
## 362 401.0331 Platino
## 363 384.3261 Bronce
## 364 527.7830 Platino
## 365 482.1450 Platino
## 366 594.2745 Platino
## 367 502.0925 Platino
## 368 407.6572 Platino
## 369 708.9352 Oro
## 370 531.9616 Platino
## 371 521.2408 Platino
## 372 447.3690 Platino
## 373 385.1523 Bronce
## 374 430.5889 Platino
## 375 418.6027 Platino
## 376 478.9514 Platino
## 377 483.7965 Platino
## 378 538.9420 Platino
## 379 486.1638 Platino
## 380 385.0950 Bronce
## 381 527.7838 Platino
## 382 547.1907 Platino
## 383 410.6029 Platino
## 384 583.9778 Platino
## 385 474.5323 Platino
## 386 414.9351 Platino
## 387 550.8134 Platino
## 388 458.7811 Platino
## 389 407.5422 Platino
## 390 581.3089 Platino
## 391 546.5567 Platino
## 392 503.1751 Platino
## 393 549.1316 Platino
## 394 482.8310 Platino
## 395 557.6083 Platino
## 396 484.8770 Platino
## 397 669.9871 Oro
## 398 547.7100 Platino
## 399 537.8253 Platino
## 400 408.2169 Platino
## 401 663.0748 Oro
## 402 506.3759 Platino
## 403 528.4193 Platino
## 404 632.1236 Oro
## 405 488.2703 Platino
## 406 508.7357 Platino
## 407 411.1870 Platino
## 408 409.0945 Platino
## 409 467.8009 Platino
## 410 512.1659 Platino
## 411 608.2718 Oro
## 412 589.0265 Platino
## 413 444.0538 Platino
## 414 493.1813 Platino
## 415 532.7248 Platino
## 416 275.9184 Bronce
## 417 511.0388 Platino
## 418 438.4177 Platino
## 419 475.7251 Platino
## 420 483.5432 Platino
## 421 663.8037 Oro
## 422 544.4093 Platino
## 423 630.1567 Oro
## 424 461.1122 Platino
## 425 491.9115 Platino
## 426 574.4157 Platino
## 427 530.7667 Platino
## 428 581.7988 Platino
## 429 556.2981 Platino
## 430 502.1328 Platino
## 431 556.1864 Platino
## 432 475.0716 Platino
## 433 486.9471 Platino
## 434 434.1442 Platino
## 435 304.1356 Bronce
## 436 571.2160 Platino
## 437 583.0796 Platino
## 438 445.7498 Platino
## 439 392.9923 Bronce
## 440 565.9944 Platino
## 441 499.1402 Platino
## 442 510.5394 Platino
## 443 308.5277 Bronce
## 444 561.5165 Platino
## 445 423.4705 Platino
## 446 513.1531 Platino
## 447 529.1945 Platino
## 448 314.4385 Bronce
## 449 478.5843 Platino
## 450 444.5822 Platino
## 451 475.0154 Platino
## 452 436.7206 Platino
## 453 521.1953 Platino
## 454 478.1831 Platino
## 455 432.4812 Platino
## 456 438.3037 Platino
## 457 388.9405 Bronce
## 458 534.7715 Platino
## 459 537.9158 Platino
## 460 407.8764 Platino
## 461 618.8460 Oro
## 462 502.7711 Platino
## 463 397.4206 Bronce
## 464 392.2852 Bronce
## 465 689.2357 Oro
## 466 543.1326 Platino
## 467 577.7360 Platino
## 468 436.5807 Platino
## 469 553.9947 Platino
## 470 427.3565 Platino
## 471 424.7288 Platino
## 472 541.0498 Platino
## 473 469.3831 Platino
## 474 444.5455 Platino
## 475 492.5568 Platino
## 476 535.3216 Platino
## 477 408.9583 Platino
## 478 487.5555 Platino
## 479 487.6462 Platino
## 480 402.1671 Platino
## 481 551.0230 Platino
## 482 497.3896 Platino
## 483 494.6386 Platino
## 484 479.2474 Platino
## 485 462.6565 Platino
## 486 515.5025 Platino
## 487 576.4776 Platino
## 488 357.8580 Bronce
## 489 597.7399 Platino
## 490 327.3780 Bronce
## 491 510.4014 Platino
## 492 510.5015 Platino
## 493 403.8195 Platino
## 494 627.6033 Oro
## 495 510.6618 Platino
## 496 573.8474 Platino
## 497 529.0490 Platino
## 498 551.6201 Platino
## 499 456.4695 Platino
## 500 497.7786 PlatinoEn base a la facturación anual, se clasificaron los clientes en tres categorías distintas:
1. Oro. Aquellos que su facturación es USD600,000 o superior;
2. Platino. Aquellos que su facturación es USD400,000 o superior;
3. Bronce. Aquellos que su facturación es inferior a los USD400,000.
4. Modelos de clasificación
#Conversión de categorías a números para SVM
dataset$Categoria.Cliente.Num[dataset$Categoria.Cliente == "Oro" ] = 1
dataset$Categoria.Cliente.Num[dataset$Categoria.Cliente == "Platino" ] = 2
dataset$Categoria.Cliente.Num[dataset$Categoria.Cliente == "Bronce" ] = 3#Data split
library(caret)## Loading required package: lattice## Loading required package: ggplot2trainIndex = createDataPartition(dataset$Yearly.Amount.Spent, p=0.7, list=FALSE)
trainSet = dataset[trainIndex, ]
testSet = dataset[-trainIndex, ]4.1. LDA
4.1.1 Membresía
library(e1071)
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select#Modelo por LDA
lda.1=lda(formula = Categoria.Cliente ~ Length.of.Membership, data = trainSet)
#Predicción
prediccionesLDA.1 = predict(object = lda.1,
newdata = testSet)
cm.411 = confusionMatrix(as.factor(prediccionesLDA.1$class),as.factor(testSet$Categoria.Cliente))
cm.411## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 6 0 1
## Oro 0 4 4
## Platino 10 7 116
##
## Overall Statistics
##
## Accuracy : 0.8514
## 95% CI : (0.7836, 0.9044)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.1694
##
## Kappa : 0.4197
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.37500 0.36364 0.9587
## Specificity 0.99242 0.97080 0.3704
## Pos Pred Value 0.85714 0.50000 0.8722
## Neg Pred Value 0.92908 0.95000 0.6667
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.04054 0.02703 0.7838
## Detection Prevalence 0.04730 0.05405 0.8986
## Balanced Accuracy 0.68371 0.66722 0.66454.1.2. App
#Modelo por LDA
lda.2=lda(formula = Categoria.Cliente ~ Time.on.App, data = trainSet)
#Predicción
prediccionesLDA.2 = predict(object = lda.2,
newdata = testSet)
cm.412 = confusionMatrix(as.factor(prediccionesLDA.2$class),as.factor(testSet$Categoria.Cliente))
cm.412## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 2 0 1
## Oro 0 0 1
## Platino 14 11 119
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0.0961
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.12500 0.000000 0.98347
## Specificity 0.99242 0.992701 0.07407
## Pos Pred Value 0.66667 0.000000 0.82639
## Neg Pred Value 0.90345 0.925170 0.50000
## Prevalence 0.10811 0.074324 0.81757
## Detection Rate 0.01351 0.000000 0.80405
## Detection Prevalence 0.02027 0.006757 0.97297
## Balanced Accuracy 0.55871 0.496350 0.528774.1.3. Web
#Modelo por LDA
lda.3=lda(formula = Categoria.Cliente ~ Time.on.Website, data = trainSet)
