Trabajo práctico TP III
Guillermo Mansilla
4/26/2021
library(ggplot2)
library(ggcorrplot)
library(funModeling) ## Loading required package: Hmisc## Loading required package: lattice## Loading required package: survival## Loading required package: Formula##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, units## funModeling v.1.9.4 :)
## Examples and tutorials at livebook.datascienceheroes.com
## / Now in Spanish: librovivodecienciadedatos.ailibrary(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riverslibrary(pls)##
## Attaching package: 'pls'## The following object is masked from 'package:stats':
##
## loadingsdfbody <- read.csv("data_multiple_regression_exercice.csv",header= TRUE, sep="")dim(dfbody)## [1] 507 24p=ncol(dfbody)-1
p## [1] 23names(dfbody)## [1] "weight" "biacromial" "pelvic.breadth" "bitrochanteric"
## [5] "chest.depth" "chest.diam" "elbow.diam" "wrist.diam"
## [9] "knee.diam" "ankle.diam" "shoulder.girth" "chest.girth"
## [13] "waist.girth" "navel.girth" "hip.girth" "thigh.girth"
## [17] "bicep.girth" "forearm.girth" "knee.girth" "calf.girth"
## [21] "ankle.girth" "wrist.girth" "age" "height"head(dfbody)## weight biacromial pelvic.breadth bitrochanteric chest.depth chest.diam
## 1 65.6 42.9 26.0 31.5 17.7 28.0
## 2 71.8 43.7 28.5 33.5 16.9 30.8
## 3 80.7 40.1 28.2 33.3 20.9 31.7
## 4 72.6 44.3 29.9 34.0 18.4 28.2
## 5 78.8 42.5 29.9 34.0 21.5 29.4
## 6 74.8 43.3 27.0 31.5 19.6 31.3
## elbow.diam wrist.diam knee.diam ankle.diam shoulder.girth chest.girth
## 1 13.1 10.4 18.8 14.1 106.2 89.5
## 2 14.0 11.8 20.6 15.1 110.5 97.0
## 3 13.9 10.9 19.7 14.1 115.1 97.5
## 4 13.9 11.2 20.9 15.0 104.5 97.0
## 5 15.2 11.6 20.7 14.9 107.5 97.5
## 6 14.0 11.5 18.8 13.9 119.8 99.9
## waist.girth navel.girth hip.girth thigh.girth bicep.girth forearm.girth
## 1 71.5 74.5 93.5 51.5 32.5 26.0
## 2 79.0 86.5 94.8 51.5 34.4 28.0
## 3 83.2 82.9 95.0 57.3 33.4 28.8
## 4 77.8 78.8 94.0 53.0 31.0 26.2
## 5 80.0 82.5 98.5 55.4 32.0 28.4
## 6 82.5 80.1 95.3 57.5 33.0 28.0
## knee.girth calf.girth ankle.girth wrist.girth age height
## 1 34.5 36.5 23.5 16.5 21.0 174.0
## 2 36.5 37.5 24.5 17.0 23.0 175.3
## 3 37.0 37.3 21.9 16.9 28.0 193.5
## 4 37.0 34.8 23.0 16.6 23.0 186.5
## 5 37.7 38.6 24.4 18.0 22.0 187.2
## 6 36.6 36.1 23.5 16.9 20.6 181.5str(dfbody) ## 'data.frame': 507 obs. of 24 variables:
## $ weight : num 65.6 71.8 80.7 72.6 78.8 74.8 86.4 78.4 62 81.6 ...
## $ biacromial : num 42.9 43.7 40.1 44.3 42.5 43.3 43.5 44.4 43.5 42 ...
## $ pelvic.breadth: num 26 28.5 28.2 29.9 29.9 27 30 29.8 26.5 28 ...
## $ bitrochanteric: num 31.5 33.5 33.3 34 34 31.5 34 33.2 32.1 34 ...
## $ chest.depth : num 17.7 16.9 20.9 18.4 21.5 19.6 21.9 21.8 15.5 22.5 ...
## $ chest.diam : num 28 30.8 31.7 28.2 29.4 31.3 31.7 28.8 27.5 28 ...
## $ elbow.diam : num 13.1 14 13.9 13.9 15.2 14 16.1 15.1 14.1 15.6 ...
## $ wrist.diam : num 10.4 11.8 10.9 11.2 11.6 11.5 12.5 11.9 11.2 12 ...
## $ knee.diam : num 18.8 20.6 19.7 20.9 20.7 18.8 20.8 21 18.9 21.1 ...
## $ ankle.diam : num 14.1 15.1 14.1 15 14.9 13.9 15.6 14.6 13.2 15 ...
## $ shoulder.girth: num 106 110 115 104 108 ...
## $ chest.girth : num 89.5 97 97.5 97 97.5 ...
## $ waist.girth : num 71.5 79 83.2 77.8 80 82.5 82 76.8 68.5 77.5 ...
## $ navel.girth : num 74.5 86.5 82.9 78.8 82.5 80.1 84 80.5 69 81.5 ...
## $ hip.girth : num 93.5 94.8 95 94 98.5 95.3 101 98 89.5 99.8 ...
## $ thigh.girth : num 51.5 51.5 57.3 53 55.4 57.5 60.9 56 50 59.8 ...
## $ bicep.girth : num 32.5 34.4 33.4 31 32 33 42.4 34.1 33 36.5 ...
## $ forearm.girth : num 26 28 28.8 26.2 28.4 28 32.3 28 26 29.2 ...
## $ knee.girth : num 34.5 36.5 37 37 37.7 36.6 40.1 39.2 35.5 38.3 ...
## $ calf.girth : num 36.5 37.5 37.3 34.8 38.6 36.1 40.3 36.7 35 38.6 ...
## $ ankle.girth : num 23.5 24.5 21.9 23 24.4 23.5 23.6 22.5 22 22.2 ...
## $ wrist.girth : num 16.5 17 16.9 16.6 18 16.9 18.8 18 16.5 16.9 ...
## $ age : num 21 23 28 23 22 20.6 25.5 26.9 22.8 21 ...
## $ height : num 174 175 194 186 187 ...anyNA(dfbody)## [1] FALSEattach(dfbody)Separar el conjunto de registros aleatoriamente en dos conjuntos de datos data_training y data_test. El primer conjunto se utilizará para calcular los parámetros de cada modelo y el segundo se utilizará para realizar predicciones y evaluar los resultados.
Para ello lo que hice fue dividir aleatoriamente el 80% de los datos para entrenamiento y el 20% para el modelo de testeo.
index_sample=get_sample(data = dfbody, percentage_tr_rows=0.8, seed = 234)
data_training = dfbody[index_sample,]
data_test = dfbody[-index_sample,]Antes de realizar el gráfico de regresión lineal y su validación, voy a entender más como estan correlacionadas las variables de entrenamiento como también entender la variabilidad de una variable vs las otras y si existen algun outlier en las variables.
Correlación con variable dependiente
correlation_table(data_training, "weight")## Variable weight
## 1 weight 1.00
## 2 waist.girth 0.91
## 3 chest.girth 0.90
## 4 shoulder.girth 0.88
## 5 bicep.girth 0.87
## 6 forearm.girth 0.87
## 7 chest.diam 0.83
## 8 wrist.girth 0.81
## 9 chest.depth 0.80
## 10 elbow.diam 0.80
## 11 knee.girth 0.79
## 12 wrist.diam 0.76
## 13 hip.girth 0.76
## 14 ankle.girth 0.76
## 15 knee.diam 0.75
## 16 calf.girth 0.74
## 17 height 0.73
## 18 biacromial 0.72
## 19 navel.girth 0.72
## 20 ankle.diam 0.71
## 21 bitrochanteric 0.65
## 22 thigh.girth 0.54
## 23 pelvic.breadth 0.50
## 24 age 0.22Matriz de correlación de variables para el conjunto de entrenamiento
cordatatraining = cor(data_training[,1:24])
cordatatraining## weight biacromial pelvic.breadth bitrochanteric chest.depth
## weight 1.0000000 0.72333708 0.4979851 0.6523826 0.8020373
## biacromial 0.7233371 1.00000000 0.3205021 0.4812884 0.5744144
## pelvic.breadth 0.4979851 0.32050211 1.0000000 0.6847879 0.3531194
## bitrochanteric 0.6523826 0.48128837 0.6847879 1.0000000 0.4476102
## chest.depth 0.8020373 0.57441443 0.3531194 0.4476102 1.0000000
## chest.diam 0.8255359 0.76660976 0.3362752 0.5049457 0.6602519
## elbow.diam 0.7981996 0.76800227 0.3221594 0.5053734 0.6663184
## wrist.diam 0.7589759 0.71692617 0.2804776 0.4575196 0.6029277
## knee.diam 0.7475840 0.63330502 0.4382057 0.5833981 0.5246282
## ankle.diam 0.7143812 0.66730766 0.3673644 0.4728103 0.5850445
## shoulder.girth 0.8793832 0.78317389 0.2884577 0.4635623 0.7404735
## chest.girth 0.8988234 0.71414861 0.3261211 0.4743455 0.8080765
## waist.girth 0.9053409 0.63430902 0.4498945 0.5624033 0.8004537
## navel.girth 0.7179399 0.31395612 0.5935838 0.6070064 0.6130228
## hip.girth 0.7576721 0.32508769 0.5728108 0.7434893 0.5440697
## thigh.girth 0.5406768 0.10567708 0.4055826 0.5168913 0.3417289
## bicep.girth 0.8656875 0.69567295 0.3085243 0.4679921 0.7294714
## forearm.girth 0.8650929 0.75197645 0.2993726 0.4619208 0.7155195
## knee.girth 0.7919113 0.50768385 0.4761210 0.6174524 0.5626738
## calf.girth 0.7447298 0.49762067 0.3879855 0.5716573 0.5297461
## ankle.girth 0.7580149 0.59830444 0.3307441 0.5307470 0.5887505
## wrist.girth 0.8109316 0.76954325 0.2676489 0.4649945 0.6775134
## age 0.2214360 0.08389303 0.2585529 0.2717645 0.3081505
## height 0.7283307 0.76144089 0.3661565 0.4741203 0.5611011
## chest.diam elbow.diam wrist.diam