Actividad 1 Concentracion
Luis Mendoza - A00829099
2024-03-5
Instalar Librerias
library(foreign)
library(ggplot2)
library(dplyr)
library(mapview)
library(naniar)
library(tmap)
library(RColorBrewer)
library(dlookr)
library(regclass)
library(mctest)
library(lmtest)
library(spdep)
library(sf)
library(spData)
library(spatialreg)
library(caret)
library(e1071)
library(SparseM)
library(Metrics)
library(randomForest)
library(jtools)
library(xgboost)
library(DiagrammeR)
library(effects)
library(shinyjs)
library(sp)
library(geoR)
library(gstat)
library(caret)
library(readtext)
library(kableExtra)
library(nortest)
library(rpart.plot)
library(neuralnet)1.Preguntas
#1)¿Qué es Supervised Machine Learning y cuáles son algunas de sus aplicaciones en Inteligencia de Negocios? Un modelo de aprendizaje supervisado es aquel a el que se le entregan datos etiquetados, para realizar predicciones o clasificaciones de estos datos de manera precisa, algunas de sus principales aplicaciones son las investigaciones de mercado, para saber cual es el mejor publico, segmento, cual es la mejor ubicacion para tu producto e incluso cual es el mejor momento para vender tu producto, tambien ppueden ayudar a fijar precios dinamicos de vuelos o viajes, a travez de datos que estan en constante cambio como la epoca del año, clima, demanda, entre otros
#3) ¿Qué es la R2 Ajustada? ¿Qué es la métrica RMSE? ¿Cuál es la diferencia entre la R2 Ajustada y la métrica RMSE? La R2 y el RMSE son medidas o metodos de evaluacion, pero se centran en cosas distintas, la R2 evalua la calidad del modelo atraves de la varianza de las variables, nos ayuda a ver que variables no son significantes para el modelo, mientras que el RMSE evalua la precision del modelo ya que se centra en la diferencia entre los valores observados y los valores predichos por el modelo
#Obtener Base de datos
df <- read.csv("C:\\Users\\Luis Rodriguez\\Downloads\\health_insurance.csv")
#df
df[ , c("sex", "smoker", "region")] <-
lapply(df[ , c("sex", "smoker", "region")], as.factor) #Es necesario cambiar variables de tipo factor a una escala adecuada para poder manejar los datos de dichas variable.2. Analisis Exploratorio de los datos (EDA):
Identificacion de NA’s:
# Identificación de NA's por columna
nas <- colSums(is.na(df))
nas## age sex bmi children smoker region expenses
## 0 0 0 0 0 0 0Remplazo de NA’s: En este caso no tenemos NA’s por lo cual no es necesario realizar un reemplazo
Medidas Descriptivas:
# Medidas descriptivas para todas las columnas numéricas
summary(df)## age sex bmi children smoker
## Min. :18.00 female:662 Min. :16.00 Min. :0.000 no :1064
## 1st Qu.:27.00 male :676 1st Qu.:26.30 1st Qu.:0.000 yes: 274
## Median :39.00 Median :30.40 Median :1.000
## Mean :39.21 Mean :30.67 Mean :1.095
## 3rd Qu.:51.00 3rd Qu.:34.70 3rd Qu.:2.000
## Max. :64.00 Max. :53.10 Max. :5.000
## region expenses
## northeast:324 Min. : 1122
## northwest:325 1st Qu.: 4740
## southeast:364 Median : 9382
## southwest:325 Mean :13270
## 3rd Qu.:16640
## Max. :63770Medidas de Dispersion:
varianza <- apply(df,2,var)
varianza## age sex bmi children smoker region
## 1.974014e+02 NA 3.719027e+01 1.453213e+00 NA NA
## expenses
## 1.466524e+08desviacion <- apply(df,2,sd)
desviacion## age sex bmi children smoker region
## 14.049960 NA 6.098382 1.205493 NA NA
## expenses
## 12110.011240Identifiacion de patrones y/o tendencias
Ejemplos de gráficos
boxplot(expenses ~ sex, data = df, col = c("red","green","blue","purple", main = "Expenses por sexo"))
# Diagrama de caja para la variable 'bmi' por género
boxplot(bmi ~ region, data = df, col = c("blue","purple", "cyan", "lightpink"), main = "BMI por Region", xlab = "Region", ylab = "BMI")
boxplot(expenses ~ region, data = df, col = c("blue","purple", "cyan", "lightpink"), main = "Expenses por Region", xlab = "Region", ylab = "Expenses")
# Gráfico de dispersión para la relación entre 'age' y 'expenses'
plot(df$children, df$expenses, main = "Children vs. Gastos Médicos", xlab = "Children", ylab = "Gastos Médicos", col = "blue")
# Gráfico de dispersión para la relación entre 'smoke' y 'expenses'
plot(df$age, df$expenses, main = "Edad vs. Gastos Médicos", xlab = "Edad", ylab = "Gastos Médicos", col = "darkgreen")
# Gráfico de dispersión para la relación entre 'bmi' y 'expenses' tomando en cuenta 'Expenses'
ggplot(df, aes(x=bmi, y=expenses, shape=smoker, color=smoker)) +
geom_point() +
theme_minimal() +
scale_color_brewer(palette = "Greens")
3.Apartir de los resultados de EDA describir la especificación del modelo de regresión lineal a estimar. Brevemente, describir cómo es el posible impacto de cada una de las variables explicativas sobre la principal variable de estudio.
Basándonos en los resultados del Análisis Exploratorio de Datos (EDA), identificamos que las variables más relevantes para predecir los gastos médicos (expenses) son el índice de masa corporal (bmi), la edad (age) y si la persona es fumadora (smoker).
Al examinar los gráficos de dispersión, notamos que existe una tendencia clara: a medida que la edad aumenta, también lo hacen los gastos médicos. Además, observamos que las personas que fuman y tienen un índice de masa corporal elevado tienden a registrar gastos médicos más altos.
4. Estimación de cada uno de los siguientes modelos de Supervised Machine Learning (SML):
a.OLS Regresión
lets split data into training and test sets the training set is used to build the model and the test set to evaluate its predictive accuracy.
set.seed(123)
partition <- createDataPartition(y = df$expenses, p=0.8, list=F)
train = df[partition, ]
test = df[-partition, ]ols_model <- lm(expenses ~ age + bmi + smoker, data = df)
summary(ols_model)##
## Call:
## lm(formula = expenses ~ age + bmi + smoker, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12413 -2970 -977 1476 28961
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11679.05 937.53 -12.46 <2e-16 ***
## age 259.53 11.93 21.75 <2e-16 ***
## bmi 322.69 27.49 11.74 <2e-16 ***
## smokeryes 23822.61 412.86 57.70 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6092 on 1334 degrees of freedom
## Multiple R-squared: 0.7475, Adjusted R-squared: 0.7469
## F-statistic: 1316 on 3 and 1334 DF, p-value: < 2.2e-16log_ols_model <- lm(log(expenses) ~ log(age) + log(bmi) + smoker, data = df)
summary(log_ols_model)##
## Call:
## lm(formula = log(expenses) ~ log(age) + log(bmi) + smoker, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.02436 -0.23021 -0.05241 0.09755 2.15745
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.98367 0.23094 12.920 < 2e-16 ***
## log(age) 1.27543 0.03232 39.468 < 2e-16 ***
## log(bmi) 0.35582 0.06233 5.708 1.4e-08 ***
## smokeryes 1.54369 0.03108 49.666 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4587 on 1334 degrees of freedom
## Multiple R-squared: 0.7517, Adjusted R-squared: 0.7512
## F-statistic: 1346 on 3 and 1334 DF, p-value: < 2.2e-16AIC(ols_model) # AIC = 27123.76## [1] 27123.76AIC(log_ols_model) # AIC = 1717.374## [1] 1717.374RMSE_ols_model <- sqrt(mean(ols_model$residuals^2)) #RMSE = 0.7475
RMSE_log_ols_model <- sqrt(mean(log_ols_model$residuals^2)) #RMSE = 7517
#Modelo OLS ABSOLUTO
residuos_ols <- resid(ols_model)
residuos_ols## 1 2 3 4 5
## -9192.855413 -2173.965911 -1787.232004 17773.835103 -2084.928837
## 6 7 8 9 10
## -903.023338 -2796.771202 419.286260 -1133.465742 16704.772732
## 11 12 13 14 15
## -542.471511 -8912.654844 -3563.955387 -4607.195589 6875.502896
## 16 17 18 19 20
## 646.952319 -958.221027 424.903768 -5256.871304 5516.915847
## 21 22 23 24 25
## -2280.969851 -2412.402994 -2859.313340 6440.345013 -755.131169
## 26 27 28 29 30
## 1429.181939 2326.140821 -910.912658 2870.148918 6808.221494
## 31 32 33 34 35
## 6244.481808 718.859812 2206.746600 -33.594614 20038.111122
## 36 37 38 39 40
## 1790.446323 551.378591 521.509286 6704.293227 7582.437560
## 41 42 43 44 45
## -87.275159 -3227.219922 276.004001 -1548.807172 -4075.386103
## 46 47 48 49 50
## 5998.625909 -2087.343917 -3260.616578 831.031590 5863.697448
## 51 52 53 54 55
## -2269.230485 -1033.746396 -10068.229342 5155.250592 96.166059
## 56 57 58 59 60
## 8360.438553 -28.079999 7258.700078 -10043.647669 -3191.942694
## 61 62 63 64 65
## 283.606147 -1179.317234 17265.081610 188.057147 -9850.765473
## 66 67 68 69 70
## -834.650829 -2534.626207 -799.674509 -4463.599663 -9491.935150
## 71 72 73 74 75
## -10575.915370 1236.280658 597.902909 -1753.358285 -855.296777
## 76 77 78 79 80
## -2729.178221 -1451.664067 -3694.220113 -4118.776184 -3039.600012
## 81 82 83 84 85
## -605.663054 -4423.726284 7178.678948 -3039.760201 6860.581096
## 86 87 88 89 90
## -10113.624280 6574.031769 -558.823575 -1171.350053 -225.352365
## 91 92 93 94 95
## -4490.485831 863.184627 -6887.266076 -2905.257043 8437.152161
## 96 97 98 99 100
## -3954.192581 -169.306875 -4728.065521 -10718.581294 -12413.054667
## 101 102 103 104 105
## -2972.722011 -690.482129 18639.292379 -6681.351067 -1015.236683
## 106 107 108 109 110
## -8809.197479 -84.995114 -1162.674154 -1983.378636 7234.927651
## 111 112 113 114 115
## -2352.912878 -297.839226 -3215.807172 -2886.498399 -719.009029
## 116 117 118 119 120
## 