#Predicción
prediccionesLDA.3 = predict(object = lda.3,
newdata = testSet)
cm.413 = confusionMatrix(as.factor(prediccionesLDA.3$class),as.factor(testSet$Categoria.Cliente))
cm.413## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 0 0 0
## Oro 0 0 0
## Platino 16 11 121
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.0000 0.00000 1.0000
## Specificity 1.0000 1.00000 0.0000
## Pos Pred Value NaN NaN 0.8176
## Neg Pred Value 0.8919 0.92568 NaN
## Prevalence 0.1081 0.07432 0.8176
## Detection Rate 0.0000 0.00000 0.8176
## Detection Prevalence 0.0000 0.00000 1.0000
## Balanced Accuracy 0.5000 0.50000 0.50004.1.4. Sesiones promedio
#Modelo por LDA
lda.4=lda(formula = Categoria.Cliente ~ Avg..Session.Length, data = trainSet)
#Predicción
prediccionesLDA.4 = predict(object = lda.4,
newdata = testSet)
cm.414 = confusionMatrix(as.factor(prediccionesLDA.4$class),as.factor(testSet$Categoria.Cliente))
cm.414## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 0 0 0
## Oro 0 0 0
## Platino 16 11 121
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.0000 0.00000 1.0000
## Specificity 1.0000 1.00000 0.0000
## Pos Pred Value NaN NaN 0.8176
## Neg Pred Value 0.8919 0.92568 NaN
## Prevalence 0.1081 0.07432 0.8176
## Detection Rate 0.0000 0.00000 0.8176
## Detection Prevalence 0.0000 0.00000 1.0000
## Balanced Accuracy 0.5000 0.50000 0.50004.1.5. Membresia + App
#Modelo por LDA
lda.5=lda(formula = Categoria.Cliente ~ Length.of.Membership + Time.on.App, data = trainSet)
#Predicción
prediccionesLDA.5 = predict(object = lda.5,
newdata = testSet)
cm.415 = confusionMatrix(as.factor(prediccionesLDA.5$class),as.factor(testSet$Categoria.Cliente))
cm.415## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 10 0 2
## Oro 0 8 0
## Platino 6 3 119
##
## Overall Statistics
##
## Accuracy : 0.9257
## 95% CI : (0.8709, 0.9623)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.0001496
##
## Kappa : 0.7347
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.62500 0.72727 0.9835
## Specificity 0.98485 1.00000 0.6667
## Pos Pred Value 0.83333 1.00000 0.9297
## Neg Pred Value 0.95588 0.97857 0.9000
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.06757 0.05405 0.8041
## Detection Prevalence 0.08108 0.05405 0.8649
## Balanced Accuracy 0.80492 0.86364 0.82514.1.6. Membresia + Website
#Modelo por LDA
lda.6=lda(formula = Categoria.Cliente ~ Length.of.Membership + Time.on.Website, data = trainSet)
#Predicción
prediccionesLDA.6 = predict(object = lda.6,
newdata = testSet)
cm.416 = confusionMatrix(as.factor(prediccionesLDA.6$class),as.factor(testSet$Categoria.Cliente))
cm.416## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 6 0 0
## Oro 0 3 4
## Platino 10 8 117
##
## Overall Statistics
##
## Accuracy : 0.8514
## 95% CI : (0.7836, 0.9044)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.1694
##
## Kappa : 0.3966
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.37500 0.27273 0.9669
## Specificity 1.00000 0.97080 0.3333
## Pos Pred Value 1.00000 0.42857 0.8667
## Neg Pred Value 0.92958 0.94326 0.6923
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.04054 0.02027 0.7905
## Detection Prevalence 0.04054 0.04730 0.9122
## Balanced Accuracy 0.68750 0.62177 0.65014.1.7.Membresia + Sesiones promedio
#Modelo por LDA
lda.7=lda(formula = Categoria.Cliente ~ Length.of.Membership + Avg..Session.Length, data = trainSet)
#Predicción
prediccionesLDA.7 = predict(object = lda.7,
newdata = testSet)
cm.417 = confusionMatrix(as.factor(prediccionesLDA.7$class),as.factor(testSet$Categoria.Cliente))
cm.417## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 5 0 0
## Oro 0 4 3
## Platino 11 7 118
##
## Overall Statistics
##
## Accuracy : 0.8581
## 95% CI : (0.7913, 0.91)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.1188
##
## Kappa : 0.4126
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.31250 0.36364 0.9752
## Specificity 1.00000 0.97810 0.3333
## Pos Pred Value 1.00000 0.57143 0.8676
## Neg Pred Value 0.92308 0.95035 0.7500
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.03378 0.02703 0.7973
## Detection Prevalence 0.03378 0.04730 0.9189
## Balanced Accuracy 0.65625 0.67087 0.65434.1.8. App + Website
#Modelo por LDA
lda.8=lda(formula = Categoria.Cliente ~ Time.on.App + Time.on.Website, data = trainSet)
#Predicción
prediccionesLDA.8 = predict(object = lda.8,
newdata = testSet)
cm.418 = confusionMatrix(as.factor(prediccionesLDA.8$class),as.factor(testSet$Categoria.Cliente))
cm.418## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 2 0 0
## Oro 0 0 1
## Platino 14 11 120
##
## Overall Statistics
##
## Accuracy : 0.8243
## 95% CI : (0.7533, 0.8819)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.4666
##
## Kappa : 0.1084
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.12500 0.000000 0.99174
## Specificity 1.00000 0.992701 0.07407
## Pos Pred Value 1.00000 0.000000 0.82759
## Neg Pred Value 0.90411 0.925170 0.66667
## Prevalence 0.10811 0.074324 0.81757
## Detection Rate 0.01351 0.000000 0.81081
## Detection Prevalence 0.01351 0.006757 0.97973
## Balanced Accuracy 0.56250 0.496350 0.532904.1.9. App + Sesiones promedio
#Modelo por LDA
lda.9=lda(formula = Categoria.Cliente ~ Time.on.App + Avg..Session.Length, data = trainSet)
#Predicción
prediccionesLDA.9 = predict(object = lda.9,
newdata = testSet)
cm.419 = confusionMatrix(as.factor(prediccionesLDA.9$class),as.factor(testSet$Categoria.Cliente))
cm.419## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 3 0 0
## Oro 0 0 1
## Platino 13 11 120
##
## Overall Statistics
##
## Accuracy : 0.8311
## 95% CI : (0.7608, 0.8876)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.3826
##
## Kappa : 0.1631
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.18750 0.000000 0.9917
## Specificity 1.00000 0.992701 0.1111
## Pos Pred Value 1.00000 0.000000 0.8333
## Neg Pred Value 0.91034 0.925170 0.7500
## Prevalence 0.10811 0.074324 0.8176
## Detection Rate 0.02027 0.000000 0.8108
## Detection Prevalence 0.02027 0.006757 0.9730
## Balanced Accuracy 0.59375 0.496350 0.55144.1.10. Website + Sesiones promedio
#Modelo por LDA