knee.diam ankle.diam
## weight 0.8255359 0.7981996 0.7589759 0.7475840 0.7143812
## biacromial 0.7666098 0.7680023 0.7169262 0.6333050 0.6673077
## pelvic.breadth 0.3362752 0.3221594 0.2804776 0.4382057 0.3673644
## bitrochanteric 0.5049457 0.5053734 0.4575196 0.5833981 0.4728103
## chest.depth 0.6602519 0.6663184 0.6029277 0.5246282 0.5850445
## chest.diam 1.0000000 0.7462998 0.7207153 0.6485177 0.6633892
## elbow.diam 0.7462998 1.0000000 0.8295361 0.7121106 0.8214705
## wrist.diam 0.7207153 0.8295361 1.0000000 0.7051048 0.7679319
## knee.diam 0.6485177 0.7121106 0.7051048 1.0000000 0.7069192
## ankle.diam 0.6633892 0.8214705 0.7679319 0.7069192 1.0000000
## shoulder.girth 0.8675862 0.8179573 0.7739053 0.6729619 0.6889967
## chest.girth 0.8647893 0.8000336 0.7582419 0.6452346 0.7002848
## waist.girth 0.7846368 0.6920480 0.6763861 0.6060924 0.6266948
## navel.girth 0.5115517 0.4397734 0.3967711 0.4504462 0.4180081
## hip.girth 0.5068641 0.4242717 0.4113337 0.5579286 0.3894831
## thigh.girth 0.2940656 0.1917599 0.1814579 0.4049156 0.1599306
## bicep.girth 0.7905738 0.8061469 0.7600526 0.6775442 0.6779734
## forearm.girth 0.7976906 0.8628347 0.8135324 0.7130703 0.7315444
## knee.girth 0.5765679 0.5801664 0.5804820 0.7135134 0.5118940
## calf.girth 0.5707056 0.5707920 0.5656750 0.6600462 0.5115481
## ankle.girth 0.6259361 0.6649994 0.6484956 0.6313086 0.6623997
## wrist.girth 0.7507846 0.8432443 0.8659224 0.7206948 0.7696373
## age 0.2102470 0.2028904 0.2215147 0.1803180 0.2484763
## height 0.6357405 0.7523124 0.6848540 0.5867066 0.6917417
## shoulder.girth chest.girth waist.girth navel.girth hip.girth
## weight 0.8793832 0.8988234 0.9053409 0.7179399 0.7576721
## biacromial 0.7831739 0.7141486 0.6343090 0.3139561 0.3250877
## pelvic.breadth 0.2884577 0.3261211 0.4498945 0.5935838 0.5728108
## bitrochanteric 0.4635623 0.4743455 0.5624033 0.6070064 0.7434893
## chest.depth 0.7404735 0.8080765 0.8004537 0.6130228 0.5440697
## chest.diam 0.8675862 0.8647893 0.7846368 0.5115517 0.5068641
## elbow.diam 0.8179573 0.8000336 0.6920480 0.4397734 0.4242717
## wrist.diam 0.7739053 0.7582419 0.6763861 0.3967711 0.4113337
## knee.diam 0.6729619 0.6452346 0.6060924 0.4504462 0.5579286
## ankle.diam 0.6889967 0.7002848 0.6266948 0.4180081 0.3894831
## shoulder.girth 1.0000000 0.9285451 0.8227046 0.5325323 0.5314731
## chest.girth 0.9285451 1.0000000 0.8819770 0.6258189 0.5760541
## waist.girth 0.8227046 0.8819770 1.0000000 0.7621070 0.6909509
## navel.girth 0.5325323 0.6258189 0.7621070 1.0000000 0.8198649
## hip.girth 0.5314731 0.5760541 0.6909509 0.8198649 1.0000000
## thigh.girth 0.3087823 0.3504549 0.4151366 0.5812397 0.8235774
## bicep.girth 0.8944054 0.9044726 0.7999314 0.5520385 0.5504800
## forearm.girth 0.8907049 0.8839423 0.7730307 0.4865365 0.4994283
## knee.girth 0.6183799 0.6070020 0.6542704 0.6221640 0.7399292
## calf.girth 0.6043730 0.5832171 0.6020694 0.4986900 0.6581096
## ankle.girth 0.6776462 0.6641805 0.6465919 0.5258192 0.5821043
## wrist.girth 0.8351320 0.8192825 0.7167030 0.4410299 0.4481897
## age 0.1971285 0.2579937 0.3739958 0.4189151 0.2278693
## height 0.6807636 0.6281098 0.5597050 0.3252731 0.3384099
## thigh.girth bicep.girth forearm.girth knee.girth calf.girth
## weight 0.540676767 0.8656875 0.8650929 0.7919113 0.7447298
## biacromial 0.105677080 0.6956730 0.7519764 0.5076838 0.4976207
## pelvic.breadth 0.405582630 0.3085243 0.2993726 0.4761210 0.3879855
## bitrochanteric 0.516891268 0.4679921 0.4619208 0.6174524 0.5716573
## chest.depth 0.341728865 0.7294714 0.7155195 0.5626738 0.5297461
## chest.diam 0.294065600 0.7905738 0.7976906 0.5765679 0.5707056
## elbow.diam 0.191759902 0.8061469 0.8628347 0.5801664 0.5707920
## wrist.diam 0.181457879 0.7600526 0.8135324 0.5804820 0.5656750
## knee.diam 0.404915646 0.6775442 0.7130703 0.7135134 0.6600462
## ankle.diam 0.159930586 0.6779734 0.7315444 0.5118940 0.5115481
## shoulder.girth 0.308782294 0.8944054 0.8907049 0.6183799 0.6043730
## chest.girth 0.350454877 0.9044726 0.8839423 0.6070020 0.5832171
## waist.girth 0.415136602 0.7999314 0.7730307 0.6542704 0.6020694
## navel.girth 0.581239686 0.5520385 0.4865365 0.6221640 0.4986900
## hip.girth 0.823577426 0.5504800 0.4994283 0.7399292 0.6581096
## thigh.girth 1.000000000 0.3977879 0.3233755 0.6394071 0.6144429
## bicep.girth 0.397787922 1.0000000 0.9393573 0.6132996 0.6166695
## forearm.girth 0.323375544 0.9393573 1.0000000 0.6485153 0.6537984
## knee.girth 0.639407107 0.6132996 0.6485153 1.0000000 0.7990788
## calf.girth 0.614442942 0.6166695 0.6537984 0.7990788 1.0000000
## ankle.girth 0.413060662 0.6658508 0.7088273 0.7338806 0.7516910
## wrist.girth 0.228736643 0.8401296 0.9011480 0.6320826 0.6415886
## age -0.007646679 0.1919124 0.1660848 0.1439582 0.1244519
## height 0.101726784 0.6070166 0.6753614 0.5259818 0.4419199
## ankle.girth wrist.girth age height
## weight 0.7580149 0.8109316 0.221435966 0.72833068
## biacromial 0.5983044 0.7695432 0.083893026 0.76144089
## pelvic.breadth 0.3307441 0.2676489 0.258552894 0.36615649
## bitrochanteric 0.5307470 0.4649945 0.271764476 0.47412032
## chest.depth 0.5887505 0.6775134 0.308150549 0.56110106
## chest.diam 0.6259361 0.7507846 0.210246962 0.63574051
## elbow.diam 0.6649994 0.8432443 0.202890359 0.75231237
## wrist.diam 0.6484956 0.8659224 0.221514688 0.68485404
## knee.diam 0.6313086 0.7206948 0.180317957 0.58670658
## ankle.diam 0.6623997 0.7696373 0.248476291 0.69174166
## shoulder.girth 0.6776462 0.8351320 0.197128476 0.68076360
## chest.girth 0.6641805 0.8192825 0.257993695 0.62810979
## waist.girth 0.6465919 0.7167030 0.373995837 0.55970503
## navel.girth 0.5258192 0.4410299 0.418915127 0.32527309
## hip.girth 0.5821043 0.4481897 0.227869290 0.33840987
## thigh.girth 0.4130607 0.2287366 -0.007646679 0.10172678
## bicep.girth 0.6658508 0.8401296 0.191912416 0.60701664
## forearm.girth 0.7088273 0.9011480 0.166084760 0.67536145
## knee.girth 0.7338806 0.6320826 0.143958165 0.52598183
## calf.girth 0.7516910 0.6415886 0.124451947 0.44191990
## ankle.girth 1.0000000 0.7599351 0.156099154 0.56742251
## wrist.girth 0.7599351 1.0000000 0.199751271 0.70132692
## age 0.1560992 0.1997513 1.000000000 0.07945014
## height 0.5674225 0.7013269 0.079450138 1.00000000Mapa de calor para el conjunto de entrenamiento
library(ggcorrplot)
library(ggplot2)
ggcorrplot(cordatatraining) + ggtitle('Matriz de Correlaciones conjunto entrenamiento')
Realizar el boxPlot para el conjunto de entrenamiento
boxplot(data_training [,] , main = "Boxplot conjunto de Entrenamiento", names=c("Weight","Biacromial", "Pelvic.Breadth", "Bitrochanteric", "Chest.depth", "Chest.diam", "Elbow.diam", "Wrist.diam", "Knee.diam", "Ankle.diam", "shoulder.girth","chest.girth","waist.girth","navel.girth","hip.girth","thigh.girth","bicep.girth","forearm.girth","knee.girth","calf.girth","ankle.girth","wrist.girth","age","height"), cex.main = 1, cex.sub= 0.5 , ylab = 'Variabilidad', xlab = 'Variables', cex.lab=0.8, col = c("orange2", "yellow3", "green3", "grey","red", "brown", "black", 'blue', 'pink', 'violet'), axes=T, xlim=c(0, 24), outpch = 25, outbg = "red", whiskcol = 'black', whisklty = 2, lty = 1, tcl=0.4, las=0.3 )
Realizar distancia de Mahalanobis para el conjunto de entrenamiento