17138.096729 -7836.681733 -9565.324649 -1213.943109 1211.779408
## 121 122 123 124 125
## -3971.913645 1033.018386 -612.182896 5860.971491 -1343.229841
## 126 127 128 129 130
## -976.922152 -9125.771984 -4250.784463 6541.670020 -3298.186672
## 131 132 133 134 135
## 630.721655 2364.687241 -2497.250242 119.580889 -347.914610
## 136 137 138 139 140
## -942.626457 -2994.416264 -116.811310 14693.142553 -3480.838751
## 141 142 143 144 145
## 23002.539609 -2065.730442 -10159.271551 12726.536790 -8444.800717
## 146 147 148 149 150
## -3229.575220 6796.387931 -3844.988969 -3185.167387 -573.995114
## 151 152 153 154 155
## -56.248746 -2572.828760 -2263.518561 -10630.171224 146.288634
## 156 157 158 159 160
## -5538.013076 -11251.130195 -9428.795629 5565.167561 9480.959109
## 161 162 163 164 165
## -10278.823799 7427.014644 -4663.761456 -1090.081124 -2447.187456
## 166 167 168 169 170
## 788.191308 -620.564333 -1210.561985 -794.385975 3400.690078
## 171 172 173 174 175
## -4657.831486 -2698.936541 3539.191538 -3388.217043 -2439.927738
## 176 177 178 179 180
## 8164.849934 -698.165807 -1322.220587 -761.969769 -1136.868298
## 181 182 183 184 185
## -866.957424 -3719.807345 3520.914124 -839.975347 -1915.598495
## 186 187 188 189 190
## 8745.824869 -735.302725 -752.455849 -2576.506868 -1282.882641
## 191 192 193 194 195
## -1791.900484 -1234.783672 -964.795796 605.951283 -2955.660769
## 196 197 198 199 200
## -1486.876260 -3377.295879 -712.079416 2246.403054 -2711.313264
## 201 202 203 204 205
## -1479.793404 -2298.047334 1374.687305 6333.791474 -308.376333
## 206 207 208 209 210
## -575.917142 -409.149202 -9181.673906 -1052.164618 -5387.046812
## 211 212 213 214 215
## -2180.358615 -510.715086 -208.748876 -758.153539 -1451.069704
## 216 217 218 219 220
## -3561.884874 -304.149946 -298.773926 -1324.302725 23045.585702
## 221 222 223 224 225
## -3007.303547 -2256.942525 -1311.382554 6475.273723 -11466.610939
## 226 227 228 229 230
## -1547.333230 -5192.918296 7332.706561 -1800.672011 477.628169
## 231 232 233 234 235
## -3459.125511 1397.072796 2731.804040 -173.579775 361.512988
## 236 237 238 239 240
## -10244.355661 7.363240 -4294.614496 -9112.325128 -4882.275075
## 241 242 243 244 245
## 8556.038311 1337.049961 23916.735920 -2896.407377 -7909.515769
## 246 247 248 249 250
## 12460.006269 -3538.771854 -4147.435456 1835.760608 -1164.899209
## 251 252 253 254 255
## -9568.253334 8420.512798 7066.366251 -845.152220 5715.367377
## 256 257 258 259 260
## 2255.703922 6401.345262 -5754.419535 2089.297046 6381.748869
## 261 262 263 264 265
## 331.473437 -8897.077764 -8610.832747 7205.142577 6092.258612
## 266 267 268 269 270
## 8386.929917 -11734.646229 502.032219 -2304.165704 -81.025108
## 271 272 273 274 275
## -760.233620 6700.587946 -3667.954874 -553.953462 -1192.389513
## 276 277 278 279 280
## 613.247596 2904.178037 278.390976 -966.192923 1327.863050
## 281 282 283 284 285
## -9260.935096 9289.571101 -776.094131 -1171.366086 -2258.717599
## 286 287 288 289 290
## -1100.949480 -6347.995219 1130.147389 8565.743916 15657.101263
## 291 292 293 294 295
## -3193.748576 14878.735933 8797.897883 -1167.440457 448.723631
## 296 297 298 299 300
## 1290.121530 -9715.387127 -10559.288702 7456.695210 -854.815616
## 301 302 303 304 305
## 176.318327 -8318.250240 -2690.215301 -1887.232004 -2730.393940
## 306 307 308 309 310
## 12849.317643 15715.780859 -2701.535280 -2691.203431 -1893.729155
## 311 312 313 314 315
## -1436.721175 514.823176 7204.153838 -4498.278548 5555.411194
## 316 317 318 319 320
## -2839.519602 -2853.003182 -2484.939734 -1225.495063 -3994.786847
## 321 322 323 324 325
## -414.415538 20051.184704 4585.065586 -4746.109086 -1758.524636
## 326 327 328 329 330
## -3105.837661 747.106931 7159.722276 8267.393586 -4514.870463
## 331 332 333 334 335
## 8796.524640 -10087.396179 -791.393912 -489.929863 8143.627280
## 336 337 338 339 340
## -2241.114401 -43.518125 619.392311 6375.961662 -965.380053
## 341 342 343 344 345
## 15499.193411 -740.637120 417.878158 -2564.721766 -3452.550554
## 346 347 348 349 350
## -415.631256 -3547.892626 -2670.632059 -1834.571962 -587.170257
## 351 352 353 354 355
## 1229.839220 -626.419745 -1491.293274 4160.602232 8781.412655
## 356 357 358 359 360
## 15437.299090 -5481.501214 -514.874979 -5973.701110 1902.982675
## 361 362 363 364 365
## -1158.216477 -2495.623896 -10232.578548 307.581898 2342.423331
## 366 367 368 369 370
## -1198.612256 152.540133 728.438502 -1950.257353 679.504950
## 371 372 373 374 375
## 2453.789528 1751.210650 -2295.271222 6577.256973 -2865.706044
## 376 377 378 379 380
## -9211.013679 -8640.429597 6781.705384 1811.637889 12424.205735
## 381 382 383 384 385
## -9952.813648 5979.193332 7537.409056 -5530.224196 1430.657801
## 386 387 388 389 390
## -3090.803693 -4134.687436 20790.678540 815.184712 323.055694
## 391 392 393 394 395
## -1529.478195 -3182.667982 -1946.984190 -1880.437114 -1271.390630
## 396 397 398 399 400
## 845.683099 -2059.453861 12811.921321 1796.469323 -3687.688202
## 401 402 403 404 405
## 1060.224479 -7762.923285 -887.207257 -1191.539401 310.821239
## 406 407 408 409 410
## -2811.115893 -541.841184 405.151885 1660.536772 -2232.299410
## 411 412 413 414 415
## 2722.161469 -10486.564496 -9986.067581 2558.498777 -2475.916836
## 416 417 418 419 420
## -3622.953577 -3679.492745 -10171.310538 -3162.284121 -8256.331768
## 421 422 423 424 425
## 7196.354443 7039.420355 6016.175185 -1956.233802 -1555.484475
## 426 427 428 429 430
## 1947.533732 -437.610092 4908.594666 3975.099623 13666.588637
## 431 432 433 434 435
## 19149.795166 2540.635372 -1932.015215 -1096.816988 -1351.858485
## 436 437 438 439 440
## -654.194705 -2005.195603 -803.537608 -4326.093902 -1690.886153
## 441 442 443 444 445
## -2180.213346 5561.061650 -5718.877064 12876.267358 -9183.933873
## 446 447 448 449 450
## -3335.940850 -713.594701 306.053569 -2342.996227 -5098.164476
## 451 452 453 454 455
## -482.133304 148.435873 -131.112584 -1326.016897 -6944.768000
## 456 457 458 459 460
## 6094.945071 -426.305798 -1115.638217 -5031.967303 -1668.417088
## 461 462 463 464 465
## -2467.092548 -10580.654660 -1476.217701 -47.084717 248.137461
## 466 467 468 469 470
## -9572.013288 70.517586 -1118.387011 19859.653434 1431.690957
## 471 472 473 474 475
## -3383.311652 -502.087621 -1123.813116 9614.155017 -8875.591738
## 476 477 478 479 480
## -8238.574779 7578.475111 -3762.700950 -4144.158114 -2985.660814
## 481 482 483 484 485
## -2443.493200 -3834.294835 -1502.866480 -4423.373542 -2283.819336
## 486 487 488 489 490
## -2055.157059 3201.753422 -1259.382543 13027.588912 -1682.190523
## 491 492 493 494 495
## -2119.856548 12261.073809 1104.369527 -5583.219355 -7944.810115
## 496 497 498 499 500
## -547.682323 949.658664 -1233.208559 726.104084 -3590.638274
## 501 502 503 504 505
## 5427.101058 -1033.475852 -10648.069251 5696.105156 -1534.606379
## 506 507 508 509 510
## -1097.976315 -1519.918175 1625.899615 330.373699 -920.293643
## 511 512 513 514 515
## -1450.191581 -3704.633081 575.909906 -1805.597974 -10315.350458
## 516 517 518 519 520
## -3531.186575 22821.671097 -1428.563133 -2167.269611 -2479.878773
## 521 522 523 524 525
## 15517.235681 -6894.787712 -2630.071536 -4951.050961 6779.401916
## 526 527 528 529 530
## 7550.844946 20933.243740 -21.540955 -4630.599781 486.822955
## 531 532 533 534 535
## 8153.275186 -597.832551 -291.440920 9609.609108 -4168.942980
## 536 537 538 539 540
## -1151.434093 -3465.856058 -1179.658627 -1093.996625 15137.331191
## 541 542 543 544 545
## -3210.896695 -716.808899 -2498.026051 22316.519379 -1849.512017
## 546 547 548 549 550
## -9378.871121 -3742.301435 -5867.000607 -824.630942 7651.391255
## 551 552 553 554 555
## -1219.863188 -1978.868837 1639.529175 -858.323314 9742.467900
## 556 557 558 559 560
## 579.739149 -2702.771202 -4245.939262 7752.440944 -3061.194265
## 561 562 563 564 565
## 2480.543956 -1963.810591 -2676.410506 -6695.445196 -549.680481
## 566 567 568 569 570
## -965.737117 -4910.916107 -1579.440581 220.977171 7999.608643
## 571 572 573 574 575
## -1995.504199 -2809.485915 -5261.301291 15300.692015 -958.585650
## 576 577 578 579 580
## 71.830578 -1013.807598 26087.446920 -1837.416169 813.965349
## 581 582 583 584 585
## 1051.963084 -1486.876260 -6736.657893 13352.446597 1311.028894
## 586 587 588 589 590
## -1238.106903 3571.698762 13230.920444 -2101.443632 -2113.000953
## 591 592 593 594 595
## -889.473996 1584.317604 -980.844898 -9301.592682 -6257.107449
## 596 597 598 599 600
## -2310.178631 -1100.422932 -2295.846975 -2559.109288 19554.376394
## 601 602 603 604 605
## -4009.009631 -2580.041247 51.650141 -1463.164978 -8737.871984
## 606 607 608 609 610
## -3277.349822 98.454071 -9425.008355 134.546574 7114.157273
## 611 612 613 614 615
## -1458.438407 -2841.325814 -1498.201053 3476.830470 -2280.358615
## 616 617 618 619 620
## 6817.737286 -425.651577 -9815.022835 6684.089153 -3853.475805
## 621 622 623 624 625
## -2580.101564 7432.195097 1270.776326 6992.525505 -797.298634
## 626 627 628 629 630
## -500.924920 -241.330532 726.784795 -4270.186863 6835.486626
## 631 632 633 634 635
## -3639.508528 -2026.782020 -3936.283502 