lda.10=lda(formula = Categoria.Cliente ~ Time.on.Website + Avg..Session.Length, data = trainSet)
#Predicción
prediccionesLDA.10 = predict(object = lda.10,
newdata = testSet)
cm.4110 = confusionMatrix(as.factor(prediccionesLDA.10$class),as.factor(testSet$Categoria.Cliente))
cm.4110## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 0 0 0
## Oro 0 0 0
## Platino 16 11 121
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.0000 0.00000 1.0000
## Specificity 1.0000 1.00000 0.0000
## Pos Pred Value NaN NaN 0.8176
## Neg Pred Value 0.8919 0.92568 NaN
## Prevalence 0.1081 0.07432 0.8176
## Detection Rate 0.0000 0.00000 0.8176
## Detection Prevalence 0.0000 0.00000 1.0000
## Balanced Accuracy 0.5000 0.50000 0.50004.1.11. Membresía + App + Website
#Modelo por LDA
lda.11=lda(formula = Categoria.Cliente ~ Length.of.Membership + Time.on.App + Time.on.Website, data = trainSet)
#Predicción
prediccionesLDA.11 = predict(object = lda.11,
newdata = testSet)
cm.4111 = confusionMatrix(as.factor(prediccionesLDA.11$class),as.factor(testSet$Categoria.Cliente))
cm.4111## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 9 0 2
## Oro 0 8 0
## Platino 7 3 119
##
## Overall Statistics
##
## Accuracy : 0.9189
## 95% CI : (0.8627, 0.9574)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.000401
##
## Kappa : 0.7055
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.56250 0.72727 0.9835
## Specificity 0.98485 1.00000 0.6296
## Pos Pred Value 0.81818 1.00000 0.9225
## Neg Pred Value 0.94891 0.97857 0.8947
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.06081 0.05405 0.8041
## Detection Prevalence 0.07432 0.05405 0.8716
## Balanced Accuracy 0.77367 0.86364 0.80664.1.12. Membresía + App + Sesión promedio
#Modelo por LDA
lda.12=lda(formula = Categoria.Cliente ~ Length.of.Membership + Time.on.App + Avg..Session.Length, data = trainSet)
#Predicción
prediccionesLDA.12 = predict(object = lda.12,
newdata = testSet)
cm.4112 = confusionMatrix(as.factor(prediccionesLDA.12$class),as.factor(testSet$Categoria.Cliente))
cm.4112## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 12 0 0
## Oro 0 8 0
## Platino 4 3 121
##
## Overall Statistics
##
## Accuracy : 0.9527
## 95% CI : (0.905, 0.9808)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 1.057e-06
##
## Kappa : 0.8312
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.75000 0.72727 1.0000
## Specificity 1.00000 1.00000 0.7407
## Pos Pred Value 1.00000 1.00000 0.9453
## Neg Pred Value 0.97059 0.97857 1.0000
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.08108 0.05405 0.8176
## Detection Prevalence 0.08108 0.05405 0.8649
## Balanced Accuracy 0.87500 0.86364 0.87044.1.13. Membresía + Website + Sesión promedio
#Modelo por LDA
lda.13=lda(formula = Categoria.Cliente ~ Length.of.Membership + Time.on.Website + Avg..Session.Length, data = trainSet)
#Predicción
prediccionesLDA.13 = predict(object = lda.13,
newdata = testSet)
cm.4113 = confusionMatrix(as.factor(prediccionesLDA.13$class),as.factor(testSet$Categoria.Cliente))
cm.4113## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 5 0 1
## Oro 0 4 4
## Platino 11 7 116
##
## Overall Statistics
##
## Accuracy : 0.8446
## 95% CI : (0.776, 0.8989)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.2312
##
## Kappa : 0.3818
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.31250 0.36364 0.9587
## Specificity 0.99242 0.97080 0.3333
## Pos Pred Value 0.83333 0.50000 0.8657
## Neg Pred Value 0.92254 0.95000 0.6429
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.03378 0.02703 0.7838
## Detection Prevalence 0.04054 0.05405 0.9054
## Balanced Accuracy 0.65246 0.66722 0.64604.1.14. App + Website + Sesión promedio
#Modelo por LDA
lda.14=lda(formula = Categoria.Cliente ~ Time.on.App + Time.on.Website + Avg..Session.Length, data = trainSet)
#Predicción
prediccionesLDA.14 = predict(object = lda.14,
newdata = testSet)
cm.4114 = confusionMatrix(as.factor(prediccionesLDA.14$class),as.factor(testSet$Categoria.Cliente))
cm.4114## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 2 0 0
## Oro 0 0 1
## Platino 14 11 120
##
## Overall Statistics
##
## Accuracy : 0.8243
## 95% CI : (0.7533, 0.8819)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.4666
##
## Kappa : 0.1084
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.12500 0.000000 0.99174
## Specificity 1.00000 0.992701 0.07407
## Pos Pred Value 1.00000 0.000000 0.82759
## Neg Pred Value 0.90411 0.925170 0.66667
## Prevalence 0.10811 0.074324 0.81757
## Detection Rate 0.01351 0.000000 0.81081
## Detection Prevalence 0.01351 0.006757 0.97973
## Balanced Accuracy 0.56250 0.496350 0.532904.1.15. Membresía + App + Website + Sesión promedio
#Modelo por LDA
lda.15=lda(formula = Categoria.Cliente ~ Length.of.Membership + Time.on.App + Time.on.Website + Avg..Session.Length, data = trainSet)
#Predicción
prediccionesLDA.15 = predict(object = lda.15,
newdata = testSet)
cm.4115 = confusionMatrix(as.factor(prediccionesLDA.15$class),as.factor(testSet$Categoria.Cliente))
cm.4115## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 12 0 1
## Oro 0 8 0
## Platino 4 3 120
##
## Overall Statistics
##
## Accuracy : 0.9459
## 95% CI : (0.8963, 0.9764)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 4.331e-06
##
## Kappa : 0.8103
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.75000 0.72727 0.9917
## Specificity 0.99242 1.00000 0.7407
## Pos Pred Value 0.92308 1.00000 0.9449
## Neg Pred Value 0.97037 0.97857 0.9524
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.08108 0.05405 0.8108
## Detection Prevalence 0.08784 0.05405 0.8581
## Balanced Accuracy 0.87121 0.86364 0.8662Hallazgos. Mediante esta primera evaluación por medio de LDA se observó un pobre rendimiento en modelos de una sola variable. Por ende en los algoritmos siguientes estas evaluaciones serán obviadas.