datatrainingmahala= mahalanobis(data_training, colMeans(data_training), cov(data_training))
datatrainingmahala## 225 31 290 174 505 274 493 440
## 26.194018 25.709546 21.490218 22.506174 35.220547 14.463441 33.499513 40.618378
## 385 196 68 55 310 319 79 238
## 32.224008 34.703966 17.731543 14.621177 15.106492 14.738978 17.436865 39.613674
## 43 370 362 301 65 382 16 355
## 14.541845 33.067279 15.034040 23.497079 15.445694 16.161802 31.624288 16.195831
## 89 277 498 134 152 282 112 147
## 20.631842 17.034460 22.548189 25.071961 18.034085 16.979922 30.593899 13.920002
## 42 489 330 415 207 212 78 99
## 41.598322 16.499088 15.610000 16.718339 34.132052 32.180960 40.733315 22.458554
## 376 163 243 391 221 86 144 327
## 25.207235 38.041555 28.078822 14.294444 53.669179 23.007066 30.735565 16.151416
## 359 200 58 241 25 45 263 183
## 64.430760 14.912236 19.348603 26.297356 28.922634 22.724439 27.788672 34.535399
## 487 326 494 349 442 234 95 271
## 10.593756 21.486398 26.659523 59.185369 40.269449 28.896443 24.681002 30.935693
## 345 40 206 185 1 322 333 188
## 15.565651 27.582477 18.835250 24.001951 22.379758 18.793111 34.414321 20.766502
## 427 469 438 85 311 167 71 46
## 16.050417 17.411243 34.757719 18.273790 26.601371 31.442345 23.771845 21.904680
## 281 193 218 194 133 216 244 392
## 11.753179 13.205066 36.808749 28.850565 24.276854 15.076133 50.424916 24.054455
## 20 92 286 334 98 298 410 291
## 23.058452 22.531952 20.100386 17.676128 23.195049 13.727310 16.008354 15.335473
## 49 97 66 109 104 434 153 88
## 23.981526 14.762105 40.122127 29.285714 14.736456 29.937988 29.122028 14.326633
## 158 324 491 60 264 422 375 108
## 21.540947 16.948088 43.996979 16.042712 16.427527 22.462780 29.389344 14.938395
## 266 157 187 466 19 418 33 429
## 24.947435 13.347754 24.871921 45.008583 24.456135 26.208250 26.298852 13.422081
## 151 368 63 120 474 354 265 96
## 19.964984 13.047505 19.528759 31.605934 91.414082 20.712715 14.637515 13.896713
## 454 453 395 222 361 424 171 313
## 16.128262 26.573235 27.922064 54.838308 24.391549 20.303558 15.113033 21.717413
## 293 273 409 471 54 154 47 235
## 28.980823 11.391618 19.333639 11.031677 23.495496 17.661168 27.243477 32.629445
## 24 249 69 233 38 335 433 125
## 28.774028 16.783349 57.056563 17.900959 15.099892 17.946416 18.603972 15.798682
## 192 126 30 401 170 114 145 197
## 37.086275 22.129321 15.167479 18.298715 17.419470 28.459303 20.164306 20.232878
## 476 146 53 384 247 118 386 331
## 27.542716 12.961243 22.010504 23.998055 19.478145 20.731118 16.452837 50.355301
## 398 159 123 300 283 230 437 94
## 20.609880 38.836689 16.574543 16.868612 17.524248 26.292944 13.172299 23.934832
## 137 190 229 15 284 122 75 268
## 31.643274 19.879805 18.603516 24.238648 24.317745 14.675723 20.075512 22.412001
## 226 480 251 208 176 232 164 485
## 20.189712 24.996192 16.301204 23.087000 39.510458 25.137316 24.587964 24.189033
## 227 337 179 342 100 460 470 117
## 44.127906 6.020223 36.164946 20.695511 30.503689 21.013894 11.811969 19.275114
## 270 357 215 44 4 140 14 482
## 25.491598 14.934868 48.298389 18.060399 28.721024 44.408489 15.462554 49.180033
## 308 365 364 90 444 350 239 91
## 18.223513 29.525728 14.202892 20.173217 16.218454 12.302168 27.458350 25.646003
## 172 106 9 374 169 447 473 358
## 21.994449 29.447384 25.407851 13.147394 27.497097 16.201828 15.821554 13.736644
## 383 73 461 278 344 378 347 201
## 9.989903 25.776707 17.155139 25.415537 9.697280 17.364157 16.337041 24.575236
## 356 317 450 210 105 173 425 414
## 22.285741 17.847435 16.001532 15.630819 28.656396 23.086847 68.233766 29.060611
## 205 186 388 387 237 346 236 285
## 20.953191 25.466880 12.762412 11.100739 24.122908 34.047751 35.299376 11.211832
## 48 416 130 17 412 141 160 259
## 33.807237 21.293973 24.196286 27.364565 24.666734 47.713484 17.702840 12.386271
## 380 379 61 110 83 287 84 340
## 22.089715 13.323916 28.752257 46.598900 10.128350 16.605756 15.589872 18.310163
## 451 486 363 3 306 316 13 341
## 11.166936 14.993567 18.495779 28.018175 15.399787 22.407768 27.321852 20.004308
## 27 36 223 138 431 240 490 446
## 22.010772 24.129807 28.183030 21.116661 23.057489 29.722444 19.286336 34.682921
## 488 155 143 312 294 305 127 111
## 27.713718 25.951955 13.294384 42.503246 11.015734 15.428816 39.501660 25.090078
## 455 393 289 257 12 432 77 184
## 24.794065 21.733564 25.475873 28.056791 22.877468 25.388307 21.444711 22.530936
## 87 296 74 231 59 439 224 492
## 30.811816 22.937145 25.359481 34.716995 22.158292 23.272522 23.715452 24.145848
## 309 421 452 10 307 499 57 397
## 18.953603 19.228821 22.841718 30.245110 20.279143 52.641616 22.798214 17.851367
## 328 39 260 394 93 329 302 132
## 43.532125 24.635011 13.320361 25.803913 23.507117 16.736233 20.616181 46.811505
## 477 135 242 2 178 62 445 403
## 40.167860 32.968381 21.537634 28.114907 36.403163 18.458722 16.492321 11.204608
## 336 50 139 116 276 150 129 21
## 11.449744 14.530366 19.740080 40.570851 14.736187 22.643353 41.305824 24.884268
## 448 280 288 177 390 204 338 303
## 35.059653 12.721675 11.151057 18.939663 17.041501 31.288922 19.763461 16.176121
## 148 29 128 161 22 246 162 406
## 15.949695 17.192242 17.439451 36.166018 25.284986 25.028278 30.860808 30.950071
## 339 497 202 441 325 32 211 275
## 17.744515 15.949515 39.605249 21.813905 25.235779 22.723012 16.147899 22.011749
## 506 255 267 420 168 245 463 373
## 22.409372 24.393988 14.446973 24.867237 21.312993 33.736314 26.200613 16.884736
## 67 217 64 198 456 405 203 175
## 16.050287 26.362549 16.609949 47.399470 32.190364 36.103400 21.929888 28.321725
## 299 7 258 6 481 478 297 80
## 21.099574 23.697328 20.791805 14.298626 27.788535 15.391506 18.433544 23.720635
## 321 252 195 272 449 199 166 372
## 26.252761 16.016476 24.779470 15.392229 15.018857 25.499805 27.579895 12.351127
## 41 315 292 56 367 475 314 351
## 21.149495 27.243038 19.835325 19.257557 32.482239 24.385143 16.099707 14.879685
## 462 34 35 70 102 436
## 14.795642 26.925216 21.461534 9.770562 25.035458 24.454800summary(datatrainingmahala)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6.02 16.61 22.41 23.94 27.77 91.41boxplot(datatrainingmahala, col = "skyblue", xlab="Distancia Mahalanobis",main = "Distancia de Mahalanobis del conjunto de entrenamiento", outpch = 25, outbg = "red")
boxplot.stats(datatrainingmahala)## $stats
## 337 287 506 481 474
## 6.020223 16.605756 22.410686 27.788535 44.408489
##
## $n
## [1] 406
##
## $conf
## [1] 21.53380 23.28757
##
## $out
## 221 359 349 244 466 474 222 69
## 53.66918 64.43076 59.18537 50.42492 45.00858 91.41408 54.83831 57.05656
## 331 215 482 425 141 110 499 132
## 50.35530 48.29839 49.18003 68.23377 47.71348 46.59890 52.64162 46.81150
## 198
## 47.39947- Realizar el modelo de regresión múltiple con todas las variables involucradas y la validación del modelo.
Modelo de regresión múltiple para el conjunto de entrenamiento
modelolm1=lm(weight~., data = data_training)
summary(modelolm1)##
## Call:
## lm(formula = weight ~ ., data = data_training)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.1245 -1.2765 0.0074 1.2548 8.5173
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -118.39184 2.85443 -41.477 < 2e-16 ***