1145.994638 -4976.631828
## 636 637 638 639 640
## -2846.942691 1551.091461 15215.901239 -10635.076742 -780.337868
## 641 642 643 644 645
## -3901.416062 611.350771 -1947.840773 -1117.790245 7934.273852
## 646 647 648 649 650
## -576.289333 -773.682443 1999.030637 -477.021334 -1591.729715
## 651 652 653 654 655
## -5016.100270 -4275.068532 -2533.616761 -3186.103425 -2747.603784
## 656 657 658 659 660
## -9135.944177 -5340.605596 -1982.987366 14029.104376 1986.557214
## 661 662 663 664 665
## -6493.202618 11333.516076 -1642.236554 -2730.846768 -9137.658973
## 666 667 668 669 670
## 6962.411836 -1595.850254 6894.175185 7149.484007 -1818.234513
## 671 672 673 674 675
## -1466.409850 -1971.780354 -2848.343676 -2779.917153 8471.828620
## 676 677 678 679 680
## 317.258878 -3275.274095 8282.484712 -2140.407299 1632.272609
## 681 682 683 684 685
## 3199.294765 1439.545466 6447.539534 -54.129658 1910.689108
## 686 687 688 689 690
## 649.128340 86.067929 -6719.752527 17940.716170 5619.818623
## 691 692 693 694 695
## -508.779532 -4132.240129 -1604.583757 155.439987 -2980.003654
## 696 697 698 699 700
## -4839.754451 16687.348904 5936.887972 -2753.247868 -3471.373393
## 701 702 703 704 705
## -3012.525255 -6180.206053 -5963.582249 -278.786110 -1107.467550
## 706 707 708 709 710
## -2127.047480 6726.128447 -34.870254 -95.332201 -1133.680816
## 711 712 713 714 715
## -2623.743913 1226.372257 -1076.655571 -4596.164337 614.930559
## 716 717 718 719 720
## -1071.740700 1236.097467 1378.269876 -2551.777539 -1920.146287
## 721 722 723 724 725
## -4814.993258 -2622.164243 -3501.293700 -3412.105122 63.593110
## 726 727 728 729 730
## 8385.648414 -1461.549435 -10046.966928 -3779.410204 -3829.613444
## 731 732 733 734 735
## -9738.882188 1083.615488 -27.825163 -140.759329 15.429648
## 736 737 738 739 740
## -2683.837975 6281.391949 767.734139 7846.965460 13459.900485
## 741 742 743 744 745
## 859.951160 -10327.037661 6351.838318 -1192.225625 -989.442889
## 746 747 748 749 750
## -1100.251179 5880.109032 1340.528322 -3578.981843 -2496.530002
## 751 752 753 754 755
## -10726.090894 -1222.835820 -2950.525262 1102.552868 11736.254833
## 756 757 758 759 760
## -241.487055 2185.718418 -10247.008133 -2746.870142 7165.835785
## 761 762 763 764 765
## -1270.040750 -3231.988531 -10412.203200 -647.509073 963.311445
## 766 767 768 769 770
## -1533.297075 -2879.173553 -1528.747217 -3422.879836 2457.553060
## 771 772 773 774 775
## 12139.668082 458.720911 1278.571213 -8651.956842 -2736.109728
## 776 777 778 779 780
## -1742.266678 -2138.503088 -5394.653429 -2538.541329 -1532.170235
## 781 782 783 784 785
## -9543.997569 -5108.363348 -3787.863538 -9506.228618 -1470.822485
## 786 787 788 789 790
## 71.022107 -3091.341281 -3761.138114 2101.615084 -602.507977
## 791 792 793 794 795
## -6269.008746 -905.951971 1214.791549 -11447.234810 -1527.103592
## 796 797 798 799 800
## -10036.913660 -6103.731864 1222.945588 -2206.808858 -10806.362912
## 801 802 803 804 805
## -629.131214 -2234.101546 1135.916759 8359.960066 -1025.653093
## 806 807 808 809 810
## -3820.427710 16415.034902 -2925.704838 -1574.047621 175.075061
## 811 812 813 814 815
## -783.443485 -4368.011777 1901.459136 1580.458008 -3180.413395
## 816 817 818 819 820
## -1798.461470 483.884272 -2664.462247 -9362.542702 22971.708790
## 821 822 823 824 825
## -3428.715708 1900.502718 -1406.369051 -1137.406208 789.269876
## 826 827 828 829 830
## 876.432459 6874.879835 -9748.474258 6874.105120 607.810705
## 831 832 833 834 835
## -1958.853476 -723.207100 1451.809149 -2730.517716 -3193.648537
## 836 837 838 839 840
## -3677.897225 -3426.688249 -329.244148 1414.436112 -1143.726351
## 841 842 843 844 845
## -2280.537822 720.066228 7323.914887 -9019.230229 -1846.226522
## 846 847 848 849 850
## 6805.954140 -2720.478965 -8115.798262 -131.075356 -2577.912658
## 851 852 853 854 855
## 5584.976815 -455.774485 6574.040782 1973.426057 -8433.818261
## 856 857 858 859 860
## -1187.937754 5691.934366 -10590.755522 13018.219911 -1216.508786
## 861 862 863 864 865
## 9007.120796 -67.474093 -1135.736659 1372.352335 -971.024383
## 866 867 868 869 870
## -1750.383656 -3887.485915 -5639.815089 1329.351810 1740.972205
## 871 872 873 874 875
## -4521.208900 -1195.836153 -1289.462355 -2344.850713 2083.796087
## 876 877 878 879 880
## -667.729380 16357.356034 -1009.643194 -1973.076007 -1131.118313
## 881 882 883 884 885
## -1817.279035 -342.895379 1683.225045 8903.519876 1452.842774
## 886 887 888 889 890
## -10054.704850 -9076.547085 -2072.701105 -5094.388755 -2011.631649
## 891 892 893 894 895
## -8103.085549 221.620325 342.594847 7308.346998 -1215.389123
## 896 897 898 899 900
## -5287.004213 -9959.253286 708.580889 -4362.440204 1604.704321
## 901 902 903 904 905
## 390.236610 7759.946130 783.004993 -4819.599977 -2574.807564
## 906 907 908 909 910
## 8.252990 -1001.162509 -2529.614782 -2344.576055 -10890.511702
## 911 912 913 914 915
## -523.804742 6688.220078 2133.453369 -987.425920 433.761387
## 916 917 918 919 920
## -3047.921739 -10209.554151 3857.195720 -210.439623 -3195.422186
## 921 922 923 924 925
## 971.840028 -1662.829695 -2698.378382 -4377.015549 -716.869848
## 926 927 928 929 930
## 13677.335961 2110.512034 2431.902652 -3590.698274 -3708.099728
## 931 932 933 934 935
## -7146.900458 -2691.908450 1512.063663 -4042.801995 -3956.737704
## 936 937 938 939 940
## -273.579775 22784.322935 2713.930417 856.938955 -2107.955092
## 941 942 943 944 945
## 642.883244 -6624.104054 -3747.271061 1083.565178 -4304.512274
## 946 947 948 949 950
## -2733.019871 -3613.598939 6264.965954 -2962.797505 -8282.357528
## 951 952 953 954 955
## 2515.287226 8239.689584 -744.197275 5690.261207 -9928.870125
## 956 957 958 959 960
## -5237.055068 5902.287112 9412.016555 6436.545268 15847.611232
## 961 962 963 964 965
## -3300.549127 -851.835777 -1555.585479 1238.355093 12775.390395
## 966 967 968 969 970
## -1403.203035 -9415.105538 -418.733917 1215.555898 -914.223023
## 971 972 973 974 975
## 305.142537 231.789893 1978.775838 -4561.741414 -4169.465588
## 976 977 978 979 980
## -10920.887501 -5946.568772 -1588.488724 -3202.921715 -2423.571962
## 981 982 983 984 985
## 14952.747703 449.671038 -9346.847637 11593.710351 1690.436531
## 986 987 988 989 990
## -441.210489 -783.830713 19433.972014 -3823.634977 -10415.633451
## 991 992 993 994 995
## 1920.810715 -9.165807 -1376.228324 -1830.901521 -9184.286507
## 996 997 998 999 1000
## 2025.032703 -2027.994737 -2690.870909 -2047.488341 -1076.717672
## 1001 1002 1003 1004 1005
## -9989.679568 5548.481106 -902.232016 10901.980383 1912.864176
## 1006 1007 1008 1009 1010
## -1643.336069 -604.473714 -8526.284705 20364.908205 -537.964672
## 1011 1012 1013 1014 1015
## 133.142105 -11021.832429 21682.194085 -2436.216477 -1705.947521
## 1016 1017 1018 1019 1020
## 262.963084 1518.952319 -2116.925872 -1392.794023 21695.795891
## 1021 1022 1023 1024 1025
## -4698.124968 7738.872384 6220.373001 1199.774101 -6567.062140
## 1026 1027 1028 1029 1030
## -2916.087826 -9013.771696 21270.840059 -2682.350018 3371.747129
## 1031 1032 1033 1034 1035
## -10052.580347 6647.191898 -972.511560 -10037.416482 -3593.742206
## 1036 1037 1038 1039 1040
## 2336.846277 7659.314663 6060.890854 -1105.619600 20432.105458
## 1041 1042 1043 1044 1045
## -10027.721334 1257.982387 6234.975661 -751.863710 -2559.932089
## 1046 1047 1048 1049 1050
## -9393.133006 -255.373565 9674.547503 1524.336779 4895.772588
## 1051 1052 1053 1054 1055
## -3656.844502 944.446179 -1366.240827 -8648.320992 1087.262361
## 1056 1057 1058 1059 1060
## -907.047223 -1826.795616 7667.778009 -4815.074602 -3070.256843
## 1061 1062 1063 1064 1065
## -2894.288880 -563.200500 8251.630768 -344.913103 1600.561652
## 1066 1067 1068 1069 1070
## -339.928927 -3836.733626 -6464.251033 2675.918822 -1700.737447
## 1071 1072 1073 1074 1075
## 6153.570808 -829.578046 -1961.856108 435.136842 3406.108454
## 1076 1077 1078 1079 1080
## -1614.832838 -2293.776125 -58.861530 5032.350841 -384.698334
## 1081 1082 1083 1084 1085
## 11856.831245 -1142.428264 1218.867345 -2714.286554 765.677165
## 1086 1087 1088 1089 1090
## -9147.336161 -1156.965225 -1925.879647 -7460.136189 590.812716
## 1091 1092 1093 1094 1095
## 5653.043858 -924.928369 -1250.739957 6244.447242 -872.960326
## 1096 1097 1098 1099 1100
## 1436.133520 7967.261879 -3263.017606 11257.739830 -2553.664663
## 1101 1102 1103 1104 1105
## -10095.251763 -51.752806 -4928.694363 -3659.743147 12880.724258
## 1106 1107 1108 1109 1110
## -2064.773447 -1698.379970 741.835397 -1845.461868 2022.520307
## 1111 1112 1113 1114 1115
## -1246.254019 7552.079026 -8777.917340 1237.510575 199.949767
## 1116 1117 1118 1119 1120
## -2339.783515 708.930849 6747.063325 6022.251361 3132.660735
## 1121 1122 1123 1124 1125
## 5920.942889 -4239.120065 8855.322315 13119.945777 8980.190590
## 1126 1127 1128 1129 1130
## 1483.527961 -2029.097512 -3152.707616 6629.008740 2474.760897
## 1131 1132 1133 1134 1135
## 2427.237846 -6446.448524 4590.225772 2269.121844 13178.494852
## 1136 1137 1138 1139 1140
## 720.361680 -184.167346 943.731284 -2958.739762 9336.574011
## 1141 1142 1143 1144 1145
## -4221.421187 -1527.023440 