Las combinaciones con mejor rendimiento son aquellas donde participan las variables tiempo en App y longevidad de la membresía.
Así mismo, la variable “tiempo en Website” no aporta mucho en la mayoría de los casos. Este comportamiento ya lo habíamos visto desde el análisis por correlación (índice 0).
Pese a ello, cabe la pena destacar que gracias a su inclusión en el conglomerado general se logró el rendimiento más alto en este algoritmo.
4.2 SVM
4.2.1. Membresía + App
#SVM
svm.1 = svm(formula = Categoria.Cliente.Num ~ Length.of.Membership + Time.on.App,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.1 = predict(object = svm.1,
newdata = testSet)
prediccionesSVMMF.1 = round(prediccionesSVMMF.1)#Matriz de confusión
cm.421 = confusionMatrix(as.factor(prediccionesSVMMF.1), as.factor(testSet$Categoria.Cliente.Num))
cm.421## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 5 2 0
## 2 6 117 14
## 3 0 2 2
##
## Overall Statistics
##
## Accuracy : 0.8378
## 95% CI : (0.7684, 0.8933)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.3031
##
## Kappa : 0.3151
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.45455 0.9669 0.12500
## Specificity 0.98540 0.2593 0.98485
## Pos Pred Value 0.71429 0.8540 0.50000
## Neg Pred Value 0.95745 0.6364 0.90278
## Prevalence 0.07432 0.8176 0.10811
## Detection Rate 0.03378 0.7905 0.01351
## Detection Prevalence 0.04730 0.9257 0.02703
## Balanced Accuracy 0.71997 0.6131 0.554924.2.2. Membresía + Website
#SVM
svm.2 = svm(formula = Categoria.Cliente.Num ~ Length.of.Membership + Time.on.Website,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.2 = predict(object = svm.2,
newdata = testSet)
prediccionesSVMMF.2 = round(prediccionesSVMMF.2)#Matriz de confusión
cm.422 = confusionMatrix(as.factor(prediccionesSVMMF.2), as.factor(testSet$Categoria.Cliente.Num))
cm.422## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 1 2 0
## 2 10 119 14
## 3 0 0 2
##
## Overall Statistics
##
## Accuracy : 0.8243
## 95% CI : (0.7533, 0.8819)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.4666
##
## Kappa : 0.1517
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.090909 0.9835 0.12500
## Specificity 0.985401 0.1111 1.00000
## Pos Pred Value 0.333333 0.8322 1.00000
## Neg Pred Value 0.931034 0.6000 0.90411
## Prevalence 0.074324 0.8176 0.10811
## Detection Rate 0.006757 0.8041 0.01351
## Detection Prevalence 0.020270 0.9662 0.01351
## Balanced Accuracy 0.538155 0.5473 0.562504.2.3. Membresía + Sesión promedio
#SVM
svm.3 = svm(formula = Categoria.Cliente.Num ~ Length.of.Membership + Avg..Session.Length,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.3 = predict(object = svm.3,
newdata = testSet)
prediccionesSVMMF.3 = round(prediccionesSVMMF.3)#Matriz de confusión
cm.423 = confusionMatrix(as.factor(prediccionesSVMMF.3), as.factor(testSet$Categoria.Cliente.Num))
cm.423## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 3 2 0
## 2 8 119 15
## 3 0 0 1
##
## Overall Statistics
##
## Accuracy : 0.8311
## 95% CI : (0.7608, 0.8876)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.3826
##
## Kappa : 0.2045
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.27273 0.9835 0.062500
## Specificity 0.98540 0.1481 1.000000
## Pos Pred Value 0.60000 0.8380 1.000000
## Neg Pred Value 0.94406 0.6667 0.897959
## Prevalence 0.07432 0.8176 0.108108
## Detection Rate 0.02027 0.8041 0.006757
## Detection Prevalence 0.03378 0.9595 0.006757
## Balanced Accuracy 0.62906 0.5658 0.5312504.2.4. App + Website
#SVM
svm.4 = svm(formula = Categoria.Cliente.Num ~ Time.on.App + Time.on.Website,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.4 = predict(object = svm.4,
newdata = testSet)
prediccionesSVMMF.4 = round(prediccionesSVMMF.4)#Matriz de confusión
cm.424 = confusionMatrix(as.factor(prediccionesSVMMF.4), as.factor(testSet$Categoria.Cliente.Num))## Warning in confusionMatrix.default(as.factor(prediccionesSVMMF.4),
## as.factor(testSet$Categoria.Cliente.Num)): Levels are not in the same order for
## reference and data. Refactoring data to match.cm.424## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 0 0 0
## 2 11 121 16
## 3 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.00000 1.0000 0.0000
## Specificity 1.00000 0.0000 1.0000
## Pos Pred Value NaN 0.8176 NaN
## Neg Pred Value 0.92568 NaN 0.8919
## Prevalence 0.07432 0.8176 0.1081
## Detection Rate 0.00000 0.8176 0.0000
## Detection Prevalence 0.00000 1.0000 0.0000
## Balanced Accuracy 0.50000 0.5000 0.50004.2.5. App + Sesión promedio
#SVM
svm.5 = svm(formula = Categoria.Cliente.Num ~ Time.on.App + Avg..Session.Length,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.5 = predict(object = svm.5,
newdata = testSet)
prediccionesSVMMF.5 = round(prediccionesSVMMF.5)#Matriz de confusión
cm.425 = confusionMatrix(as.factor(prediccionesSVMMF.5), as.factor(testSet$Categoria.Cliente.Num))## Warning in levels(reference) != levels(data): longitud de objeto mayor no es
## múltiplo de la longitud de uno menor## Warning in confusionMatrix.default(as.factor(prediccionesSVMMF.5),
## as.factor(testSet$Categoria.Cliente.Num)): Levels are not in the same order for
## reference and data. Refactoring data to match.cm.425## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 1 3 0
## 2 10 118 16
## 3 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.8041
## 95% CI : (0.7309, 0.8647)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.7082
##
## Kappa : 0.0325
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.090909 0.97521 0.0000
## Specificity 0.978102 0.03704 1.0000
## Pos Pred Value 0.250000 0.81944 NaN
## Neg Pred Value 0.930556 0.25000 0.8919
## Prevalence 0.074324 0.81757 0.1081
## Detection Rate 0.006757 0.79730 0.0000
## Detection Prevalence 0.027027 0.97297 0.0000
## Balanced Accuracy 0.534506 0.50612 0.50004.2.6. Website + Sesión promedio
#SVM
svm.6 = svm(formula = Categoria.Cliente.Num ~ Time.on.Website + Avg..Session.Length,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.6 = predict(object = svm.6,
newdata = testSet)
prediccionesSVMMF.6 = round(prediccionesSVMMF.6)#Matriz de confusión
cm.426 = confusionMatrix(as.factor(prediccionesSVMMF.6), as.factor(testSet$Categoria.Cliente.Num))## Warning in confusionMatrix.default(as.factor(prediccionesSVMMF.6),