## biacromial -0.05318 0.07416 -0.717 0.473760
## pelvic.breadth 0.08507 0.07289 1.167 0.243865
## bitrochanteric -0.05284 0.10320 -0.512 0.608924
## chest.depth 0.31068 0.07741 4.014 7.20e-05 ***
## chest.diam 0.15778 0.09031 1.747 0.081415 .
## elbow.diam 0.03080 0.20745 0.148 0.882052
## wrist.diam 0.21581 0.25379 0.850 0.395665
## knee.diam 0.41704 0.15175 2.748 0.006275 **
## ankle.diam 0.04212 0.17336 0.243 0.808177
## shoulder.girth 0.05592 0.03517 1.590 0.112663
## chest.girth 0.14624 0.04225 3.461 0.000598 ***
## waist.girth 0.33340 0.02752 12.116 < 2e-16 ***
## navel.girth 0.02950 0.02723 1.083 0.279383
## hip.girth 0.25363 0.05468 4.638 4.83e-06 ***
## thigh.girth 0.22158 0.05884 3.766 0.000192 ***
## bicep.girth 0.13134 0.09050 1.451 0.147524
## forearm.girth 0.35670 0.15183 2.349 0.019316 *
## knee.girth 0.21726 0.09190 2.364 0.018569 *
## calf.girth 0.39131 0.07802 5.015 8.12e-07 ***
## ankle.girth 0.05629 0.11433 0.492 0.622776
## wrist.girth -0.31358 0.24225 -1.294 0.196288
## age -0.05850 0.01370 -4.270 2.47e-05 ***
## height 0.30778 0.02034 15.132 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.108 on 382 degrees of freedom
## Multiple R-squared: 0.9765, Adjusted R-squared: 0.975
## F-statistic: 688.9 on 23 and 382 DF, p-value: < 2.2e-16Validación del modelo de regresión múltiple para el conjunto de entrenamiento
Análisis de los residuos
residuosmodelo1=rstandard(modelolm1)
valores.ajustados1=fitted(modelolm1)
plot(valores.ajustados1, residuosmodelo1, xlab = "Valores ajustados", main="Gráfico dispersión de residuos - conjunto entrenamiento" , ylab = "Residuos estandarizados", col = "blue")
Entender la normalidad de residuos con gráfico de histograma incluyendo curva de distribución empírica y teórica para el conjunto de entrenamiento
x=seq(-2,4,0.01)
hist(residuosmodelo1, breaks = "FD", col = "lightblue", main="Histograma de residuos - datos entrenamiento",
xlab="Residuos", prob = TRUE, ylim = c(0,0.5))
theo.res=dnorm(x, mean = 0, sd = 1)
lines(theo.res ~ x, col="violet", lwd = 2)
lines(density(residuosmodelo1), col = "blue", lwd = 2)
Gráfico de QQ plot para el conjunto de entrenamiento
qqnorm(residuosmodelo1, main= "QQ plot de residuos - datos entrenamiento")
qqline(residuosmodelo1, col="blue", lwd = 2)
- Comparar el primer modelo utilizando el comando predict () sobre el segundo conjunto de datos data.body2 y calculando el error cuadratico medio para cada caso
prediccion1=predict(modelolm1, data_test)
prediccion1## 5 8 11 18 23 26 28 37
## 79.96526 78.89438 80.38535 67.33191 67.65617 89.38856 73.43100 69.90253
## 51 52 72 76 81 82 101 103
## 75.59995 82.38469 77.76965 65.94783 96.77197 80.45650 86.71403 57.25589
## 107 113 115 119 121 124 131 136
## 84.40548 62.94834 82.80462 81.74278 81.73293 107.47256 75.38555 79.64496
## 142 149 156 165 180 181 182 189
## 87.76814 73.90585 66.92714 68.59073 81.14602 70.35148 83.18543 78.33134
## 191 209 213 214 219 220 228 248
## 79.67180 73.60900 93.78390 68.42034 79.11079 81.95546 78.09756 51.46534
## 250 253 254 256 261 262 269 279
## 47.69543 56.84060 44.30635 70.04823 40.35570 49.56773 83.43927 54.78193
## 295 304 318 320 323 332 343 348
## 50.67515 63.32607 45.91001 48.91492 54.20725 52.58160 47.86306 53.29895
## 352 353 360 366 369 371 377 381
## 59.45190 59.05218 54.48530 42.38543 62.37061 56.30421 56.83411 39.85894
## 389 396 399 400 402 404 407 408
## 53.29277 65.52477 55.67100 63.13899 72.76570 54.57043 86.46361 55.50647
## 411 413 417 419 423 426 428 430
## 77.74966 67.43435 60.16900 59.30239 63.54912 57.09038 78.95714 54.61854
## 435 443 457 458 459 464 465 467
## 58.51437 61.90194 80.50878 69.45860 59.26224 49.99025 64.50755 67.51135
## 468 472 479 483 484 495 496 500
## 64.85336 55.82649 72.72166 62.06329 55.62538 56.70487 62.46031 68.66276
## 501 502 503 504 507
## 62.57023 74.67758 70.99442 56.14787 71.02845Datos verdaderos de conjunto dato testeo
data_test[,1]## [1] 78.8 78.4 76.6 70.0 66.2 89.6 76.4 67.2 75.6 86.2 78.9 63.9
## [13] 93.0 80.9 86.4 53.9 83.2 65.0 84.1 82.7 79.5 116.4 75.0 76.4
## [25] 86.4 72.7 68.6 65.9 80.5 70.0 81.8 73.6 82.7 72.3 91.1 67.3
## [37] 76.6 85.0 77.3 51.6 49.2 59.0 47.6 66.8 42.0 50.0 82.5 55.0
## [49] 50.2 60.7 48.7 50.0 55.7 52.8 48.6 53.6 58.4 56.2 51.8 45.0
## [61] 60.2 58.8 54.4 43.2 54.6 63.6 56.8 64.1 72.3 55.9 84.5 55.9
## [73] 76.4 65.9 58.6 59.1 60.0 54.1 75.9 57.3 58.6 62.0 80.9 70.5
## [85] 60.9 52.7 62.7 66.4 67.3 57.7 72.3 63.6 53.4 57.3 64.1 68.2
## [97] 61.4 76.8 71.8 55.5 67.3Cálculo suma errores totales
Error1=sum((data_test[,1]-prediccion1)^2)
Error1## [1] 482.2333Cálculo error medio
ME1.test = mean((data_test[,1]-prediccion1)^2)
ME1.test## [1] 4.774587Calculo error cuadrático medio
MEC1.test = mean((residuosmodelo1)^2)
MEC1.test## [1] 1.009834Análisis de valores verdaderos vs calculados conjunto entrenamiento.
plot(data_test[,1], prediccion1, main = 'Predicción valores verdaderos vs calculados - dato test' , xlab = "Valores verdaderos - weight",
ylab = "Valores calculados - weight", col = "blue")
abline(0,1, col = "orange", lwd = 2)
- Realizar el modelo de regresión lineal múltiple utilizando el método de selección de variables Mixed Selection.
pent: variables con p-valor menor 0.05 serán incluídas en el modelo.
prem: variables con p-valor mayor 0.5 serán eliminadas del modelo.
progress: lógica que muestra las variables incluidas en cada paso
details: muestra el modelo en cada paso
modelolm2 = ols_step_both_p(modelolm1, pent= 0.05, prem = 0.5, details = TRUE, progress = TRUE,
print_plot=TRUE)## Stepwise Selection Method
## ---------------------------
##
## Candidate Terms:
##
## 1. biacromial
## 2. pelvic.breadth
## 3. bitrochanteric
## 4. chest.depth
## 5. chest.diam
## 6. elbow.diam
## 7. wrist.diam
## 8. knee.diam
## 9. ankle.diam
## 10. shoulder.girth
## 11. chest.girth
## 12. waist.girth
## 13. navel.girth
## 14. hip.girth
## 15. thigh.girth
## 16. bicep.girth
## 17. forearm.girth
## 18. knee.girth
## 19. calf.girth
## 20. ankle.girth
## 21. wrist.girth
## 22. age
## 23. height
##
## We are selecting variables based on p value...
##
##
## Stepwise Selection: Step 1
##
## - waist.girth added
##
## Model Summary
## --------------------------------------------------------------
## R 0.905 RMSE 5.675
## R-Squared 0.820 Coef. Var 8.140
## Adj. R-Squared 0.819 MSE 32.203
## Pred R-Squared 0.818 MAE 4.458
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 59124.940 1 59124.940 1835.991 0.0000
## Residual 13010.126 404 32.203
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------
## (Intercept) -14.579 1.987 -7.336 0.000 -18.485 -10.672
## waist.girth 1.089 0.025 0.905 42.848 0.000 1.039 1.139
## -------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 2
##
## - height added
##
## Model Summary
## --------------------------------------------------------------
## R 0.944 RMSE 4.414
## R-Squared 0.891 Coef. Var 6.332
## Adj. R-Squared 0.891 MSE 19.483
## Pred R-Squared 0.889 MAE 3.372
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 64283.477 2 32141.738 1649.745 0.0000
## Residual 7851.589 403 19.483
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------
## (Intercept) -74.949 4.019 -18.648 0.000 -82.851 -67.048
## waist.girth 0.872 0.024 0.725 36.544 0.000 0.825 0.918
## height 0.450 0.028 0.323 16.272 0.000 0.396 0.504
## --------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.944 RMSE 4.414
## R-Squared 0.891 Coef. Var 6.332
## Adj. R-Squared 0.891 MSE 19.483
## Pred R-Squared 0.889 MAE 3.372
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 64283.477 2 32141.738 1649.745 0.0000
## Residual 7851.589 403 19.483
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## --------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## --------------------------------------------------------------------------------------------
## (Intercept) -74.949 4.019 -18.648 0.000 -82.851 -67.048
## waist.girth 0.872 0.024 0.725 36.544 0.000 0.825 0.918
## height 0.450 0.028 0.323 16.272 0.000 0.396 0.504
## --------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 3
##
## - thigh.girth added
##
## Model Summary
## -------------------------------------------------------------
## R 0.972 RMSE 3.155
## R-Squared 0.945 Coef. Var 4.526
## Adj. R-Squared 0.944 MSE 9.955
## Pred R-Squared 0.943 MAE 2.416
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 68133.199 3 22711.066 2281.398 0.0000
## Residual 4001.867 402 9.955
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------------
## (Intercept) -119.047 3.645 -32.664 0.000 -126.212 -111.882
## waist.girth 0.710 0.019 0.590 37.501 0.000 0.673 0.747
## height 0.518 0.020 0.372 25.827 0.000 0.479 0.558
## thigh.girth 0.789 0.040 0.258 19.665 0.000 0.710 0.867
## -----------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.972 RMSE 3.155
## R-Squared 0.945 Coef. Var 4.526
## Adj. R-Squared 0.944 MSE 9.955
## Pred R-Squared 0.943 MAE 2.416
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 68133.199 3 22711.066 2281.398 0.0000
## Residual 4001.867 402 9.955
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------------