17266.308408 -2527.590164 -2090.132324
## 1146 1147 1148 1149 1150
## -1111.833887 14291.016711 -1543.898042 1258.830498 -4245.383508
## 1151 1152 1153 1154 1155
## -566.355907 -2916.259719 7118.074699 -3326.498473 1233.545814
## 1156 1157 1158 1159 1160
## 2432.601190 8159.220283 12649.418625 -926.249183 -5898.784279
## 1161 1162 1163 1164 1165
## -2918.742147 -5606.191557 10335.801856 108.386095 -940.420292
## 1166 1167 1168 1169 1170
## -598.861605 -5168.563371 743.863082 -3314.104844 -2815.098890
## 1171 1172 1173 1174 1175
## -8478.216774 -9440.735865 -5281.947592 -1180.222951 -1771.882641
## 1176 1177 1178 1179 1180
## -621.255027 -9528.474461 -1047.125082 -2652.651102 -10454.914213
## 1181 1182 1183 1184 1185
## -4897.721802 -1347.536877 -1953.836373 -172.898472 -8981.281965
## 1186 1187 1188 1189 1190
## 988.367732 8643.307655 -1119.203981 -9696.227864 9801.109763
## 1191 1192 1193 1194 1195
## -1623.352489 7728.994001 -809.904857 -3917.849625 732.933237
## 1196 1197 1198 1199 1200
## 16583.530600 6552.122585 -4104.394870 -1795.797941 242.797519
## 1201 1202 1203 1204 1205
## 433.677121 -4562.971210 -2333.752175 -2016.005248 -7401.177631
## 1206 1207 1208 1209 1210
## 1935.718119 22047.552788 6150.832021 -9710.317751 -3258.077500
## 1211 1212 1213 1214 1215
## -2261.943391 14116.505263 1772.048674 -1755.449602 -1472.513650
## 1216 1217 1218 1219 1220
## 7280.279512 -1386.164794 -3825.678076 6414.403069 -391.325238
## 1221 1222 1223 1224 1225
## 1544.317018 -176.045651 -1019.022317 917.781668 184.351998
## 1226 1227 1228 1229 1230
## -4932.998345 3036.119920 -4063.446941 -3361.151869 -1213.152855
## 1231 1232 1233 1234 1235
## 23249.274670 -4201.550615 2205.769989 452.947153 -454.996272
## 1236 1237 1238 1239 1240
## -2404.942440 2775.918822 -249.410852 1736.743409 -5156.145243
## 1241 1242 1243 1244 1245
## 8142.077233 8884.411011 3392.265265 -3097.351147 -2602.230196
## 1246 1247 1248 1249 1250
## 2186.093434 808.695730 -313.497476 -4201.704489 6316.485430
## 1251 1252 1253 1254 1255
## -9340.133747 1600.201181 -9910.843478 7671.691201 -1668.464969
## 1256 1257 1258 1259 1260
## -4977.330941 -1866.360110 63.915700 15302.849337 894.663838
## 1261 1262 1263 1264 1265
## 1303.049172 -4282.566866 -1259.242007 -1791.592427 -1412.780830
## 1266 1267 1268 1269 1270
## -9507.212117 -1732.882369 5845.997394 -2376.746044 -258.648843
## 1271 1272 1273 1274 1275
## -2715.518444 -2920.320378 6768.829863 -1563.838750 -10593.012735
## 1276 1277 1278 1279 1280
## 197.213505 -1098.546745 -1852.901981 -9451.776746 731.703631
## 1281 1282 1283 1284 1285
## -3240.477907 -8712.189847 -9534.095625 -952.938478 7715.113783
## 1286 1287 1288 1289 1290
## 174.267884 2562.193442 -549.396243 8296.310222 -3661.247642
## 1291 1292 1293 1294 1295
## 2496.867345 6492.034580 257.754473 749.252806 425.443437
## 1296 1297 1298 1299 1300
## 1353.957112 294.138098 201.242289 -498.083759 1165.581746
## 1301 1302 1303 1304 1305
## 28960.509997 8512.394580 1687.532209 5555.423562 -9722.770939
## 1306 1307 1308 1309 1310
## -1023.675732 -10621.656071 -8043.761706 5523.486757 -2476.506868
## 1311 1312 1313 1314 1315
## -767.210357 -929.990615 -6452.274700 8125.502866 -8811.453568
## 1316 1317 1318 1319 1320
## 9147.616952 1832.158037 -8964.000504 9281.264951 272.178414
## 1321 1322 1323 1324 1325
## -977.157059 -8749.131415 -3951.071702 7815.704471 -484.291624
## 1326 1327 1328 1329 1330
## -1819.284201 -2787.863793 -1859.974960 20296.397196 -3947.344179
## 1331 1332 1333 1334 1335
## 1221.670646 5727.836042 -4829.281900 -700.483466 -1080.422195
## 1336 1337 1338
## -3270.029343 -88.633245 -8224.027923valores_ajustados_ols <- fitted(ols_model)
plot(valores_ajustados_ols, residuos_ols, main = "Residuos vs. Ajustes", xlab = "Valores Ajustados", ylab = "Residuos")
#Modelo LOG_OLS
residuos_log_ols <- resid(log_ols_model)
residuos_log_ols## 1 2 3 4 5
## 0.2670031558 -0.4694858711 -0.0772532082 1.4438703371 -0.3406981112
## 6 7 8 9 10
## -0.2873723967 -0.0984221194 0.1221176890 -0.0319233722 0.9101277680
## 11 12 13 14 15
## -0.3422712754 -0.7215004549 -0.7313417518 -0.1146548484 0.5251328550
## 16 17 18 19 20
## -0.3626773391 0.0442709592 -0.3294016825 -0.1641263716 0.3808251112
## 21 22 23 24 25
## 0.0093465807 -0.2284569458 -0.8897739292 0.2804188731 -0.0418753643
## 26 27 28 29 30
## 0.1807763746 0.1934119950 0.0780925332 -0.0706885588 0.3786724758
## 31 32 33 34 35
## 0.7388201577 -0.1381252140 0.5204137496 0.0728480956 0.7870199050
## 36 37 38 39 40
## -0.4185558819 0.1641377267 -0.4773776160 0.2470823001 -0.2785312929
## 41 42 43 44 45
## -0.1828650423 -0.1373554661 -0.0727503246 -0.0582353272 -0.1962486108
## 46 47 48 49 50
## 0.5520609751 0.1586184613 -0.3200384553 0.0999491741 0.1988571790
## 51 52 53 54 55
## -0.2399896475 0.0657867135 -0.5828106892 0.1817494154 0.1115996706
## 56 57 58 59 60
## -0.2225929848 0.1249375278 0.9993444474 -0.6514708493 -0.0712401235
## 61 62 63 64 65
## 0.1014646818 0.0721506578 0.8854108717 -0.0646751216 0.1419327433
## 66 67 68 69 70
## -0.4725343307 0.0321812397 -0.0895638802 -0.2795285942 -0.1289292738
## 71 72 73 74 75
## -0.1576288410 0.2691547937 0.1364703482 -0.0074556499 -0.0356407878
## 76 77 78 79 80
## -0.0574899724 -0.2030434576 -0.8022202152 -0.3156917410 -0.1737749476
## 81 82 83 84 85
## -0.1362030769 -0.1568511251 0.7628028955 0.0644944558 0.1966855236
## 86 87 88 89 90
## -0.5396494843 -0.2258256713 0.0192050464 -0.0581421410 0.0456609335
## 91 92 93 94 95
## -0.5605490823 0.1103927340 -0.6207057327 -0.1279949579 -0.2929525379
## 96 97 98 99 100
## -0.2902220640 0.1104809863 -0.1591518087 -0.7099716925 -0.5510329258
## 101 102 103 104 105
## -0.2187094003 -0.2729099414 2.0870309329 -0.6396385681 -0.1425874114
## 106 107 108 109 110
## 0.2395333429 -0.1755322355 -0.0969816771 -0.5017491918 -0.3186303410
## 111 112 113 114 115
## -0.0322430104 0.0813439978 -0.3647965033 -0.3536623877 0.0904852174
## 116 117 118 119 120
## 0.9186516404 -0.2082651206 -0.1486469880 -0.0630939786 0.0968849859
## 121 122 123 124 125
## -0.1417360559 -0.3562903865 -0.2806635756 0.0052166828 0.0738095501
## 126 127 128 129 130
## -0.2076057886 0.2734885272 -0.1387587749 0.4240392926 -0.1720017925
## 131 132 133 134 135
## 0.1080474456 0.1923692623 -0.0011872937 -0.4949703987 -0.1934237344
## 136 137 138 139 140
## -0.4371504240 -0.8548810330 -0.4507636624 0.9120687436 -0.5201915644
## 141 142 143 144 145
## 1.6298555162 -0.2200245504 -0.3238210042 1.3218014343 -0.1196878609
## 146 147 148 149 150
## -0.0356896925 -0.0121277191 -0.0919191016 -0.0341839983 -0.4109184510
## 151 152 153 154 155
## -0.1086342113 -0.1672049230 0.0639697713 -0.5145753084 0.0236672548
## 156 157 158 159 160
## -0.2719311585 -0.6386261037 0.2877697608 0.3818719768 0.7345804734
## 161 162 163 164 165
## -0.4931594364 0.9977220937 -0.1259319902 -0.0646425411 -0.2717742011
## 166 167 168 169 170
## 0.1677802771 0.3933786978 0.0705029497 -0.0619205580 0.2490744836
## 171 172 173 174 175
## -0.0902135489 -0.1594934729 -0.2213595450 -0.2160622864 -0.3274215267
## 176 177 178 179 180
## -0.3071540114 -0.0335280711 -0.0189115525 0.0213917835 0.0859667614
## 181 182 183 184 185
## 0.0147148437 -0.5698093047 0.3033836844 -0.0630040780 -0.0755118844
## 186 187 188 189 190
## 0.2593504618 -0.0586358867 0.0378987806 -0.1343307614 -0.0110517091
## 191 192 193 194 195
## -0.0174233314 -0.2225275884 -0.5768251593 0.1112107403 -0.8924861277
## 196 197 198 199 200
## -0.5541727336 -0.2588901406 0.0177878214 0.1452540614 0.0148879586
## 201 202 203 204 205
## -0.3091875720 -0.0659522465 0.1371070461 0.5152460842 -0.0970458804
## 206 207 208 209 210
## -0.0554773433 0.0220248715 -0.2922658538 0.0393757744 -0.2153172523
## 211 212 213 214 215
## -0.4577565711 0.0980227739 -0.0577862011 -0.1322966117 -0.0093589664
## 216 217 218 219 220
## -0.1004559833 0.0303721553 -0.4869741532 -0.2187064784 1.9740887816
## 221 222 223 224 225
## -0.2132085229 -0.0295573297 -0.0568987164 0.9109810361 -0.5551271356
## 226 227 228 229 230
## 0.0431466086 -0.6318142912 0.6036657637 -0.0452064700 0.0830492695
## 231 232 233 234 235
## -0.1127504548 0.1795055685 -0.3089739856 0.0565626404 0.0169433825
## 236 237 238 239 240
## -0.4600309415 -0.4513188467 -0.2579089322 0.2793451160 -0.2301597976
## 241 242 243 244 245
## 0.7503167848 0.0409225093 1.2028447074 -0.0752775602 -0.7005364429
## 246 247 248 249 250
## 0.8239128273 -0.0556723325 -0.7168072091 -0.3074867902 -0.1724331694
## 251 252 253 254 255
## 0.2313386429 -0.2826522083 -0.1740092891 -0.0438359736 -0.1241208456
## 256 257 258 259 260
## 0.2306061310 -0.2217974785 -0.3431731299 0.2167124966 0.9118988025
## 261 262 263 264 265
## 0.0683412413 0.2276906284 -0.5807155106 0.9297326971 0.5836122171
## 266 267 268 269 270
## -0.0041540068 -0.5431559625 0.1662517144 -0.1366135214 0.0319203137
## 271 272 273 274 275
## -0.4234082950 -0.1080837989 -0.1149491788 0.0189200135 -0.4363949503
## 276 277 278 279 280
## 0.1198342006 0.1231402586 -0.3878720655 0.0519798045 0.1039820595
## 281 282 283 284 285
## -0.4054405552 -0.1425683933 -0.1505634419 0.0501934261 -0.0751606705
## 286 287 288 289 290