## as.factor(testSet$Categoria.Cliente.Num)): Levels are not in the same order for
## reference and data. Refactoring data to match.cm.426## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 0 0 0
## 2 11 121 16
## 3 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.00000 1.0000 0.0000
## Specificity 1.00000 0.0000 1.0000
## Pos Pred Value NaN 0.8176 NaN
## Neg Pred Value 0.92568 NaN 0.8919
## Prevalence 0.07432 0.8176 0.1081
## Detection Rate 0.00000 0.8176 0.0000
## Detection Prevalence 0.00000 1.0000 0.0000
## Balanced Accuracy 0.50000 0.5000 0.50004.2.7. Membresía + App + Website
#SVM
svm.7 = svm(formula = Categoria.Cliente.Num ~ Length.of.Membership + Time.on.App + Time.on.Website,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.7 = predict(object = svm.7,
newdata = testSet)
prediccionesSVMMF.7 = round(prediccionesSVMMF.7)#Matriz de confusión
cm.427 = confusionMatrix(as.factor(prediccionesSVMMF.7), as.factor(testSet$Categoria.Cliente.Num))## Warning in confusionMatrix.default(as.factor(prediccionesSVMMF.7),
## as.factor(testSet$Categoria.Cliente.Num)): Levels are not in the same order for
## reference and data. Refactoring data to match.cm.427## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 0 0 0
## 2 11 121 16
## 3 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.00000 1.0000 0.0000
## Specificity 1.00000 0.0000 1.0000
## Pos Pred Value NaN 0.8176 NaN
## Neg Pred Value 0.92568 NaN 0.8919
## Prevalence 0.07432 0.8176 0.1081
## Detection Rate 0.00000 0.8176 0.0000
## Detection Prevalence 0.00000 1.0000 0.0000
## Balanced Accuracy 0.50000 0.5000 0.50004.2.8. Membresía + App + Sesión promedio
#SVM
svm.8 = svm(formula = Categoria.Cliente.Num ~ Length.of.Membership + Time.on.App + Avg..Session.Length,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.8 = predict(object = svm.8,
newdata = testSet)
prediccionesSVMMF.8 = round(prediccionesSVMMF.8)#Matriz de confusión
cm.428 = confusionMatrix(as.factor(prediccionesSVMMF.8), as.factor(testSet$Categoria.Cliente.Num))## Warning in levels(reference) != levels(data): longitud de objeto mayor no es
## múltiplo de la longitud de uno menor## Warning in confusionMatrix.default(as.factor(prediccionesSVMMF.8),
## as.factor(testSet$Categoria.Cliente.Num)): Levels are not in the same order for
## reference and data. Refactoring data to match.cm.428## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 2 1 0
## 2 9 120 16
## 3 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.8243
## 95% CI : (0.7533, 0.8819)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.4666
##
## Kappa : 0.1105
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.18182 0.99174 0.0000
## Specificity 0.99270 0.07407 1.0000
## Pos Pred Value 0.66667 0.82759 NaN
## Neg Pred Value 0.93793 0.66667 0.8919
## Prevalence 0.07432 0.81757 0.1081
## Detection Rate 0.01351 0.81081 0.0000
## Detection Prevalence 0.02027 0.97973 0.0000
## Balanced Accuracy 0.58726 0.53290 0.50004.2.9. Membresía + Website + Sesión promedio
#SVM
svm.9 = svm(formula = Categoria.Cliente.Num ~ Length.of.Membership + Time.on.Website + Avg..Session.Length,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.9 = predict(object = svm.9,
newdata = testSet)
prediccionesSVMMF.9 = round(prediccionesSVMMF.9)#Matriz de confusión
cm.429 = confusionMatrix(as.factor(prediccionesSVMMF.9), as.factor(testSet$Categoria.Cliente.Num))## Warning in confusionMatrix.default(as.factor(prediccionesSVMMF.9),
## as.factor(testSet$Categoria.Cliente.Num)): Levels are not in the same order for
## reference and data. Refactoring data to match.cm.429## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 0 0 0
## 2 11 121 16
## 3 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.00000 1.0000 0.0000
## Specificity 1.00000 0.0000 1.0000
## Pos Pred Value NaN 0.8176 NaN
## Neg Pred Value 0.92568 NaN 0.8919
## Prevalence 0.07432 0.8176 0.1081
## Detection Rate 0.00000 0.8176 0.0000
## Detection Prevalence 0.00000 1.0000 0.0000
## Balanced Accuracy 0.50000 0.5000 0.50004.2.10. App + Website + Sesión promedio
#SVM
svm.10 = svm(formula = Categoria.Cliente.Num ~ Time.on.App + Time.on.Website + Avg..Session.Length,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.10 = predict(object = svm.10,
newdata = testSet)
prediccionesSVMMF.10 = round(prediccionesSVMMF.10)#Matriz de confusión
cm.4210 = confusionMatrix(as.factor(prediccionesSVMMF.10), as.factor(testSet$Categoria.Cliente.Num))## Warning in confusionMatrix.default(as.factor(prediccionesSVMMF.10),
## as.factor(testSet$Categoria.Cliente.Num)): Levels are not in the same order for
## reference and data. Refactoring data to match.cm.4210## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 0 0 0
## 2 11 121 16
## 3 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.00000 1.0000 0.0000
## Specificity 1.00000 0.0000 1.0000
## Pos Pred Value NaN 0.8176 NaN
## Neg Pred Value 0.92568 NaN 0.8919
## Prevalence 0.07432 0.8176 0.1081
## Detection Rate 0.00000 0.8176 0.0000
## Detection Prevalence 0.00000 1.0000 0.0000
## Balanced Accuracy 0.50000 0.5000 0.50004.2.11. Membresía + App + Website + Sesión promedio
#SVM
svm.11 = svm(formula = Categoria.Cliente.Num ~ Length.of.Membership + Time.on.App + Time.on.Website + Avg..Session.Length,
data = trainSet,
kernel = "radial",
gamma = 5)
#Predicción
prediccionesSVMMF.11 = predict(object = svm.11,
newdata = testSet)
prediccionesSVMMF.11 = round(prediccionesSVMMF.11)#Matriz de confusión
cm.4211 = confusionMatrix(as.factor(prediccionesSVMMF.11), as.factor(testSet$Categoria.Cliente.Num))## Warning in confusionMatrix.default(as.factor(prediccionesSVMMF.11),
## as.factor(testSet$Categoria.Cliente.Num)): Levels are not in the same order for
## reference and data. Refactoring data to match.cm.4211## Confusion Matrix and Statistics
##
## Reference
## Prediction 1 2 3
## 1 0 0 0
## 2 11 121 16
## 3 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: 1 Class: 2 Class: 3
## Sensitivity 0.00000 1.0000 0.0000
## Specificity 1.00000 0.0000 1.0000
## Pos Pred Value NaN 0.8176 NaN
## Neg Pred Value 0.92568 NaN 0.8919
## Prevalence 0.07432 0.8176 0.1081
## Detection Rate 0.00000 0.8176 0.0000
## Detection Prevalence 0.00000 1.0000 0.0000
## Balanced Accuracy 0.50000 0.5000 0.5000Hallazgos. Existen algunas diferencias y similitudes respecto al LDA. La diferencia más resaltante es que la combinación de las 4 variables no generó el mejor modelo (como en el caso anterior).