## (Intercept) -119.047 3.645 -32.664 0.000 -126.212 -111.882
## waist.girth 0.710 0.019 0.590 37.501 0.000 0.673 0.747
## height 0.518 0.020 0.372 25.827 0.000 0.479 0.558
## thigh.girth 0.789 0.040 0.258 19.665 0.000 0.710 0.867
## -----------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 4
##
## - forearm.girth added
##
## Model Summary
## -------------------------------------------------------------
## R 0.981 RMSE 2.609
## R-Squared 0.962 Coef. Var 3.743
## Adj. R-Squared 0.962 MSE 6.807
## Pred R-Squared 0.961 MAE 1.960
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 69405.425 4 17351.356 2549.015 0.0000
## Residual 2729.641 401 6.807
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -113.358 3.042 -37.260 0.000 -119.339 -107.377
## waist.girth 0.555 0.019 0.461 28.705 0.000 0.517 0.593
## height 0.398 0.019 0.285 21.158 0.000 0.361 0.435
## thigh.girth 0.745 0.033 0.243 22.352 0.000 0.679 0.810
## forearm.girth 1.132 0.083 0.237 13.671 0.000 0.969 1.294
## -------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.981 RMSE 2.609
## R-Squared 0.962 Coef. Var 3.743
## Adj. R-Squared 0.962 MSE 6.807
## Pred R-Squared 0.961 MAE 1.960
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 69405.425 4 17351.356 2549.015 0.0000
## Residual 2729.641 401 6.807
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -113.358 3.042 -37.260 0.000 -119.339 -107.377
## waist.girth 0.555 0.019 0.461 28.705 0.000 0.517 0.593
## height 0.398 0.019 0.285 21.158 0.000 0.361 0.435
## thigh.girth 0.745 0.033 0.243 22.352 0.000 0.679 0.810
## forearm.girth 1.132 0.083 0.237 13.671 0.000 0.969 1.294
## -------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 5
##
## - calf.girth added
##
## Model Summary
## -------------------------------------------------------------
## R 0.983 RMSE 2.491
## R-Squared 0.966 Coef. Var 3.574
## Adj. R-Squared 0.965 MSE 6.207
## Pred R-Squared 0.964 MAE 1.842
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 69652.373 5 13930.475 2244.414 0.0000
## Residual 2482.693 400 6.207
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -115.077 2.918 -39.439 0.000 -120.813 -109.340
## waist.girth 0.550 0.018 0.457 29.757 0.000 0.513 0.586
## height 0.385 0.018 0.276 21.332 0.000 0.350 0.421
## thigh.girth 0.614 0.038 0.201 16.155 0.000 0.539 0.688
## forearm.girth 0.948 0.084 0.199 11.255 0.000 0.782 1.113
## calf.girth 0.457 0.072 0.094 6.308 0.000 0.314 0.599
## -------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.983 RMSE 2.491
## R-Squared 0.966 Coef. Var 3.574
## Adj. R-Squared 0.965 MSE 6.207
## Pred R-Squared 0.964 MAE 1.842
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 69652.373 5 13930.475 2244.414 0.0000
## Residual 2482.693 400 6.207
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -115.077 2.918 -39.439 0.000 -120.813 -109.340
## waist.girth 0.550 0.018 0.457 29.757 0.000 0.513 0.586
## height 0.385 0.018 0.276 21.332 0.000 0.350 0.421
## thigh.girth 0.614 0.038 0.201 16.155 0.000 0.539 0.688
## forearm.girth 0.948 0.084 0.199 11.255 0.000 0.782 1.113
## calf.girth 0.457 0.072 0.094 6.308 0.000 0.314 0.599
## -------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 6
##
## - chest.girth added
##
## Model Summary
## -------------------------------------------------------------
## R 0.985 RMSE 2.350
## R-Squared 0.969 Coef. Var 3.371
## Adj. R-Squared 0.969 MSE 5.522
## Pred R-Squared 0.968 MAE 1.765
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 69931.748 6 11655.291 2110.663 0.0000
## Residual 2203.318 399 5.522
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -118.274 2.789 -42.412 0.000 -123.756 -112.792
## waist.girth 0.439 0.023 0.365 18.844 0.000 0.394 0.485
## height 0.378 0.017 0.271 22.163 0.000 0.345 0.412
## thigh.girth 0.600 0.036 0.196 16.714 0.000 0.529 0.670
## forearm.girth 0.488 0.102 0.102 4.764 0.000 0.287 0.689
## calf.girth 0.539 0.069 0.111 7.782 0.000 0.403 0.675
## chest.girth 0.243 0.034 0.182 7.113 0.000 0.176 0.310
## -------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.985 RMSE 2.350
## R-Squared 0.969 Coef. Var 3.371
## Adj. R-Squared 0.969 MSE 5.522
## Pred R-Squared 0.968 MAE 1.765
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 69931.748 6 11655.291 2110.663 0.0000
## Residual 2203.318 399 5.522
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -118.274 2.789 -42.412 0.000 -123.756 -112.792
## waist.girth 0.439 0.023 0.365 18.844 0.000 0.394 0.485
## height 0.378 0.017 0.271 22.163 0.000 0.345 0.412
## thigh.girth 0.600 0.036 0.196 16.714 0.000 0.529 0.670
## forearm.girth 0.488 0.102 0.102 4.764 0.000 0.287 0.689
## calf.girth 0.539 0.069 0.111 7.782 0.000 0.403 0.675
## chest.girth 0.243 0.034 0.182 7.113 0.000 0.176 0.310
## -------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 7
##
## - hip.girth added
##
## Model Summary
## -------------------------------------------------------------
## R 0.986 RMSE 2.229
## R-Squared 0.973 Coef. Var 3.197
## Adj. R-Squared 0.972 MSE 4.968
## Pred R-Squared 0.971 MAE 1.670
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70157.849 7 10022.550 2017.469 0.0000
## Residual 1977.217 398 4.968
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -122.360 2.713 -45.093 0.000 -127.695 -117.026
## waist.girth 0.358 0.025 0.298 14.191 0.000 0.308 0.407
## height 0.357 0.016 0.256 21.666 0.000 0.325 0.389
## thigh.girth 0.326 0.053 0.107 6.148 0.000 0.222 0.430
## forearm.girth 0.591 0.098 0.124 6.008 0.000 0.398 0.784
## calf.girth 0.512 0.066 0.106 7.774 0.000 0.382 0.641
## chest.girth 0.250 0.032 0.187 7.712 0.000 0.186 0.314
## hip.girth 0.282 0.042 0.138 6.746 0.000 0.200 0.364
## -------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.986 RMSE 2.229
## R-Squared 0.973 Coef. Var 3.197
## Adj. R-Squared 0.972 MSE 4.968
## Pred R-Squared 0.971 MAE 1.670
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70157.849 7 10022.550 2017.469 0.0000
## Residual 1977.217 398 4.968
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -122.360 2.713 -45.093 0.000 -127.695 -117.026
## waist.girth 0.358 0.025 0.298 14.191 0.000 0.308 0.407
## height 0.357 0.016 0.256 21.666 0.000 0.325 0.389
## thigh.girth 0.326 0.053 0.107 6.148 0.000 0.222 0.430
## forearm.girth 0.591 0.098 0.124 6.008 0.000 0.398 0.784
## calf.girth 0.512 0.066 0.106 7.774 0.000 0.382 0.641
## chest.girth 0.250 0.032 0.187 7.712 0.000 0.186 0.314
## hip.girth 0.282 0.042 0.138 6.746 0.000 0.200 0.364
## -------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 8
##
## - knee.diam added
##
## Model Summary
## -------------------------------------------------------------
## R 0.987 RMSE 2.199
## R-Squared 0.973 Coef. Var 3.154
## Adj. R-Squared 0.973 MSE 4.834
## Pred R-Squared 0.972 MAE 1.654
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70216.126 8 8777.016 1815.834 0.0000
## Residual 1918.940 397 4.834
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -123.356 2.692 -45.825 0.000 -128.648 -118.064
## waist.girth 0.364 0.025 0.303 14.594 0.000 0.315 0.413
## height 0.345 0.017 0.248 20.788 0.000 0.313 0.378
## thigh.girth 0.335 0.052 0.110 6.409 0.000 0.233 0.438
## forearm.girth 0.503 0.100 0.105 5.018 0.000 0.306 0.700
## calf.girth 0.456 0.067 0.094 6.812 0.000 0.324 0.587
## chest.girth 0.250 0.032 0.188 7.830 0.000 0.187 0.313
## hip.girth 0.257 0.042 0.126 6.155 0.000 0.175 0.339
## knee.diam 0.459 0.132 0.046 3.472 0.001 0.199 0.719
## -------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.987 RMSE 2.199
## R-Squared 0.973 Coef. Var 3.154
## Adj. R-Squared 0.973 MSE 4.834
## Pred R-Squared 0.972 MAE 1.654
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70216.126 8 8777.016 1815.834 0.0000
## Residual 1918.940 397 4.834
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -123.356 2.692 -45.825 0.000 -128.648 -118.064
## waist.girth 0.364 0.025 0.303 14.594 0.000 0.315 0.413
## height 0.345 0.017 0.248 20.788 0.000 0.313 0.378
## thigh.girth 0.335 0.052 0.110 6.409 0.000 0.233 0.438
## forearm.girth 0.503 0.100 0.105 5.018 0.000 0.306 0.700
## calf.girth 0.456 0.067 0.094 6.812 0.000 0.324 0.587
## chest.girth 0.250 0.032 0.188 7.830 0.000 0.187 0.313
## hip.girth 0.257 0.042 0.126 6.155 0.000 0.175 0.339
## knee.diam 0.459 0.132 0.046 3.472 0.001 0.199 0.719
## -------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 9
##
## - age added
##
## Model Summary
## -------------------------------------------------------------
## R 0.987 RMSE 2.165
## R-Squared 0.974 Coef. Var 3.106
## Adj. R-Squared 0.974 MSE 4.689
## Pred R-Squared 0.973 MAE 1.630
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70278.408 9 7808.712 1665.493 0.0000
## Residual 1856.657 396 4.689
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -121.271 2.712 -44.713 0.000 -126.603 -115.939