## -0.0798193979 -0.0930640044 0.1349742499 -0.2340745187 0.9776413067
## 291 292 293 294 295
## -0.4199543729 1.4334240595 0.6568691876 -0.4454094100 0.0111021484
## 296 297 298 299 300
## -0.3447402357 0.2341753004 -0.5911104347 0.3987147663 0.0142857375
## 301 302 303 304 305
## 0.0820712328 -0.5790615224 0.0072081883 -0.0999842492 0.0104869937
## 306 307 308 309 310
## 1.3494410571 1.4994141534 -0.2378952190 -0.0384940902 -0.0099361792
## 311 312 313 314 315
## -0.0993293723 -0.4200070419 0.0487940001 -0.2188848372 0.5010809677
## 316 317 318 319 320
## -0.0883274034 -0.1220717956 -0.0603777527 -0.0785904316 -0.2432817029
## 321 322 323 324 325
## -0.1349630278 1.7688282724 0.2324922621 -0.1049432250 -0.4930672310
## 326 327 328 329 330
## -0.1495160811 -0.1279853584 0.0008867241 -0.3069154269 -0.1842302380
## 331 332 333 334 335
## -0.2598267458 -0.6427717653 0.0542021316 0.0503662378 0.8068465755
## 336 337 338 339 340
## -0.0139049708 0.0435859096 0.1142629665 -0.1098694126 -0.0328051471
## 341 342 343 344 345
## 1.6322340019 0.0416725983 0.1029995714 -0.0053424288 0.0304851481
## 346 347 348 349 350
## 0.0466593044 -0.2213789324 -0.0860284100 -0.1547215713 -0.5223656061
## 351 352 353 354 355
## 0.1193930371 -0.0295572741 -0.3276064634 0.7155327006 1.5890100576
## 356 357 358 359 360
## 1.0632454020 -0.1137639702 0.0695351405 -0.7958212393 -0.3675921931
## 361 362 363 364 365
## 0.0570407651 -0.2682385665 0.1578935638 -0.1690612170 0.0998177130
## 366 367 368 369 370
## 0.0209323929 0.1510425300 0.0931797531 -0.0416920224 0.2702611291
## 371 372 373 374 375
## 0.1923360861 0.1517247067 -0.0560070766 0.5677615737 -0.8137050150
## 376 377 378 379 380
## 0.0840965055 -0.3606675948 0.6535659949 0.2089940799 0.7285115950
## 381 382 383 384 385
## -0.1431731828 -0.2042209854 0.6029465790 -0.1853817622 0.1127082985
## 386 387 388 389 390
## -0.8576648221 -0.0863376660 1.1942248437 -0.1849374605 0.1881006258
## 391 392 393 394 395
## 0.0892100620 -0.3600996288 -0.0465815309 -0.0371496393 0.0463021375
## 396 397 398 399 400
## -0.0047798587 0.0106767943 1.6277178049 0.1732189664 -0.5689709834
## 401 402 403 404 405
## 0.0590788388 -0.2703571330 0.0629411578 0.0530159586 -0.3469248029
## 406 407 408 409 410
## 0.0198391350 -0.2391707289 0.0333779796 0.0946027467 -0.3016970663
## 411 412 413 414 415
## -0.3665160848 -0.5402874046 -0.1162657172 0.3146356433 -0.3400119555
## 416 417 418 419 420
## -0.1500557877 -0.1584807910 -0.3759517997 -0.0171718698 -0.7110179896
## 421 422 423 424 425
## -0.3298784523 -0.2952495887 0.1002974982 -0.3952771808 -0.0322404485
## 426 427 428 429 430
## 0.2149634340 -0.0118196402 1.0281416207 0.1900366485 1.4396582818
## 431 432 433 434 435
## 2.0625503706 0.1503950641 -0.2277559313 0.0226626112 -0.2035250985
## 436 437 438 439 440
## 0.0901439831 -0.4350883694 -0.0279421857 0.0492112817 -0.3718366444
## 441 442 443 444 445
## -0.1409311646 0.2844314622 -0.9614513725 0.7859090718 -0.6601118735
## 446 447 448 449 450
## -0.1822203558 0.0406362203 0.0732040452 -0.2094560335 -0.3496759632
## 451 452 453 454 455
## 0.0625679006 -0.1518770268 -0.5732712151 -0.5326854742 -0.3177098965
## 456 457 458 459 460
## 0.5165800582 0.0766351401 0.0229092100 -0.1579840148 0.0140168517
## 461 462 463 464 465
## 0.0193942925 -0.4993829750 0.0882402400 0.0449264832 -0.4896853960
## 466 467 468 469 470
## -0.1767613951 0.0896685151 0.0745132579 1.6868340466 -0.1057189189
## 471 472 473 474 475
## -0.6052959760 -0.1837461694 -0.4827236304 0.8048765105 -0.6199799690
## 476 477 478 479 480
## -0.6894337288 0.6946060094 -0.5225246956 -0.8147894655 -0.7136153215
## 481 482 483 484 485
## 0.0602428691 -0.0987533205 -0.5050474860 -0.1082657088 -0.0133323441
## 486 487 488 489 490
## -0.2092622159 0.2684941394 -0.7995009994 0.1481426172 -0.0161670590
## 491 492 493 494 495
## -0.5154751406 0.7333984741 -0.1222908253 -0.1290173560 0.2293086187
## 496 497 498 499 500
## -0.4046337831 0.0151131761 -0.0425666444 0.0722870606 -0.0446466022
## 501 502 503 504 505
## 0.4157337894 -0.1099558855 -0.6522141754 0.8939460242 -0.1248437677
## 506 507 508 509 510
## 0.0143406484 -0.2727494479 0.0371599448 -0.1656435880 0.0114548039
## 511 512 513 514 515
## 0.0207004932 -0.6154657403 0.0396369873 -0.8180965032 -0.4332471736
## 516 517 518 519 520
## -0.0964954467 2.1574466774 -0.0173098745 -0.1759257977 -0.3263704474
## 521 522 523 524 525
## 1.0014153377 -0.4594843190 -0.0552607064 -0.3209493690 0.0966295014
## 526 527 528 529 530
## 1.4247525813 2.1319367636 0.0413581359 -0.1448668867 -0.3794449772
## 531 532 533 534 535
## -0.2218374967 0.0725446352 0.0760647890 0.9972287770 -0.0703562802
## 536 537 538 539 540
## -0.0981813284 -0.0509752365 0.0059407290 -0.0378507149 0.9423833220
## 541 542 543 544 545
## -0.0438905430 -0.0104742831 -0.0072672892 0.0750437836 -0.0506928898
## 546 547 548 549 550
## -0.5699040392 -0.4105777478 -0.0855842421 -0.2071769205 0.0450642528
## 551 552 553 554 555
## 0.0147773594 -0.3136395787 0.1318424725 0.0695342286 1.3782983870
## 556 557 558 559 560
## -0.1062785634 -0.0870797379 -0.4604211463 0.2784723349 -0.6028421574
## 561 562 563 564 565
## 0.1935122487 -0.0135077333 -0.5817238871 -0.2145998086 0.0333995859
## 566 567 568 569 570
## -0.2920513153 -0.1811183588 -0.0476490279 0.1752119486 -0.0527790443
## 571 572 573 574 575
## -0.3303395931 -0.2528320817 -0.1941302509 0.8301290879 0.0916177562
## 576 577 578 579 580
## 0.0732337563 -0.6785771750 0.7755691369 -0.0533773365 -0.1395128882
## 581 582 583 584 585
## 0.1293950220 -0.5541727336 -0.2567254613 1.2468304555 -0.6921398237
## 586 587 588 589 590
## -0.1605661738 0.3225084033 0.4531084041 0.0195412588 -0.1459327551
## 591 592 593 594 595
## 0.0188117010 0.0863051871 -0.1772573536 0.1307989474 -0.3854804644
## 596 597 598 599 600
## -0.0332016292 -0.0138470950 -0.0990421579 -0.1057785610 1.1056449199
## 601 602 603 604 605
## -0.5773265176 -0.1029978350 0.0447324070 0.0931353894 0.2959438456
## 606 607 608 609 610
## -0.1182335838 -0.1583271523 -0.7008893700 -0.0090855050 0.4196955583
## 611 612 613 614 615
## -0.0438739121 -0.0956785293 -0.2167074059 0.2887609268 -0.5095797586
## 616 617 618 619 620
## -0.0506651304 0.0528235240 -0.5883903015 0.9189849656 -0.1012682160
## 621 622 623 624 625
## -0.3430619634 0.2125570519 0.0892541156 0.9888243679 0.0234312374
## 626 627 628 629 630
## -0.2118225954 0.0659685192 0.5575493923 -0.1184304989 0.0111770968
## 631 632 633 634 635
## -0.1046864203 -0.6491180737 -0.4268521495 0.0785510972 -0.1607933244
## 636 637 638 639 640
## -0.0084869568 0.0271277514 1.3096982029 -0.4537751514 0.0994647016
## 641 642 643 644 645
## 0.0282799305 -0.0861478515 0.0032054171 0.1565498695 0.7930201482
## 646 647 648 649 650
## 0.0836605343 -0.0984092317 0.2078598318 -0.4165477016 0.0213352961
## 651 652 653 654 655
## -0.0930057681 -0.0898080538 -0.1224710426 -0.0657879085 -0.0385415617
## 656 657 658 659 660
## -0.6032374929 -0.3378930722 -0.1249363054 0.9856113197 0.2386056527
## 661 662 663 664 665
## -0.1856939366 0.7363916557 -0.0850782019 -0.8861120598 -0.7423973861
## 666 667 668 669 670
## 0.0389156489 -0.0703906141 0.1224901156 -0.2943287882 -0.1168179050
## 671 672 673 674 675
## -0.0661920824 -0.2227407775 -0.3715377098 -0.2120193181 0.0412507503
## 676 677 678 679 680
## -0.0438218208 0.0179800715 -0.2366193718 0.0287077996 0.1597289527
## 681 682 683 684 685
## -0.0255495790 -0.6856474747 0.1311553527 0.0138573736 -0.0121557914
## 686 687 688 689 690
## 0.1153947473 0.0413501619 -0.4146604970 1.1483504342 0.5035664322
## 691 692 693 694 695
## -0.3930548884 -0.1756391881 -0.2747537003 -0.3999612018 -0.2677450449
## 696 697 698 699 700
## -0.3821992960 0.9974619601 0.0665899997 -0.0658323719 -0.1283759584
## 701 702 703 704 705
## -0.5196660254 -0.1618619480 -0.2136759220 -0.0545893212 -0.0012226669
## 706 707 708 709 710
## -0.0967472888 -0.1363816994 0.0945742328 0.1386342731 -0.1291774506
## 711 712 713 714 715
## -0.4827743119 0.1244987282 0.0260765116 -0.5284168048 -0.3395846192
## 716 717 718 719 720
## 0.0021917558 0.1092294349 0.1403723245 0.0113686484 0.0008825169
## 721 722 723 724 725
## -0.1193588945 0.0009454370 -0.0650893689 -0.8667599770 0.0736747570
## 726 727 728 729 730
## 0.4498534330 -0.1062055271 -0.1980821919 -0.2811915002 -0.1742151788
## 731 732 733 734 735
## -0.3275825626 0.0793435996 0.1026685556 0.0557055936 0.1287550557
## 736 737 738 739 740
## -0.0426013149 0.1761750185 -0.1094527532 0.7402278217 0.6129461856
## 741 742 743 744 745
## 0.0904205801 -0.1198330351 -0.1721256833 -0.2992950743 -0.0523167227
## 746 747 748 749 750
## 0.0167552642 0.7165526158 -0.4410359088 -0.1148579102 -0.4274054890
## 751 752 753 754 755
## -0.4173774822 -0.5119455543 -0.0196845364 0.1036672995 1.4609009554
## 756 757 758 759 760
## -0.0205983201 0.2165714796 -0.5749746165 -0.0108618668 0.9897722441
## 761 762 763 764 765
## 0.0882629495 -0.4595990155 -0.3066031525 -0.3168788737 0.1285096017
## 766 767 768 769 770
## 0.0082128297 -0.1357518979 -0.0880843486 -0.0285891064 0.1639921638
## 771 772 773 774 775
## 0.7349830490 0.1030151482 0.3668470407 