Por otro lado, al igual que en LDA, los modelos con mejor rendimiento fueron aquellos donde se encontraba presente tiempo en app y membresía.
En cuanto al performance, este no fue superior al obtenido mediante LDA, por lo que dicho algoritmo sigue siendo el mejor modelo al momento.
4.3 KNN
#Cross Validation
trControl = trainControl(method = "repeatedcv",
number = 10,
repeats = 3)4.3.1. Membresía + App
library(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, var#KNN
KNN.1 = train(as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.App,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.1 = predict(object = KNN.1,
newdata = testSet)#Matriz de Confusión
cm.431 = confusionMatrix(prediccionKNN.1, as.factor(testSet$Categoria.Cliente))
cm.431## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 4 0 1
## Oro 0 5 1
## Platino 12 6 119
##
## Overall Statistics
##
## Accuracy : 0.8649
## 95% CI : (0.799, 0.9155)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.07959
##
## Kappa : 0.4287
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.25000 0.45455 0.9835
## Specificity 0.99242 0.99270 0.3333
## Pos Pred Value 0.80000 0.83333 0.8686
## Neg Pred Value 0.91608 0.95775 0.8182
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.02703 0.03378 0.8041
## Detection Prevalence 0.03378 0.04054 0.9257
## Balanced Accuracy 0.62121 0.72362 0.65844.3.2. Membresía + Website
#KNN
KNN.2 = train(as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.Website,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.2 = predict(object = KNN.2,
newdata = testSet)#Matriz de Confusión
cm.432 = confusionMatrix(prediccionKNN.2, as.factor(testSet$Categoria.Cliente))
cm.432## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 2 0 0
## Oro 0 2 1
## Platino 14 9 120
##
## Overall Statistics
##
## Accuracy : 0.8378
## 95% CI : (0.7684, 0.8933)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.3031
##
## Kappa : 0.2169
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.12500 0.18182 0.9917
## Specificity 1.00000 0.99270 0.1481
## Pos Pred Value 1.00000 0.66667 0.8392
## Neg Pred Value 0.90411 0.93793 0.8000
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.01351 0.01351 0.8108
## Detection Prevalence 0.01351 0.02027 0.9662
## Balanced Accuracy 0.56250 0.58726 0.56994.3.3. Membresía + Sesión promedio
#KNN
KNN.3 = train(as.factor(Categoria.Cliente) ~ Length.of.Membership + Avg..Session.Length,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.3 = predict(object = KNN.3,
newdata = testSet)#Matriz de Confusión
cm.433 = confusionMatrix(prediccionKNN.3, as.factor(testSet$Categoria.Cliente))
cm.433## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 4 0 0
## Oro 0 3 3
## Platino 12 8 118
##
## Overall Statistics
##
## Accuracy : 0.8446
## 95% CI : (0.776, 0.8989)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.2312
##
## Kappa : 0.3294
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.25000 0.27273 0.9752
## Specificity 1.00000 0.97810 0.2593
## Pos Pred Value 1.00000 0.50000 0.8551
## Neg Pred Value 0.91667 0.94366 0.7000
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.02703 0.02027 0.7973
## Detection Prevalence 0.02703 0.04054 0.9324
## Balanced Accuracy 0.62500 0.62541 0.61724.3.4. App + Website
#KNN
KNN.4 = train(as.factor(Categoria.Cliente) ~ Time.on.App + Time.on.Website,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.4 = predict(object = KNN.4,
newdata = testSet)#Matriz de Confusión
cm.434 = confusionMatrix(prediccionKNN.4, as.factor(testSet$Categoria.Cliente))
cm.434## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 0 0 0
## Oro 0 0 0
## Platino 16 11 121
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.0000 0.00000 1.0000
## Specificity 1.0000 1.00000 0.0000
## Pos Pred Value NaN NaN 0.8176
## Neg Pred Value 0.8919 0.92568 NaN
## Prevalence 0.1081 0.07432 0.8176
## Detection Rate 0.0000 0.00000 0.8176
## Detection Prevalence 0.0000 0.00000 1.0000
## Balanced Accuracy 0.5000 0.50000 0.50004.3.5. App + Sesión promedio
#KNN
KNN.5 = train(as.factor(Categoria.Cliente) ~ Time.on.App + Avg..Session.Length,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.5 = predict(object = KNN.5,
newdata = testSet)#Matriz de Confusión
cm.435 = confusionMatrix(prediccionKNN.5, as.factor(testSet$Categoria.Cliente))
cm.435## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 3 0 1
## Oro 0 0 1
## Platino 13 11 119
##
## Overall Statistics
##
## Accuracy : 0.8243
## 95% CI : (0.7533, 0.8819)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.4666
##
## Kappa : 0.1498
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.18750 0.000000 0.9835
## Specificity 0.99242 0.992701 0.1111
## Pos Pred Value 0.75000 0.000000 0.8322
## Neg Pred Value 0.90972 0.925170 0.6000
## Prevalence 0.10811 0.074324 0.8176
## Detection Rate 0.02027 0.000000 0.8041
## Detection Prevalence 0.02703 0.006757 0.9662
## Balanced Accuracy 0.58996 0.496350 0.54734.3.6. Website + Sesión promedio
#KNN
KNN.6 = train(as.factor(Categoria.Cliente) ~ Time.on.Website + Avg..Session.Length,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.6 = predict(object = KNN.6,
newdata = testSet)#Matriz de Confusión
cm.436 = confusionMatrix(prediccionKNN.6, as.factor(testSet$Categoria.Cliente))
cm.436## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 0 0 0
## Oro 0 0 0
## Platino 16 11 121
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.0000 0.00000 1.0000