## waist.girth 0.386 0.025 0.321 15.260 0.000 0.337 0.436
## height 0.334 0.017 0.240 20.069 0.000 0.301 0.367
## thigh.girth 0.280 0.054 0.091 5.196 0.000 0.174 0.385
## forearm.girth 0.472 0.099 0.099 4.758 0.000 0.277 0.666
## calf.girth 0.462 0.066 0.095 7.006 0.000 0.332 0.591
## chest.girth 0.248 0.031 0.186 7.868 0.000 0.186 0.310
## hip.girth 0.285 0.042 0.140 6.812 0.000 0.203 0.367
## knee.diam 0.503 0.131 0.050 3.845 0.000 0.246 0.760
## age -0.047 0.013 -0.034 -3.645 0.000 -0.073 -0.022
## -------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.987 RMSE 2.165
## R-Squared 0.974 Coef. Var 3.106
## Adj. R-Squared 0.974 MSE 4.689
## Pred R-Squared 0.973 MAE 1.630
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70278.408 9 7808.712 1665.493 0.0000
## Residual 1856.657 396 4.689
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -121.271 2.712 -44.713 0.000 -126.603 -115.939
## waist.girth 0.386 0.025 0.321 15.260 0.000 0.337 0.436
## height 0.334 0.017 0.240 20.069 0.000 0.301 0.367
## thigh.girth 0.280 0.054 0.091 5.196 0.000 0.174 0.385
## forearm.girth 0.472 0.099 0.099 4.758 0.000 0.277 0.666
## calf.girth 0.462 0.066 0.095 7.006 0.000 0.332 0.591
## chest.girth 0.248 0.031 0.186 7.868 0.000 0.186 0.310
## hip.girth 0.285 0.042 0.140 6.812 0.000 0.203 0.367
## knee.diam 0.503 0.131 0.050 3.845 0.000 0.246 0.760
## age -0.047 0.013 -0.034 -3.645 0.000 -0.073 -0.022
## -------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 10
##
## - chest.depth added
##
## Model Summary
## -------------------------------------------------------------
## R 0.987 RMSE 2.132
## R-Squared 0.975 Coef. Var 3.058
## Adj. R-Squared 0.974 MSE 4.546
## Pred R-Squared 0.973 MAE 1.611
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70339.455 10 7033.945 1547.333 0.0000
## Residual 1795.611 395 4.546
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -120.430 2.680 -44.929 0.000 -125.699 -115.160
## waist.girth 0.364 0.026 0.303 14.194 0.000 0.314 0.415
## height 0.324 0.017 0.232 19.477 0.000 0.291 0.356
## thigh.girth 0.262 0.053 0.086 4.934 0.000 0.158 0.367
## forearm.girth 0.476 0.098 0.100 4.877 0.000 0.284 0.668
## calf.girth 0.451 0.065 0.093 6.938 0.000 0.323 0.578
## chest.girth 0.216 0.032 0.162 6.710 0.000 0.153 0.279
## hip.girth 0.294 0.041 0.144 7.111 0.000 0.212 0.375
## knee.diam 0.549 0.129 0.055 4.240 0.000 0.294 0.803
## age -0.053 0.013 -0.039 -4.147 0.000 -0.079 -0.028
## chest.depth 0.279 0.076 0.053 3.665 0.000 0.129 0.428
## -------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.987 RMSE 2.132
## R-Squared 0.975 Coef. Var 3.058
## Adj. R-Squared 0.974 MSE 4.546
## Pred R-Squared 0.973 MAE 1.611
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70339.455 10 7033.945 1547.333 0.0000
## Residual 1795.611 395 4.546
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -120.430 2.680 -44.929 0.000 -125.699 -115.160
## waist.girth 0.364 0.026 0.303 14.194 0.000 0.314 0.415
## height 0.324 0.017 0.232 19.477 0.000 0.291 0.356
## thigh.girth 0.262 0.053 0.086 4.934 0.000 0.158 0.367
## forearm.girth 0.476 0.098 0.100 4.877 0.000 0.284 0.668
## calf.girth 0.451 0.065 0.093 6.938 0.000 0.323 0.578
## chest.girth 0.216 0.032 0.162 6.710 0.000 0.153 0.279
## hip.girth 0.294 0.041 0.144 7.111 0.000 0.212 0.375
## knee.diam 0.549 0.129 0.055 4.240 0.000 0.294 0.803
## age -0.053 0.013 -0.039 -4.147 0.000 -0.079 -0.028
## chest.depth 0.279 0.076 0.053 3.665 0.000 0.129 0.428
## -------------------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 11
##
## - knee.girth added
##
## Model Summary
## -------------------------------------------------------------
## R 0.988 RMSE 2.118
## R-Squared 0.975 Coef. Var 3.038
## Adj. R-Squared 0.975 MSE 4.486
## Pred R-Squared 0.974 MAE 1.597
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70367.485 11 6397.044 1425.923 0.0000
## Residual 1767.581 394 4.486
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -119.942 2.670 -44.923 0.000 -125.192 -114.693
## waist.girth 0.358 0.026 0.297 13.955 0.000 0.307 0.408
## height 0.315 0.017 0.226 18.671 0.000 0.282 0.348
## thigh.girth 0.244 0.053 0.080 4.575 0.000 0.139 0.349
## forearm.girth 0.461 0.097 0.097 4.745 0.000 0.270 0.652
## calf.girth 0.380 0.070 0.079 5.403 0.000 0.242 0.519
## chest.girth 0.226 0.032 0.170 7.017 0.000 0.163 0.290
## hip.girth 0.277 0.042 0.136 6.676 0.000 0.196 0.359
## knee.diam 0.464 0.133 0.046 3.494 0.001 0.203 0.726
## age -0.053 0.013 -0.038 -4.114 0.000 -0.078 -0.027
## chest.depth 0.273 0.076 0.052 3.613 0.000 0.124 0.422
## knee.girth 0.215 0.086 0.041 2.500 0.013 0.046 0.384
## -------------------------------------------------------------------------------------------------
##
##
##
## Model Summary
## -------------------------------------------------------------
## R 0.988 RMSE 2.118
## R-Squared 0.975 Coef. Var 3.038
## Adj. R-Squared 0.975 MSE 4.486
## Pred R-Squared 0.974 MAE 1.597
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70367.485 11 6397.044 1425.923 0.0000
## Residual 1767.581 394 4.486
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -119.942 2.670 -44.923 0.000 -125.192 -114.693
## waist.girth 0.358 0.026 0.297 13.955 0.000 0.307 0.408
## height 0.315 0.017 0.226 18.671 0.000 0.282 0.348
## thigh.girth 0.244 0.053 0.080 4.575 0.000 0.139 0.349
## forearm.girth 0.461 0.097 0.097 4.745 0.000 0.270 0.652
## calf.girth 0.380 0.070 0.079 5.403 0.000 0.242 0.519
## chest.girth 0.226 0.032 0.170 7.017 0.000 0.163 0.290
## hip.girth 0.277 0.042 0.136 6.676 0.000 0.196 0.359
## knee.diam 0.464 0.133 0.046 3.494 0.001 0.203 0.726
## age -0.053 0.013 -0.038 -4.114 0.000 -0.078 -0.027
## chest.depth 0.273 0.076 0.052 3.613 0.000 0.124 0.422
## knee.girth 0.215 0.086 0.041 2.500 0.013 0.046 0.384
## -------------------------------------------------------------------------------------------------
##
##
##
## No more variables to be added/removed.
##
##
## Final Model Output
## ------------------
##
## Model Summary
## -------------------------------------------------------------
## R 0.988 RMSE 2.118
## R-Squared 0.975 Coef. Var 3.038
## Adj. R-Squared 0.975 MSE 4.486
## Pred R-Squared 0.974 MAE 1.597
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 70367.485 11 6397.044 1425.923 0.0000
## Residual 1767.581 394 4.486
## Total 72135.066 405
## ------------------------------------------------------------------------
##
## Parameter Estimates
## -------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -------------------------------------------------------------------------------------------------
## (Intercept) -119.942 2.670 -44.923 0.000 -125.192 -114.693
## waist.girth 0.358 0.026 0.297 13.955 0.000 0.307 0.408
## height 0.315 0.017 0.226 18.671 0.000 0.282 0.348
## thigh.girth 0.244 0.053 0.080 4.575 0.000 0.139 0.349
## forearm.girth 0.461 0.097 0.097 4.745 0.000 0.270 0.652
## calf.girth 0.380 0.070 0.079 5.403 0.000 0.242 0.519
## chest.girth 0.226 0.032 0.170 7.017 0.000 0.163 0.290
## hip.girth 0.277 0.042 0.136 6.676 0.000 0.196 0.359
## knee.diam 0.464 0.133 0.046 3.494 0.001 0.203 0.726
## age -0.053 0.013 -0.038 -4.114 0.000 -0.078 -0.027
## chest.depth 0.273 0.076 0.052 3.613 0.000 0.124 0.422
## knee.girth 0.215 0.086 0.041 2.500 0.013 0.046 0.384
## -------------------------------------------------------------------------------------------------modelolm2 = modelolm2$modelcoef.estimados2 = summary(modelolm2)[["coefficients"]][1:12]
coef.estimados2## [1] -119.94238480 0.35764567 0.31508021 0.24398655 0.46092806
## [6] 0.38040510 0.22623013 0.27722863 0.46439092 -0.05257939
## [11] 0.27296379 0.21472081summary(modelolm2)##
## Call:
## lm(formula = paste(response, "~", paste(preds, collapse = " + ")),
## data = l)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.4622 -1.3170 0.0429 1.1664 8.4828
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -119.94238 2.66995 -44.923 < 2e-16 ***
## waist.girth 0.35765 0.02563 13.955 < 2e-16 ***
## height 0.31508 0.01688 18.671 < 2e-16 ***
## thigh.girth 0.24399 0.05333 4.575 6.39e-06 ***
## forearm.girth 0.46093 0.09715 4.745 2.93e-06 ***
## calf.girth 0.38041 0.07040 5.403 1.14e-07 ***
## chest.girth 0.22623 0.03224 7.017 9.93e-12 ***
## hip.girth 0.27723 0.04153 6.676 8.36e-11 ***
## knee.diam 0.46439 0.13290 3.494 0.000529 ***
## age -0.05258 0.01278 -4.114 4.73e-05 ***
## chest.depth 0.27296 0.07556 3.613 0.000342 ***
## knee.girth 0.21472 0.08590 2.500 0.012839 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.118 on 394 degrees of freedom
## Multiple R-squared: 0.9755, Adjusted R-squared: 0.9748
## F-statistic: 1426 on 11 and 394 DF, p-value: < 2.2e-16Validación del modelo de regresión multiple utilizando el método de selección de variables mixed selection
Análisis de los residuos
residuosmodelo2=modelolm2$residuals
valores.ajustados2=modelolm2$fitted.values
residuos2_sd=(residuosmodelo2-mean(residuosmodelo2))/sd(residuosmodelo2)
plot(valores.ajustados2, residuos2_sd, main="Gráfico dispersión de residuos - mixed selection", xlab = "Valores ajustados", ylab = "Residuos estandarizados", col = 'red')
Entender la normalidad de residuos con gráfico de histograma incluyendo curva de distribución empírica y teórica para el método de selección de variables mixed selection.