0.3043536603 -0.0865337379
## 776 777 778 779 780
## 0.0190881500 -0.0733130629 -0.2338413024 -0.0876257107 -0.0471867818
## 781 782 783 784 785
## -0.1896162043 -0.9476357944 -0.1265354970 -0.5901581424 -0.1872456262
## 786 787 788 789 790
## 0.0661661157 -0.0379640751 -0.5919353388 0.1719828160 0.0507577209
## 791 792 793 794 795
## -0.3429530854 -0.7868159943 -0.1320744848 -0.7112303390 -0.0051981248
## 796 797 798 799 800
## -0.1076847187 -0.3112917096 0.0236814730 -0.0277597516 -0.3365799929
## 801 802 803 804 805
## -0.0525118491 0.0058596882 -0.3202612582 1.0205373024 -0.6445217490
## 806 807 808 809 810
## -0.1588030457 1.2434466151 -0.3529626674 -0.8502265360 -0.1410293356
## 811 812 813 814 815
## 0.0636376404 -0.0227634630 0.1522529109 0.0543891293 -0.1853932685
## 816 817 818 819 820
## -0.4941659363 -0.2182928012 -0.0805483549 -0.5380646809 0.6605296964
## 821 822 823 824 825
## -0.1749769637 -0.2676899183 -0.5018227111 -0.0037456981 0.0944135888
## 826 827 828 829 830
## 0.1656693610 -0.2046523692 -0.3421089276 0.1031833614 -0.0356138713
## 831 832 833 834 835
## -0.0106093103 -0.1416499529 0.0980073796 -0.0503014662 -0.2168770902
## 836 837 838 839 840
## -0.1495830581 -0.3919062484 0.0565412977 0.1228187898 0.0324828845
## 841 842 843 844 845
## -0.7591642062 0.0939693333 0.7234345785 -0.6686457772 -0.0460754931
## 846 847 848 849 850
## -0.2734844224 -0.0577472372 -0.5786265692 -0.3218674341 -0.0679453020
## 851 852 853 854 855
## 0.1735406958 0.0920190888 -0.0325514670 0.1945394818 -0.5286845705
## 856 857 858 859 860
## -0.4734094058 -0.0893092114 -0.0961979189 1.4856580920 -0.0247289427
## 861 862 863 864 865
## 0.2315592898 0.0661977881 0.0706651167 -0.0135094784 -0.0689150085
## 866 867 868 869 870
## -0.1027248373 -0.9177921152 -0.1276553689 0.1294819102 0.1631038551
## 871 872 873 874 875
## -0.2073947194 -0.2140940240 -0.2007400324 -0.1603541586 0.1844368262
## 876 877 878 879 880
## -0.2723697218 1.0497802294 0.1113064017 -0.1702789401 -0.0431775343
## 881 882 883 884 885
## -0.0449872409 -0.2272710837 -0.1104043188 -0.0859946178 0.2346164018
## 886 887 888 889 890
## -0.2552086270 -0.6704866692 -0.1942130508 -0.8060840115 -0.0027597343
## 891 892 893 894 895
## -0.7167257821 0.1355531522 0.0496062123 -0.0440648708 0.0326801428
## 896 897 898 899 900
## -0.0956868219 -0.4971066225 -0.1869100818 -0.5862372574 -0.1890310285
## 901 902 903 904 905
## 0.0145304647 -0.2770093589 0.1312466916 -0.2284920980 -0.0268154460
## 906 907 908 909 910
## 0.0838264617 0.0590312454 -0.1063077036 0.0483366812 -0.3175154672
## 911 912 913 914 915
## -0.2373649811 0.9825740745 0.2207481956 -0.0499450392 -0.0154097343
## 916 917 918 919 920
## -0.4784842100 -0.5074215292 -0.0315257022 0.0609233542 -0.2100302865
## 921 922 923 924 925
## 0.1139348511 0.0138452625 -0.2346720007 -0.3832963306 -0.1591635961
## 926 927 928 929 930
## 0.9324053394 0.1162320287 0.1873360495 -0.0446510563 -0.2302318832
## 931 932 933 934 935
## -0.5235442345 -0.1565189970 0.1966072808 -0.2047007050 -0.2410889273
## 936 937 938 939 940
## 0.0484218120 1.3601032297 0.3111173229 -0.0897572614 -0.0939891016
## 941 942 943 944 945
## -0.7661368864 -0.1720107627 -0.2803661000 -0.4531286045 -0.0878424936
## 946 947 948 949 950
## -0.0257002422 -0.1476342905 0.1828632400 -0.2185231531 0.0607106997
## 951 952 953 954 955
## 0.1784960145 -0.1119029216 -0.0945173275 0.0048762211 -0.3041273530
## 956 957 958 959 960
## -0.4090926222 -0.1891911860 1.2351021055 0.0325941046 1.0535114320
## 961 962 963 964 965
## -0.1359993553 -0.3186510883 0.0451152287 0.1497895397 0.8775437370
## 966 967 968 969 970
## -0.2271792761 -0.6001582460 -0.0360690069 0.0736472787 0.1449862830
## 971 972 973 974 975
## 0.1168655936 -0.0904635037 -0.1604480095 -0.5833987970 -0.6578005121
## 976 977 978 979 980
## -0.2472480350 -0.2730562876 -0.3662721064 0.0289831065 -0.2684729789
## 981 982 983 984 985
## 0.9233767733 -0.1594043116 -0.2024285002 1.3243807068 0.4841443149
## 986 987 988 989 990
## -0.0275491376 0.0449662242 1.2326885043 -0.3272890383 -0.0686189001
## 991 992 993 994 995
## -0.0762014698 0.0678769005 0.0202279218 -0.2029386152 -0.0906213291
## 996 997 998 999 1000
## 0.2089353940 -0.0003468499 -0.0130450803 0.0662257921 -0.1562307591
## 1001 1002 1003 1004 1005
## -0.2189907144 0.6263085802 -0.6063185499 0.8367184533 0.1170335411
## 1006 1007 1008 1009 1010
## -0.1113272868 -0.0374594767 -0.5029135024 1.8192319422 0.0258318501
## 1011 1012 1013 1014 1015
## -0.0134072881 -0.5523252963 1.0331140726 -0.0790649615 -0.2126010616
## 1016 1017 1018 1019 1020
## 0.0663524143 0.0257263681 -0.1049532197 0.0886606756 2.0589573688
## 1021 1022 1023 1024 1025
## -0.2009293673 0.7883320325 -0.0635852403 -0.3455687024 -0.1951087290
## 1026 1027 1028 1029 1030
## -0.5167773190 0.2660578180 1.9554336594 -0.1047730054 0.2325978663
## 1031 1032 1033 1034 1035
## -0.5528398544 -0.2039901429 -0.1781997548 0.2214912330 -0.0559983241
## 1036 1037 1038 1039 1040
## 0.2134916733 0.7761206962 -0.0088342130 -0.4039417333 2.1052365781
## 1041 1042 1043 1044 1045
## -0.3324569414 -0.3462076607 0.8519554244 -0.3314262340 -0.0209871236
## 1046 1047 1048 1049 1050
## -0.4721827714 -0.0285240059 0.8234989002 -0.0099038325 -0.1220306764
## 1051 1052 1053 1054 1055
## -0.1048914268 0.1218415992 -0.0187676089 -0.5068493395 -0.1612034047
## 1056 1057 1058 1059 1060
## -0.0071990965 -0.0967403519 0.7244418039 -0.5287476070 -0.2531106329
## 1061 1062 1063 1064 1065
## -0.6785837053 0.0301139530 -0.2512317403 0.0395380600 0.2175765622
## 1066 1067 1068 1069 1070
## -0.0402473203 -0.1062734024 -0.3338630446 0.2085757007 -0.0042441313
## 1071 1072 1073 1074 1075
## 0.1747959473 0.0505938594 -0.5374410271 0.1324206408 0.2482421031
## 1076 1077 1078 1079 1080
## -0.1837114263 -0.0735983946 -0.3752730312 0.4465161826 0.1069709236
## 1081 1082 1083 1084 1085
## 1.6162103663 -0.1854407699 -0.0138939409 -0.3185545465 0.1534841429
## 1086 1087 1088 1089 1090
## -0.3808886087 -0.0059319473 -0.0306170527 -0.2135147335 0.0472515424
## 1091 1092 1093 1094 1095
## -0.0773263512 0.0287880447 -0.0373316180 0.7467023295 0.1077210356
## 1096 1097 1098 1099 1100
## 0.5287589802 -0.1007761523 -0.7553811268 0.8012913253 -0.2645251766
## 1101 1102 1103 1104 1105
## -0.3087424305 0.0877176299 -0.4287592225 -0.1004142873 1.1273217714
## 1106 1107 1108 1109 1110
## -0.0518389393 -0.0527779537 0.1233490459 -0.3754830275 0.1483502420
## 1111 1112 1113 1114 1115
## 0.0433414265 0.1793213545 -0.5294074669 0.1807136400 -0.3393278057
## 1116 1117 1118 1119 1120
## -0.0476271802 0.2038806748 0.6145747888 0.2927428307 0.2594668544
## 1121 1122 1123 1124 1125
## 0.6860921649 -0.1333519995 -0.1243861751 1.4222240198 0.7558779815
## 1126 1127 1128 1129 1130
## 0.1501250673 -0.0721928613 -0.1204760386 0.8488268115 -0.3239746867
## 1131 1132 1133 1134 1135
## 0.2718404805 -0.3345012694 0.4827889427 0.1519042947 1.4007054422
## 1136 1137 1138 1139 1140
## 0.1532852339 -0.0164868909 -0.1787502204 -0.4397126837 0.9944565580
## 1141 1142 1143 1144 1145
## -0.1486772829 0.0216356166 1.0408323936 -0.1384543996 -0.0370008846
## 1146 1147 1148 1149 1150
## 0.0664237337 -0.1210736542 -0.3127666752 0.1001377911 -0.3104706278
## 1151 1152 1153 1154 1155
## -0.1859800717 -0.0303529563 0.0556027503 -0.1554271000 0.2015198035
## 1156 1157 1158 1159 1160
## 0.2300812767 0.9532034689 1.4752663396 -0.2139741912 -0.4346974866
## 1161 1162 1163 1164 1165
## -0.0892839454 -0.2703524492 1.2268553878 -0.1617444339 -0.0341651347
## 1166 1167 1168 1169 1170
## -0.1171479412 -0.1523591476 0.0003405481 -0.2220140030 -0.1268716528
## 1171 1172 1173 1174 1175
## 0.3596448628 -0.4729336961 -0.1326892523 -0.0519202638 -0.1156694908
## 1176 1177 1178 1179 1180
## -0.4248695280 -0.6180686540 -0.0874568887 -0.2745291594 -0.2445332787
## 1181 1182 1183 1184 1185
## -0.1322023405 -0.2907685427 -0.4270002341 0.0544183675 0.0977765627
## 1186 1187 1188 1189 1190
## 0.0963241724 0.9118574716 0.0472449335 -0.4857388760 1.3139635133
## 1191 1192 1193 1194 1195
## -0.0248264130 0.7103310956 0.0740970643 -0.1343246390 -0.1330660733
## 1196 1197 1198 1199 1200
## 1.9201808411 0.9205442745 -0.3224172495 -0.1285510702 -0.0159799312
## 1201 1202 1203 1204 1205
## 0.0077238028 -0.1080619204 -0.5321798373 -0.0281979155 0.4199859957
## 1206 1207 1208 1209 1210
## -0.0045123891 1.0689447274 0.2099176683 -0.3683868847 -0.0488997250
## 1211 1212 1213 1214 1215
## -0.1857211754 1.1553521077 -0.3219819324 0.0173813062 -0.1295813138
## 1216 1217 1218 1219 1220
## 1.4895955081 -0.2382892037 -0.2576555164 -0.0341591952 0.0918651862
## 1221 1222 1223 1224 1225
## 0.0392891799 -0.0400776897 -0.0817135715 0.6857748327 -0.0161604690
## 1226 1227 1228 1229 1230
## -0.2785479399 0.1738879696 -0.1610157160 -0.1085719010 0.0112670280
## 1231 1232 1233 1234 1235
## 0.1756211741 0.4670122429 0.2209169987 0.0538133695 0.0277570256
## 1236 1237 1238 1239 1240
## -0.4613238284 0.2155202453 0.0605055164 0.1514495172 -0.3370576089
## 1241 1242 1243 1244 1245
## -0.1315022415 -0.3052620071 0.3510747869 -0.4168732136 -0.8822682879
## 1246 1247 1248 1249 1250
## 