## Specificity 1.0000 1.00000 0.0000
## Pos Pred Value NaN NaN 0.8176
## Neg Pred Value 0.8919 0.92568 NaN
## Prevalence 0.1081 0.07432 0.8176
## Detection Rate 0.0000 0.00000 0.8176
## Detection Prevalence 0.0000 0.00000 1.0000
## Balanced Accuracy 0.5000 0.50000 0.50004.3.7. Membresía + App + Website
#KNN
KNN.7 = train(as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.App + Time.on.Website,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.7 = predict(object = KNN.7,
newdata = testSet)#Matriz de Confusión
cm.437 = confusionMatrix(prediccionKNN.7, as.factor(testSet$Categoria.Cliente))
cm.437## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 5 0 0
## Oro 0 5 1
## Platino 11 6 120
##
## Overall Statistics
##
## Accuracy : 0.8784
## 95% CI : (0.8146, 0.9263)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.03066
##
## Kappa : 0.4858
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.31250 0.45455 0.9917
## Specificity 1.00000 0.99270 0.3704
## Pos Pred Value 1.00000 0.83333 0.8759
## Neg Pred Value 0.92308 0.95775 0.9091
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.03378 0.03378 0.8108
## Detection Prevalence 0.03378 0.04054 0.9257
## Balanced Accuracy 0.65625 0.72362 0.68114.3.8. Membresía + App + Sesión promedio
#KNN
KNN.8 = train(as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.App + Avg..Session.Length,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.8 = predict(object = KNN.8,
newdata = testSet)#Matriz de Confusión
cm.438 = confusionMatrix(prediccionKNN.8, as.factor(testSet$Categoria.Cliente))
cm.438## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 11 0 1
## Oro 0 7 1
## Platino 5 4 119
##
## Overall Statistics
##
## Accuracy : 0.9257
## 95% CI : (0.8709, 0.9623)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.0001496
##
## Kappa : 0.7347
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.68750 0.63636 0.9835
## Specificity 0.99242 0.99270 0.6667
## Pos Pred Value 0.91667 0.87500 0.9297
## Neg Pred Value 0.96324 0.97143 0.9000
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.07432 0.04730 0.8041
## Detection Prevalence 0.08108 0.05405 0.8649
## Balanced Accuracy 0.83996 0.81453 0.82514.3.9. Membresía + Website + Sesión promedio
#KNN
KNN.9 = train(as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.Website + Avg..Session.Length,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.9 = predict(object = KNN.9,
newdata = testSet)#Matriz de Confusión
cm.439 = confusionMatrix(prediccionKNN.9, as.factor(testSet$Categoria.Cliente))
cm.439## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 4 0 0
## Oro 0 2 2
## Platino 12 9 119
##
## Overall Statistics
##
## Accuracy : 0.8446
## 95% CI : (0.776, 0.8989)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.2312
##
## Kappa : 0.299
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.25000 0.18182 0.9835
## Specificity 1.00000 0.98540 0.2222
## Pos Pred Value 1.00000 0.50000 0.8500
## Neg Pred Value 0.91667 0.93750 0.7500
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.02703 0.01351 0.8041
## Detection Prevalence 0.02703 0.02703 0.9459
## Balanced Accuracy 0.62500 0.58361 0.60284.3.10. App + Website + Sesión promedio
#KNN
KNN.10 = train(as.factor(Categoria.Cliente) ~ Time.on.App + Time.on.Website + Avg..Session.Length,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.10 = predict(object = KNN.10,
newdata = testSet)#Matriz de Confusión
cm.4310 = confusionMatrix(prediccionKNN.10, as.factor(testSet$Categoria.Cliente))
cm.4310## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 0 0 0
## Oro 0 0 0
## Platino 16 11 121
##
## Overall Statistics
##
## Accuracy : 0.8176
## 95% CI : (0.7458, 0.8762)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.5512
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.0000 0.00000 1.0000
## Specificity 1.0000 1.00000 0.0000
## Pos Pred Value NaN NaN 0.8176
## Neg Pred Value 0.8919 0.92568 NaN
## Prevalence 0.1081 0.07432 0.8176
## Detection Rate 0.0000 0.00000 0.8176
## Detection Prevalence 0.0000 0.00000 1.0000
## Balanced Accuracy 0.5000 0.50000 0.50004.3.11. Membresía + App + Website + Sesión promedio
#KNN
KNN.11 = train(as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.App + Time.on.Website + Avg..Session.Length,
data = trainSet,
method = 'knn',
tuneLength = 20,
trControl = trControl,
preProc = c("center", "scale"))
#Predicción
prediccionKNN.11 = predict(object = KNN.11,
newdata = testSet)#Matriz de Confusión
cm.4311 = confusionMatrix(prediccionKNN.11, as.factor(testSet$Categoria.Cliente))
cm.4311## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 5 0 0
## Oro 0 4 0
## Platino 11 7 121
##
## Overall Statistics
##
## Accuracy : 0.8784
## 95% CI : (0.8146, 0.9263)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 0.03066
##
## Kappa : 0.463
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.31250 0.36364 1.0000
## Specificity 1.00000 1.00000 0.3333
## Pos Pred Value 1.00000 1.00000 0.8705
## Neg Pred Value 0.92308 0.95139 1.0000
## Prevalence 0.10811 0.07432 0.8176
## Detection Rate 0.03378 0.02703 0.8176
## Detection Prevalence 0.03378 0.02703 0.9392
## Balanced Accuracy 0.65625 0.68182 0.6667Hallazgos. El rendimiento general de estos modelos estuvo mejor que el obtenido en SVM. Algunos modelos llegan a superar en ocasiones el 95% de accuracy.
Pese a ello, en los intentos realizados ninguno superó el índice máximo obtenido en LDA.