x=seq(-4,4,0.01)
hist(residuos2_sd, col = "yellow", main="Histograma de residuos - mixed selection", xlab="Residuos",prob = TRUE, ylim = c(0,0.45))
theo.res=dnorm(x, mean = 0, sd = 1)
lines(theo.res ~ x, col="orange", lwd = 2 )
lines(density(residuos2_sd), col="violet", lwd = 2)
Entender la normalidad de residuos con gráfico de QQ-plot incluyendo curva de distribución empírica y teórica para el método de selección de variables mixed selection
qqnorm(residuos2_sd, main = 'QQ plot residuos - mixed selection')
qqline(residuos2_sd, col="yellow", lwd = 2)
- Comparar el primer modelo utilizando el comando predict () sobre el segundo conjunto de datos data_test y calculando el error cuadrático medio para el caso de método de selección de variables de mixed selection
Valores calculados
prediccion2=predict(modelolm2, data_test)
prediccion2## 5 8 11 18 23 26 28 37
## 80.72743 79.24969 79.95961 66.83213 67.33634 89.48429 73.07341 69.40112
## 51 52 72 76 81 82 101 103
## 75.27207 82.32266 77.85605 65.78213 96.03548 80.70151 86.45037 56.68141
## 107 113 115 119 121 124 131 136
## 83.78599 63.10515 83.11556 81.51716 81.30201 107.30961 75.92296 80.34579
## 142 149 156 165 180 181 182 189
## 88.54618 74.04851 66.59301 67.89705 81.54746 70.03948 82.76415 78.32543
## 191 209 213 214 219 220 228 248
## 79.67837 73.32619 93.50596 69.31488 79.25658 81.44547 78.08806 51.70696
## 250 253 254 256 261 262 269 279
## 48.20772 56.53656 44.27263 70.34666 40.34998 49.44525 83.52371 54.91052
## 295 304 318 320 323 332 343 348
## 50.81201 63.48092 45.82615 48.78875 54.47768 52.29242 47.90619 53.58749
## 352 353 360 366 369 371 377 381
## 59.45335 58.94962 54.43594 42.40387 62.86626 56.58972 56.67717 39.74312
## 389 396 399 400 402 404 407 408
## 52.94583 65.40099 55.52300 63.22358 71.75722 54.26886 86.43317 54.60946
## 411 413 417 419 423 426 428 430
## 77.61650 66.86771 59.56761 59.18733 63.50211 56.83988 78.47048 54.29735
## 435 443 457 458 459 464 465 467
## 58.14458 61.71876 79.97678 69.09143 59.03228 49.83376 64.46797 67.59804
## 468 472 479 483 484 495 496 500
## 64.42073 55.63807 72.86264 61.82624 56.12825 56.60151 62.66825 68.62638
## 501 502 503 504 507
## 62.26284 74.90940 70.61341 55.54792 70.89471Valores verdaderos de datos de testeo
data_test[,1]## [1] 78.8 78.4 76.6 70.0 66.2 89.6 76.4 67.2 75.6 86.2 78.9 63.9
## [13] 93.0 80.9 86.4 53.9 83.2 65.0 84.1 82.7 79.5 116.4 75.0 76.4
## [25] 86.4 72.7 68.6 65.9 80.5 70.0 81.8 73.6 82.7 72.3 91.1 67.3
## [37] 76.6 85.0 77.3 51.6 49.2 59.0 47.6 66.8 42.0 50.0 82.5 55.0
## [49] 50.2 60.7 48.7 50.0 55.7 52.8 48.6 53.6 58.4 56.2 51.8 45.0
## [61] 60.2 58.8 54.4 43.2 54.6 63.6 56.8 64.1 72.3 55.9 84.5 55.9
## [73] 76.4 65.9 58.6 59.1 60.0 54.1 75.9 57.3 58.6 62.0 80.9 70.5
## [85] 60.9 52.7 62.7 66.4 67.3 57.7 72.3 63.6 53.4 57.3 64.1 68.2
## [97] 61.4 76.8 71.8 55.5 67.3Cálculo error total método mixed selection
Error2=sum((data_test[,1]-prediccion2)^2)
Error2## [1] 493.5445Cálculo error medio
ME2.test = mean((data_test[,1]-prediccion2)^2)
ME2.test## [1] 4.886579Cálculo error cuadrático medio
ME2C.test = mean((residuos2_sd)^2)
ME2C.test## [1] 0.9975369plot(data_test[,1], prediccion2, main = 'Predicción valores verdaderos vs calculados - mixed selection' , xlab = "Valores verdaderos - weight",
ylab = "Valores calculados - weight", col = "red")
abline(0,1, col = "yellow", lwd = 2)
Estudiar el comando pcr() del paquete pls.
Realizar el modelo de regresión múltiple tomando las componentes principales del conjunto de variables explicativas
modelolm3 = pcr(weight~., data = data_training, scale = TRUE)
summary(modelolm3)## Data: X dimension: 406 23
## Y dimension: 406 1
## Fit method: svdpc
## Number of components considered: 23
## TRAINING: % variance explained
## 1 comps 2 comps 3 comps 4 comps 5 comps 6 comps 7 comps 8 comps
## X 60.60 71.61 77.19 81.79 84.95 86.90 88.66 90.07
## weight 93.57 94.29 94.32 94.92 95.91 96.16 96.18 96.22
## 9 comps 10 comps 11 comps 12 comps 13 comps 14 comps 15 comps
## X 91.43 92.68 93.82 94.8 95.68 96.42 97.11
## weight 96.61 96.71 96.72 96.8 96.87 96.90 96.91
## 16 comps 17 comps 18 comps 19 comps 20 comps 21 comps 22 comps
## X 97.71 98.23 98.67 99.05 99.39 99.64 99.83
## weight 97.32 97.43 97.52 97.61 97.64 97.64 97.64
## 23 comps
## X 100.00
## weight 97.65Cargas de las primeras trece componentes, opte por las primeras 13 ya que con esta llego al 95% de variabilidad
modelolm3$loadings[,1]## biacromial pelvic.breadth bitrochanteric chest.depth chest.diam
## -0.21032753 -0.13388929 -0.18091096 -0.21269802 -0.22926149
## elbow.diam wrist.diam knee.diam ankle.diam shoulder.girth
## -0.23317205 -0.22389980 -0.21600375 -0.21327140 -0.24254593
## chest.girth waist.girth navel.girth hip.girth thigh.girth
## -0.24407644 -0.23582105 -0.18316191 -0.18964057 -0.12644436
## bicep.girth forearm.girth knee.girth calf.girth ankle.girth
## -0.23980088 -0.24409088 -0.21190311 -0.20314335 -0.21612029
## wrist.girth age height
## -0.23790957 -0.07430121 -0.19764948coef(modelolm3, intercept = TRUE, ncomp = 13)## , , 13 comps
##
## weight
## (Intercept) -122.16079039
## biacromial 0.56549094
## pelvic.breadth 0.25760855
## bitrochanteric -0.25466220
## chest.depth 1.52779938
## chest.diam 1.13388545
## elbow.diam 0.50846417
## wrist.diam 0.46329245
## knee.diam -0.03418391
## ankle.diam 0.21734385
## shoulder.girth 1.08100745
## chest.girth 1.13542875
## waist.girth 1.33782447
## navel.girth 1.24795181
## hip.girth 1.26289524
## thigh.girth 1.40420794
## bicep.girth 0.49869093
## forearm.girth 0.42438275
## knee.girth 1.40056835
## calf.girth 0.55131043
## ankle.girth -0.12412805
## wrist.girth 0.04528131
## age -0.42755690
## height 2.12424903Validación del modelo de regresión multiple tomando los componentes principales del conjunto de varialbes explicativas
residuosmodelo3= residuals(modelolm3)
residuosmodelo3## , , 1 comps
##
## weight
## 225 0.76999003
## 31 -1.61414021
## 290 3.51931070
## 174 -0.41364923
## 505 -3.45560446
## 274 -1.16562918
## 493 3.28417841
## 440 2.74599687
## 385 4.53672223
## 196 -3.17368294
## 68 -2.02891085
## 55 0.36392400
## 310 4.43429804
## 319 1.90363676
## 79 -0.12328796
## 238 -6.42347837
## 43 -0.73819440
## 370 4.06071248
## 362 3.79749967
## 301 1.34931288
## 65 -0.64075607
## 382 1.57668989
## 16 -0.69453779
## 355 -2.39689067
## 89 1.34344039
## 277 -0.53158845
## 498 1.55298172
## 134 0.29377543
## 152 2.44058709
## 282 1.47636113
## 112 2.57922933
## 147 -3.81198432
## 42 2.00412425
## 489 3.62967740
## 330 -1.60774475
## 415 -4.64188080
## 207 -2.82131154
## 212 7.76583531
## 78 -2.34475807
## 99 1.59326083
## 376 0.33874016
## 163 -6.89676735
## 243 3.21484641
## 391 0.36321209
## 221 11.90461891
## 86 0.19602948
## 144 1.01011852
## 327 3.60969232
## 359 7.07353469
## 200 0.01851722
## 58 -6.51062098
## 241 -9.64543767
## 25 -1.81075499
## 45 -1.55684617
## 263 -0.39382731
## 183 0.73122277
## 487 0.54724155
## 326 -1.33725294
## 494 -3.34544430
## 349 5.19206176
## 442 -0.86316825
## 234 -5.17936497
## 95 6.07110770
## 271 3.87599001
## 345 -1.80878883
## 40 -2.89317626
## 206 -0.86509221
## 185 4.16856478
## 1 -1.62092175
## 322 -5.08076823
## 333 0.37519498
## 188 -0.19559103
## 427 -1.46605347
## 469 -0.37784577
## 438 -3.56525869
## 85 0.59960707
## 311 -0.91565190
## 167 2.83815078
## 71 -5.82846519
## 46 -1.32979728
## 281 0.87260828
## 193 -3.83615532
## 218 -2.69927133
## 194 6.66874496
## 133 2.72940432
## 216 -2.39956617
## 244 5.17967622
## 392 2.29987879
## 20 -2.58998033
## 92 1.28011873
## 286 3.40652255
## 334 -0.98323102
## 98 0.88578570
## 298 -1.23061681
## 410 4.17575006
## 291 0.61024653
## 49 4.46250345
## 97 0.02650534
## 66 -7.48600224
## 109 -0.91692308
## 104 1.10233469
## 434 2.06552961
## 153 4.24324457
## 88 -0.69415023
## 158 0.15776974
## 324 -1.18835224
## 491 -1.22256777
## 60 -2.59643945
## 264 2.39606696
## 422 0.51543224
## 375 2.01914212
## 108 -2.70364687
## 266 7.17884250
## 157 -3.02062729
## 187 -1.63511794
## 466 8.61459342
## 19 -7.84838372
## 418 -1.47706930
## 33 -4.95909171
## 429 -2.33272847
## 151 -1.80727541
## 368 2.32947718
## 63 -4.13640404
## 120 -0.91127275
## 474 6.50797265
## 354 2.09199637
## 265 -0.66794054
## 96 -2.36995772
## 454 -8.76359149
## 453 1.97883240
## 395 1.28201523
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## 361 0.27898074
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## 171 0.82862132
## 313 2.74691890
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## 273 -1.27795296