0.2643633872 0.1222585057 0.0630813757 -0.5821682659 0.3367615756
## 1251 1252 1253 1254 1255
## 0.0449420085 -0.6773293056 0.1699336500 0.7791961020 -0.2703293671
## 1256 1257 1258 1259 1260
## -0.2686439946 0.0671274728 0.0811963353 0.9248201047 0.0879660759
## 1261 1262 1263 1264 1265
## -0.0570882812 -0.4247285593 -0.0867211674 -0.0890568005 0.0519972937
## 1266 1267 1268 1269 1270
## -0.7586919906 -0.0324229284 0.6377921045 -0.5125764950 0.0432388002
## 1271 1272 1273 1274 1275
## -0.2934342594 -0.3354538222 0.6472033411 -0.2335348053 -0.1133550360
## 1276 1277 1278 1279 1280
## 0.0353068889 -0.2245806914 -0.2310638019 -0.3894164719 0.0810433353
## 1281 1282 1283 1284 1285
## -0.1464216820 -0.5106108383 0.2580660437 -0.4300677090 -0.2820695871
## 1286 1287 1288 1289 1290
## 0.0223918318 -0.0231342966 -0.1046413390 0.8989668885 -0.1935014958
## 1291 1292 1293 1294 1295
## 0.1835144286 0.9113687735 -0.6621025686 0.1159713320 0.0762484563
## 1296 1297 1298 1299 1300
## -0.3212361203 -0.3871758727 -0.0240066639 -0.0543091723 0.0107479154
## 1301 1302 1303 1304 1305
## 0.4469918963 -0.2600710565 -0.0953690000 0.0332322909 -0.4695399971
## 1306 1307 1308 1309 1310
## -0.4090945870 -0.2328153004 -0.1600655707 0.5858047988 -0.1196805454
## 1311 1312 1313 1314 1315
## -0.0689967238 -0.1843932786 -0.3989200045 0.9574756835 -0.1518888127
## 1316 1317 1318 1319 1320
## 1.4705125153 -0.3587076793 -1.0243627672 1.0498350999 0.0624071135
## 1321 1322 1323 1324 1325
## 0.0122688173 -0.7164045104 -0.0780122620 0.0789775515 -0.1691129922
## 1326 1327 1328 1329 1330
## 0.0073892799 -0.1330684563 -0.0625423489 1.9000844088 -0.0807621928
## 1331 1332 1333 1334 1335
## 0.1482979104 1.0557375974 -0.0329186663 0.0735973121 -0.2032739967
## 1336 1337 1338
## -0.5577794189 -0.4184240324 -0.6899507897valores_ajustados_log_ols <- fitted(ols_model)
plot(valores_ajustados_log_ols, residuos_log_ols, main = "Residuos vs. Ajustes del LOG", xlab = "Valores Ajustados", ylab = "Residuos")
# Pruebas del modelo ols y ols log
# Prueba de multicolinealidad
vif_result <- car::vif(ols_model)# Factor de inflación de la varianza
vif_result## age bmi smoker
## 1.012764 1.012146 1.000672#No hay multicolinealidad entre la variable predictora y el resto de las variables predictoras.
# Prueba de heterocedasticidad (Test de Breusch-Pagan)
bp_test <- bptest(ols_model)
bp_test##
## studentized Breusch-Pagan test
##
## data: ols_model
## BP = 112.59, df = 3, p-value < 2.2e-16#El valor p es menor que el nivel de significancia (p < 0.05), hay evidencia de heterocedasticidad y se rechaza la hipótesis nula de homocedasticidad.
# Prueba de autocorrelación serial (Test de Durbin-Watson)
dw_test <- dwtest(ols_model)
dw_test##
## Durbin-Watson test
##
## data: ols_model
## DW = 2.0765, p-value = 0.9191
## alternative hypothesis: true autocorrelation is greater than 0#El valor del estadístico de prueba está cerca de 2, lo que sugiere que los residuos del modelo de regresión no muestran una autocorrelación serial significativa. Un valor de DW cercano a 2 indica que no hay autocorrelación serial.
# Prueba de normalidad de los residuos (Anderson-Darling)
ad_test <- ad.test(ols_model$residuals)
ad_test##
## Anderson-Darling normality test
##
## data: ols_model$residuals
## A = 41.885, p-value < 2.2e-16#Dado que el valor p es extremadamente bajo, se rechaza la hipótesis nula de que los residuos siguen una distribución normal. Los residuos del modelo de regresión no se ajustan a una distribución normal según el test de Anderson-Darling.
# Imprimir resultados
print("Prueba de Multicolinealidad (VIF):")## [1] "Prueba de Multicolinealidad (VIF):"print(vif_result)## age bmi smoker
## 1.012764 1.012146 1.000672print("Prueba de Heterocedasticidad (Breusch-Pagan):")## [1] "Prueba de Heterocedasticidad (Breusch-Pagan):"print(bp_test)##
## studentized Breusch-Pagan test
##
## data: ols_model
## BP = 112.59, df = 3, p-value < 2.2e-16print("Prueba de Autocorrelación Serial (Durbin-Watson):")## [1] "Prueba de Autocorrelación Serial (Durbin-Watson):"print(dw_test)##
## Durbin-Watson test
##
## data: ols_model
## DW = 2.0765, p-value = 0.9191
## alternative hypothesis: true autocorrelation is greater than 0#print("Prueba de Autocorrelación Espacial (Moran's I):")
#print(moran_test)
print("Prueba de Normalidad de los Residuos (Anderson-Darling):")## [1] "Prueba de Normalidad de los Residuos (Anderson-Darling):"print(ad_test)##
## Anderson-Darling normality test
##
## data: ols_model$residuals
## A = 41.885, p-value < 2.2e-16# Prueba de multicolinealidad
vif_result <- car::vif(log_ols_model)# Factor de inflación de la varianza
vif_result## log(age) log(bmi) smoker
## 1.012653 1.012136 1.000521#Los valores de VIF cercanos a 1 para todas las variables indican que no hay evidencia sustancial de multicolinealidad entre las variables incluidas en el modelo.
# Prueba de heterocedasticidad (Test de Breusch-Pagan)
bp_test <- bptest(log_ols_model)
bp_test##
## studentized Breusch-Pagan test
##
## data: log_ols_model
## BP = 102.39, df = 3, p-value < 2.2e-16#Dado que el valor p es muy pequeño, se rechaza la hipótesis nula de que no hay heterocedasticidad en los residuos. En otras palabras, hay evidencia de heterocedasticidad en los residuos del modelo de regresión. Podriamos utilizar métodos de ponderación para dar más peso a las observaciones con menor varianza y menos peso a las observaciones con mayor varianza. Esto puede ayudar a compensar la heterocedasticidad y mejorar la precisión de las estimaciones.
# Prueba de autocorrelación serial (Test de Durbin-Watson)
dw_test <- dwtest(log_ols_model)
dw_test##
## Durbin-Watson test
##
## data: log_ols_model
## DW = 2.0265, p-value = 0.6861
## alternative hypothesis: true autocorrelation is greater than 0#El valor del estadístico de prueba está cerca de 2, lo que sugiere que los residuos del modelo de regresión no muestran una autocorrelación serial significativa. Un valor de DW cercano a 2 indica que no hay autocorrelación serial.
# Prueba de normalidad de los residuos (Anderson-Darling)
ad_test <- ad.test(log_ols_model$residuals)
ad_test##
## Anderson-Darling normality test
##
## data: log_ols_model$residuals
## A = 55.307, p-value < 2.2e-16#Dado que el valor p es mayor que el nivel de significancia, no hay suficiente evidencia para rechazar la hipótesis nula de que no hay autocorrelación serial en los residuos del modelo. En este caso, la hipótesis nula sugiere que no hay autocorrelación positiva en los residuos del modelo.
# Imprimir resultados
print("Prueba de Multicolinealidad (VIF):")## [1] "Prueba de Multicolinealidad (VIF):"print(vif_result)## log(age) log(bmi) smoker
## 1.012653 1.012136 1.000521print("Prueba de Heterocedasticidad (Breusch-Pagan):")## [1] "Prueba de Heterocedasticidad (Breusch-Pagan):"print(bp_test)##
## studentized Breusch-Pagan test
##
## data: log_ols_model
## BP = 102.39, df = 3, p-value < 2.2e-16print("Prueba de Autocorrelación Serial (Durbin-Watson):")## [1] "Prueba de Autocorrelación Serial (Durbin-Watson):"print(dw_test)##
## Durbin-Watson test
##
## data: log_ols_model
## DW = 2.0265, p-value = 0.6861
## alternative hypothesis: true autocorrelation is greater than 0#print("Prueba de Autocorrelación Espacial (Moran's I):")
#print(moran_test)
print("Prueba de Normalidad de los Residuos (Anderson-Darling):")## [1] "Prueba de Normalidad de los Residuos (Anderson-Darling):"print(ad_test)##
## Anderson-Darling normality test
##
## data: log_ols_model$residuals
## A = 55.307, p-value < 2.2e-16b.SAR
No podemos realizar este modelo
c.SEM
No podemos realizar este modelo
d.XGBoost Regresión
df_alt <- df %>% select(age,bmi,smoker,expenses,children,sex, region)
df_alt$bmi <- as.numeric(df_alt$bmi)
df_alt$expenses <- as.numeric(df_alt$expenses)
df_alt$smoker_numeric <- as.numeric(df_alt$smoker == "yes")
df_alt$sex_numeric <- as.numeric(df_alt$sex == "yes")
df_alt$reg_numeric <- as.numeric(df_alt$region == "yes")
df_alt$age <- log(df_alt$age)
df_alt$bmi <- log(df_alt$bmi)
df_alt$smoker_numeric <- log(df_alt$smoker_numeric)
df_alt$expenses <- log(df_alt$expenses)
df_alt$children <- log(df_alt$children + 0.01)
df_alt$sex_numeric <- log(df_alt$sex_numeric)
df_alt$reg_numeric <- log(df_alt$reg_numeric)
summary(df_alt)## age bmi smoker expenses children
## Min. :2.890 Min. :2.773 no :1064 Min. : 7.023 Min. :-4.60517
## 1st Qu.:3.296 1st Qu.:3.270 yes: 274 1st Qu.: 8.464 1st Qu.:-4.60517
## Median :3.664 Median :3.414 Median : 9.147 Median : 0.00995
## Mean :3.597 Mean :3.403 Mean : 9.099 Mean :-1.67105
## 3rd Qu.:3.932 3rd Qu.:3.547 3rd Qu.: 9.720 3rd Qu.: 0.69813
## Max. :4.159 Max. :3.972 Max. :11.063 Max. : 1.61144
## sex region smoker_numeric sex_numeric reg_numeric
## female:662 northeast:324 Min. :-Inf Min. :-Inf Min. :-Inf
## male :676 northwest:325 1st Qu.:-Inf 1st Qu.:-Inf 1st Qu.:-Inf
## southeast:364 Median :-Inf Median :-Inf Median :-Inf
## southwest:325 Mean :-Inf Mean :-Inf Mean :-Inf
## 3rd Qu.:-Inf 3rd Qu.:-Inf 3rd Qu.:-Inf
## Max. : 0 Max. :-Inf Max. :-Infset.seed(123) # What is set.seed()? We want to make sure that we get the same results for randomization each time you run the script.