4.4 ANN
Debido al nivel computacional que solicitan las ANN, se tomó la decisión de únicamente evaluar aquellas variables que en ocasiones anteriores han logrado obtener rendimientos encima del 90% bajo los 3 algoritmos anteriores.
library(neuralnet)##
## Attaching package: 'neuralnet'## The following object is masked from 'package:dplyr':
##
## compute4.4.1 Membresía + App
RedNeural.1=neuralnet(formula = as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.App,
data = trainSet,
hidden=(2:2),
linear.output = FALSE)#Predicciones
prediccionesANN.1 = neuralnet::compute(RedNeural.1, testSet)
ANN.1 = prediccionesANN.1$net.result
ANN.1 = round(prediccionesANN.1$net.result)
ANN.1 = data.frame("ANN.1" = ifelse((ANN.1[ ,1]) %in% 1, "Oro",
ifelse((ANN.1[ ,2]) %in% 1,"Platino","Bronce")))#Matriz de Confusión
cm.441 = confusionMatrix(ANN.1$ANN.1, as.factor(testSet$Categoria.Cliente))
cm.441## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 6 3 116
## Oro 10 0 4
## Platino 0 8 1
##
## Overall Statistics
##
## Accuracy : 0.0473
## 95% CI : (0.0192, 0.095)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 1
##
## Kappa : -0.1183
##
## Mcnemar's Test P-Value : <2e-16
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.37500 0.00000 0.008264
## Specificity 0.09848 0.89781 0.703704
## Pos Pred Value 0.04800 0.00000 0.111111
## Neg Pred Value 0.56522 0.91791 0.136691
## Prevalence 0.10811 0.07432 0.817568
## Detection Rate 0.04054 0.00000 0.006757
## Detection Prevalence 0.84459 0.09459 0.060811
## Balanced Accuracy 0.23674 0.44891 0.3559844.4.2 Membresía + App + Website
RedNeural.2=neuralnet(formula = as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.App + Time.on.Website,
data = trainSet,
hidden=(1:2),
linear.output = FALSE)#Predicciones
prediccionesANN.2 = neuralnet::compute(RedNeural.2, testSet)
ANN.2 = prediccionesANN.2$net.result
ANN.2 = round(prediccionesANN.2$net.result)
ANN.2 = data.frame("ANN.2" = ifelse((ANN.2[ ,1]) %in% 1, "Oro",
ifelse((ANN.2[ ,2]) %in% 1,"Platino","Bronce")))#Matriz de Confusión
cm.442 = confusionMatrix(ANN.2$ANN.2, as.factor(testSet$Categoria.Cliente))## Warning in confusionMatrix.default(ANN.2$ANN.2,
## as.factor(testSet$Categoria.Cliente)): Levels are not in the same order for
## reference and data. Refactoring data to match.cm.442## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 16 11 121
## Oro 0 0 0
## Platino 0 0 0
##
## Overall Statistics
##
## Accuracy : 0.1081
## 95% CI : (0.0631, 0.1696)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 1
##
## Kappa : 0
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 1.0000 0.00000 0.0000
## Specificity 0.0000 1.00000 1.0000
## Pos Pred Value 0.1081 NaN NaN
## Neg Pred Value NaN 0.92568 0.1824
## Prevalence 0.1081 0.07432 0.8176
## Detection Rate 0.1081 0.00000 0.0000
## Detection Prevalence 1.0000 0.00000 0.0000
## Balanced Accuracy 0.5000 0.50000 0.50004.4.3 Membresía + App + Sesión promedio
RedNeural.3=neuralnet(formula = as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.App + Avg..Session.Length,
data = trainSet,
hidden=(2:2),
linear.output = FALSE)#Predicciones
prediccionesANN.3 = neuralnet::compute(RedNeural.3, testSet)
ANN.3 = prediccionesANN.3$net.result
ANN.3 = round(prediccionesANN.3$net.result)
ANN.3 = data.frame("ANN.3" = ifelse((ANN.3[ ,1]) %in% 1, "Oro",
ifelse((ANN.3[ ,2]) %in% 1,"Platino","Bronce")))#Matriz de Confusión
cm.443 = confusionMatrix(ANN.3$ANN.3, as.factor(testSet$Categoria.Cliente))
cm.443## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 0 0 118
## Oro 16 0 1
## Platino 0 11 2
##
## Overall Statistics
##
## Accuracy : 0.0135
## 95% CI : (0.0016, 0.048)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 1
##
## Kappa : -0.1836
##
## Mcnemar's Test P-Value : <2e-16
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.00000 0.00000 0.01653
## Specificity 0.10606 0.87591 0.59259
## Pos Pred Value 0.00000 0.00000 0.15385
## Neg Pred Value 0.46667 0.91603 0.11852
## Prevalence 0.10811 0.07432 0.81757
## Detection Rate 0.00000 0.00000 0.01351
## Detection Prevalence 0.79730 0.11486 0.08784
## Balanced Accuracy 0.05303 0.43796 0.304564.4.4 Membresía + App + Website + Sesión promedio
RedNeural.4=neuralnet(formula = as.factor(Categoria.Cliente) ~ Length.of.Membership + Time.on.App + Time.on.Website + Avg..Session.Length,
data = trainSet,
hidden=(1:2),
linear.output = FALSE)#Predicciones
prediccionesANN.4 = neuralnet::compute(RedNeural.4, testSet)
ANN.4 = prediccionesANN.4$net.result
ANN.4 = round(prediccionesANN.4$net.result)
ANN.4 = data.frame("ANN.4" = ifelse((ANN.4[ ,1]) %in% 1, "Oro",
ifelse((ANN.4[ ,2]) %in% 1,"Platino","Bronce")))#Matriz de Confusión
cm.444 = confusionMatrix(ANN.4$ANN.4, as.factor(testSet$Categoria.Cliente))
cm.444## Confusion Matrix and Statistics
##
## Reference
## Prediction Bronce Oro Platino
## Bronce 0 0 119
## Oro 16 0 1
## Platino 0 11 1
##
## Overall Statistics
##
## Accuracy : 0.0068
## 95% CI : (2e-04, 0.0371)
## No Information Rate : 0.8176
## P-Value [Acc > NIR] : 1
##
## Kappa : -0.1849
##
## Mcnemar's Test P-Value : <2e-16
##
## Statistics by Class:
##
## Class: Bronce Class: Oro Class: Platino
## Sensitivity 0.00000 0.00000 0.008264
## Specificity 0.09848 0.87591 0.592593
## Pos Pred Value 0.00000 0.00000 0.083333
## Neg Pred Value 0.44828 0.91603 0.117647
## Prevalence 0.10811 0.07432 0.817568
## Detection Rate 0.00000 0.00000 0.006757
## Detection Prevalence 0.80405 0.11486 0.081081
## Balanced Accuracy 0.04924 0.43796 0.300429