## 409 -2.79460121
## 471 1.40017495
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## 154 -0.99607076
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## 24 3.25207494
## 249 -0.07489862
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## 233 1.73522174
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## 335 4.41700837
## 433 -3.05885563
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## 126 3.64916359
## 30 -0.39793976
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## 145 2.66703078
## 197 -5.59415915
## 476 3.92868815
## 146 2.76226323
## 53 -6.52767492
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## 129 0.09074971
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## 280 5.64964749
## 288 1.77940658
## 177 2.91591349
## 390 -0.12630214
## 204 4.64380062
## 338 1.52021474
## 303 -1.08003723
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## 29 -1.88927502
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## 161 5.11609466
## 22 -3.06348595
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## 441 -3.54590477
## 325 -6.47931410
## 32 -2.34572233
## 211 -5.82506877
## 275 1.26841009
## 506 0.23861102
## 255 -0.42456484
## 267 1.16280303
## 420 2.03300847
## 168 1.11796688
## 245 -4.57292946
## 463 0.45507790
## 373 0.28394419
## 67 1.22027943
## 217 -4.42868060
## 64 -2.95214452
## 198 7.56214315
## 456 -5.45217876
## 405 1.02653445
## 203 -2.79983578
## 175 -1.43430156
## 299 6.59613095
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## 258 4.55989125
## 6 -1.47790794
## 481 0.86218549
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## 297 -1.33994288
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## 321 -1.78268741
## 252 -0.93812258
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## 372 -0.15347195
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## 70 -2.74797389
## 102 -1.72286941
## 436 -2.68953046
##
## , , 2 comps
##
## weight
## 225 1.591393632
## 31 -0.956807410
## 290 3.375719522
## 174 0.484237951
## 505 -2.318963754
## 274 -2.040402660
## 493 2.997409202
## 440 1.693565237
## 385 5.905877472
## 196 -3.530273208
## 68 -2.237076959
## 55 1.990070713
## 310 3.369394421
## 319 2.396433147
## 79 0.665485034
## 238 -4.319928595
## 43 -0.335106490
## 370 4.698482529
## 362 3.294690130
## 301 2.781692080
## 65 0.245675918
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## 16 0.319576034
## 355 -3.160254325
## 89 2.460835397
## 277 0.227200696
## 498 2.001058775
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## 282 1.497289595
## 112 3.306164435
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## , , 10 comps
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## , , 12 comps
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## , , 14 comps
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## , , 16 comps
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## , , 18 comps
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## , , 19 comps
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## , , 20 comps
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## , , 22 comps
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##
## , , 23 comps
##
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## 436 -3.067595778Calculo de R-cuadrado para análisis de componentes principales.
coefd <- R2(modelolm3, ncomp = 13, intercept = FALSE)
coefd## [1] 0.9687Cálculo de R-cuadrado ajustado
coefdnum <- as.numeric(coefd[[1]])
numerador <- (1 - coefdnum) * (nrow (data_training) - 1)
denominador <- (nrow (data_training) - (ncol(data_training) - 1))
R2ajustado <- 1 - (numerador / denominador)
R2ajustado## [1] 0.9668812residuosmodelo313comp = residuosmodelo3 [,,13]
residuosmodelo313comp.stand = (residuosmodelo313comp-mean(residuosmodelo313comp))/sd(residuosmodelo313comp)
valores.ajustados3=data.frame(fitted(modelolm3))
valores.ajustados313comp= valores.ajustados3[,13]plot(valores.ajustados313comp, residuosmodelo313comp, xlab = "Valores ajustados", ylab = "Residuos estandarizados", col = 'green', main = 'Distribución de residuos utilizados 13 componentes')
Entender la normalidad de residuos con gráfico de histograma incluyendo curva de distribución empírica y teórica para el método de selección de variables mixed selection.
x=seq(-4,4,0.01)
hist(residuosmodelo313comp.stand, col = "green", main="Histograma de residuos", xlab="Residuos",prob = TRUE, ylim = c(0,0.5))
theo.res=dnorm(x, mean = 0, sd = 1)
lines(theo.res ~ x, col="orange", lwd = 2 )
lines(density(residuosmodelo313comp.stand), col="violet", lwd = 2)
Entender la normalidad de residuos con gráfico de QQ-plot incluyendo curva de distribución empírica y teórica para el método de selección de variables mixed selection
qqnorm(residuosmodelo313comp.stand, main = 'QQ plot residuos - componentes principales')
qqline(residuosmodelo313comp.stand, col="green", lwd = 2)
- Comparar el primer modelo utilizando el comando predict () sobre el segundo conjunto de datos data.body2 y calculando el error cuadrático medio para el caso de método de selección de variables de mixed selection
prediccion3 = predict(modelolm3, ncomp = 13, newdata = data_test)
prediccion3## , , 13 comps
##
## weight
## 5 78.99250
## 8 80.71268
## 11 79.08964
## 18 69.82355
## 23 69.09613
## 26 89.88562
## 28 73.79119
## 37 71.06397
## 51 75.33331
## 52 83.31154
## 72 77.11092
## 76 64.96217
## 81 96.93187
## 82 80.66615
## 101 86.24698
## 103 55.83876
## 107 84.10844
## 113 62.14339
## 115 83.20583
## 119 82.58590
## 121 82.61561
## 124 106.43816
## 131 75.36220
## 136 77.31425
## 142 84.77339
## 149 71.74536
## 156 67.36020
## 165 70.41981
## 180 82.10919
## 181 69.86927
## 182 81.72756
## 189 78.29949
## 191 80.04390
## 209 72.88804
## 213 93.51790
## 214 67.98783
## 219 78.84356
## 220 81.89716
## 228 77.22901
## 248 50.70654
## 250 46.26964
## 253 55.51272
## 254 44.08843
## 256 69.41785
## 261 40.16608
## 262 49.60882
## 269 83.75974
## 279 54.61523
## 295 49.99194
## 304 62.99001
## 318 46.33040
## 320 51.32229
## 323 55.67755
## 332 52.45393
## 343 48.77523
## 348 51.54317
## 352 58.90693
## 353 57.35700
## 360 52.95002
## 366 41.18437
## 369 61.86465
## 371 58.79459
## 377 55.14328
## 381 38.87844
## 389 54.11732
## 396 65.00981
## 399 56.45117
## 400 64.59893
## 402 74.08800
## 404 55.42645
## 407 89.10492
## 408 56.13909
## 411 76.91659
## 413 68.01905
## 417 60.98648
## 419 61.19109
## 423 63.07545
## 426 57.95397
## 428 80.58313
## 430 54.51957
## 435 59.30819
## 443 63.63091
## 457 79.73377
## 458 69.39135
## 459 60.19132
## 464 48.37826
## 465 65.43916
## 467 67.36109
## 468 65.17165
## 472 57.88589
## 479 74.08501
## 483 62.91988
## 484 55.54147
## 495 56.21704
## 496 63.91993
## 500 68.84966
## 501 65.48560
## 502 74.73369
## 503 71.21565
## 504 57.68403
## 507 72.71986Valores verdaderos conjunto de datos testeo
data_test[,1]## [1] 78.8 78.4 76.6 70.0 66.2 89.6 76.4 67.2 75.6 86.2 78.9 63.9
## [13] 93.0 80.9 86.4 53.9 83.2 65.0 84.1 82.7 79.5 116.4 75.0 76.4
## [25] 86.4 72.7 68.6 65.9 80.5 70.0 81.8 73.6 82.7 72.3 91.1 67.3
## [37] 76.6 85.0 77.3 51.6 49.2 59.0 47.6 66.8 42.0 50.0 82.5 55.0
## [49] 50.2 60.7 48.7 50.0 55.7 52.8 48.6 53.6 58.4 56.2 51.8 45.0
## [61] 60.2 58.8 54.4 43.2 54.6 63.6 56.8 64.1 72.3 55.9 84.5 55.9
## [73] 76.4 65.9 58.6 59.1 60.0 54.1 75.9 57.3 58.6 62.0 80.9 70.5
## [85] 60.9 52.7 62.7 66.4 67.3 57.7 72.3 63.6 53.4 57.3 64.1 68.2
## [97] 61.4 76.8 71.8 55.5 67.3Cálculo suma errores total método componentes principales
Error3=sum((data_test[,1]-prediccion3)^2)
Error3## [1] 573.973Cálculo error medio
ME3.test = mean((data_test[,1]-prediccion3)^2)
ME3.test## [1] 5.682901Cálculo error cuadrático
ME3C.test = mean((residuosmodelo313comp.stand )^2)
ME3C.test## [1] 0.9975369Gráfico valores verdaderos vs calculados utilizando componentes principales.
plot(data_test[,1], prediccion3, main = 'Predicción valores verdaderos vs calculados - componentes principales' , xlab = "Valores verdaderos - weight",
ylab = "Valores calculados - weight", col = "red")
abline(0,1, col = "green", lwd = 2)
Cálculo del mínimo error
RSSE_v = vector ()
for (i in 1:23) {
prediccion3 = predict (modelolm3, ncomp = i, newdata = data_test)
RSSE_v = rbind(RSSE_v, mean ((data_test[,1]-prediccion3)^2))
}
indice = c (1:23)
qplot (x = indice, y = RSSE_v, geom = 'point', xlab = 'Cantidad de componentes', ylab = 'Errores', main = 'Error mínimo considerando cada componente')