cv_data <- createDataPartition(y = df$expenses, p=0.7, list=F)
cv_train = df_alt[cv_data, ]
cv_test = df_alt[-cv_data, ]
# define explanatory variables (X's) and dependent variable (Y) in training set
train_x = data.matrix(cv_train[, -7])
train_y = cv_train[,7]
# define explanatory variables (X's) and dependent variable (Y) in testing set
test_x = data.matrix(cv_test[, -7])
test_y = cv_test[, 7]
any(is.infinite(test_y))## [1] FALSEtrain_x[is.infinite(train_x)] <- NA
test_x[is.infinite(test_x)] <- NA
# Calcular la media de cada columna
means <- colMeans(train_x, na.rm = TRUE)
# Imputar los valores NA con la media de cada columna
for (i in 1:ncol(train_x)) {
train_x[is.na(train_x[, i]), i] <- means[i]
}
# Calcular la media de cada columna
means2 <- colMeans(test_x, na.rm = TRUE)
# Imputar los valores NA con la media de cada columna
for (i in 1:ncol(test_x)) {
test_x[is.na(test_x[, i]), i] <- means2[i]
}
any(is.na(train_x))## [1] TRUEany(is.infinite(train_x))## [1] FALSEany(is.na(train_y))## [1] FALSEany(is.infinite(train_y))## [1] FALSEany(is.na(test_x))## [1] TRUEany(is.infinite(test_x))## [1] FALSEany(is.na(test_y))## [1] FALSE# define final training and testing sets
xgb_train = xgb.DMatrix(data = train_x, label = train_y)
xgb_test = xgb.DMatrix(data = test_x, label = test_y)
# Lets fit XGBoost regression model and display RMSE for both training and testing data at each round
watchlist = list(train=xgb_train, test=xgb_test)
model_xgb = xgb.train(data=xgb_train, max.depth=3, watchlist=watchlist, nrounds=70) # the more the number of rounds selected, the longer the time to display the results. ## [1] train-rmse:1.786677 test-rmse:1.777907
## [2] train-rmse:1.465217 test-rmse:1.468778
## [3] train-rmse:1.269669 test-rmse:1.282215
## [4] train-rmse:1.158307 test-rmse:1.183643
## [5] train-rmse:1.094564 test-rmse:1.134762
## [6] train-rmse:1.061324 test-rmse:1.107692
## [7] train-rmse:1.035595 test-rmse:1.101080
## [8] train-rmse:1.023131 test-rmse:1.092040
## [9] train-rmse:1.014099 test-rmse:1.092320
## [10] train-rmse:1.007996 test-rmse:1.090938
## [11] train-rmse:1.002551 test-rmse:1.092058
## [12] train-rmse:0.997948 test-rmse:1.094961
## [13] train-rmse:0.993285 test-rmse:1.093392
## [14] train-rmse:0.990637 test-rmse:1.093819
## [15] train-rmse:0.984490 test-rmse:1.093381
## [16] train-rmse:0.977267 test-rmse:1.095828
## [17] train-rmse:0.975728 test-rmse:1.095132
## [18] train-rmse:0.968872 test-rmse:1.095716
## [19] train-rmse:0.964503 test-rmse:1.096894
## [20] train-rmse:0.958036 test-rmse:1.099029
## [21] train-rmse:0.956294 test-rmse:1.098408
## [22] train-rmse:0.955054 test-rmse:1.099032
## [23] train-rmse:0.952409 test-rmse:1.099591
## [24] train-rmse:0.945499 test-rmse:1.098905
## [25] train-rmse:0.937576 test-rmse:1.099639
## [26] train-rmse:0.932956 test-rmse:1.097553
## [27] train-rmse:0.931134 test-rmse:1.097739
## [28] train-rmse:0.925727 test-rmse:1.099623
## [29] train-rmse:0.919428 test-rmse:1.100694
## [30] train-rmse:0.916376 test-rmse:1.097990
## [31] train-rmse:0.915067 test-rmse:1.097510
## [32] train-rmse:0.912523 test-rmse:1.096620
## [33] train-rmse:0.911708 test-rmse:1.098472
## [34] train-rmse:0.904880 test-rmse:1.098580
## [35] train-rmse:0.903390 test-rmse:1.098503
## [36] train-rmse:0.898203 test-rmse:1.098510
## [37] train-rmse:0.890675 test-rmse:1.106326
## [38] train-rmse:0.886732 test-rmse:1.107119
## [39] train-rmse:0.881864 test-rmse:1.108591
## [40] train-rmse:0.881127 test-rmse:1.109747
## [41] train-rmse:0.878628 test-rmse:1.110082
## [42] train-rmse:0.873657 test-rmse:1.111683
## [43] train-rmse:0.872837 test-rmse:1.112750
## [44] train-rmse:0.870946 test-rmse:1.113360
## [45] train-rmse:0.866501 test-rmse:1.114206
## [46] train-rmse:0.863333 test-rmse:1.114701
## [47] train-rmse:0.859833 test-rmse:1.113659
## [48] train-rmse:0.856513 test-rmse:1.109477
## [49] train-rmse:0.855377 test-rmse:1.109559
## [50] train-rmse:0.849853 test-rmse:1.109603
## [51] train-rmse:0.847040 test-rmse:1.108344
## [52] train-rmse:0.838973 test-rmse:1.112409
## [53] train-rmse:0.835755 test-rmse:1.109960
## [54] train-rmse:0.833828 test-rmse:1.110243
## [55] train-rmse:0.832112 test-rmse:1.109300
## [56] train-rmse:0.827406 test-rmse:1.109738
## [57] train-rmse:0.825360 test-rmse:1.109940
## [58] train-rmse:0.821850 test-rmse:1.110381
## [59] train-rmse:0.819852 test-rmse:1.108141
## [60] train-rmse:0.818262 test-rmse:1.108806
## [61] train-rmse:0.816802 test-rmse:1.109459
## [62] train-rmse:0.814251 test-rmse:1.110088
## [63] train-rmse:0.811915 test-rmse:1.109807
## [64] train-rmse:0.807707 test-rmse:1.112655
## [65] train-rmse:0.804693 test-rmse:1.114469
## [66] train-rmse:0.803032 test-rmse:1.113363
## [67] train-rmse:0.797515 test-rmse:1.110922
## [68] train-rmse:0.796676 test-rmse:1.111487
## [69] train-rmse:0.793327 test-rmse:1.110766
## [70] train-rmse:0.788872 test-rmse:1.108805# Looks like the lowest RMSE for both training and test dataset is achieved at 59 round.
# Lets estimate our final regression model
reg_xgb = xgboost(data = xgb_train, max.depth = 3, nrounds = 59, verbose = 0) # setting verbose = 0 avoids to display the training and testing error for each round.
prediction_xgb_test<-predict(reg_xgb, xgb_test)
rmse(prediction_xgb_test, cv_test$expenses)## [1] 6.662972# Lets do some diagnostic check of regression residuals
xgb_reg_residuals<-cv_test$expenses - prediction_xgb_test
plot(xgb_reg_residuals, xlab= "Dependent Variable", ylab = "Residuals", main = 'XGBoost Regression Residuals')
abline(0,0)
# Plot first 3 trees of model
xgb.plot.tree(model=reg_xgb, trees=0:2)importance_matrix <- xgb.importance(model = reg_xgb)
xgb.plot.importance(importance_matrix, xlab = "Explanatory Variables X's Importance")
e.Decision Trees
decision_tree_model <- rpart(log(expenses) ~ log(bmi) + log(age) + log(children + 0.01) + smoker , data = train)
# summary(decision_tree_regression)
plot(decision_tree_model, compress = TRUE)
text(decision_tree_model, use.n = TRUE)
rpart.plot(decision_tree_model)
# Hacer predicciones con el modelo de árbol de decisión en los datos de entrenamiento
decision_tree_predictions <- predict(decision_tree_model, train)
# Calcular los residuos
residuals <- decision_tree_predictions - log(train$expenses)
# Calcular el RMSE
rmsedt <- sqrt(mean(residuals^2))
# Mostrar el valor del RMSE
print(rmsedt) #0.4010## [1] 0.4010215f.Random Forest
rf_model <- randomForest(expenses ~ age + bmi + children + smoker + sex + region, data = train, proximity=TRUE)
print(rf_model)##
## Call:
## randomForest(formula = expenses ~ age + bmi + children + smoker + sex + region, data = train, proximity = TRUE)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 2
##
## Mean of squared residuals: 21873431
## % Var explained: 85.31# Prediction & Confusion Matrix – test data
rf_prediction <- predict(rf_model,cv_test)
# confusionMatrix(rf_prediction_train_data, train$MEDV) # a confusion matrix is essentially a table that categorizes predictions against actual values.
RMSE_rf <- rmse(rf_prediction, cv_test$expenses)
RMSE_rf #8521.414## [1] 8303.481# Evalute Variables' Importance
# How to interpret varImpPlot()? The higher the value of mean decrease accuracy, the higher the importance of the variable in the model.
# In other words, mean decrease accuracy represents how much removing each variable reduces the accuracy of the model.
varImpPlot(rf_model, n.var = 5, main = "Top 5 - Variable") # It displays a variable importance plot from the random forest model. 
importance(rf_model) # It is worth mentioning that IncNodePurity by how much the model error increases by dropping each of the specified explanatory variables. ## IncNodePurity
## age 19733986905
## bmi 21699766084
## children 3102584526
## smoker 98443051346
## sex 1307424273
## region 3137177082 # Briefly, varImpPlot() indicates each variable's importance in explaining the performance of the dependent variable (Y).g.Neural Networks Regresión
# Lets estimate a Neural Network Regression
summary(train)## age sex bmi children smoker
## Min. :18.00 female:530 Min. :16.00 Min. :0.000 no :850
## 1st Qu.:27.00 male :542 1st Qu.:26.40 1st Qu.:0.000 yes:222
## Median :39.00 Median :30.50 Median :1.000
## Mean :39.19 Mean :30.76 Mean :1.081
## 3rd Qu.:51.00 3rd Qu.:34.80 3rd Qu.:2.000
## Max. :64.00 Max. :53.10 Max. :5.000
## region expenses
## northeast:254 Min. : 1122
## northwest:257 1st Qu.: 4745
## southeast:309 Median : 9382
## southwest:252 Mean :13318
## 3rd Qu.:16604
## Max. :63770train$bmi <- as.numeric(train$bmi)
train$expenses <- as.numeric(train$expenses)
train$smoker_numeric <- as.numeric(train$smoker == "yes")
train$sex_numeric <- as.numeric(train$sex == "yes")
train$reg_numeric <- as.numeric(train$region == "yes")
nn_model <- neuralnet(expenses ~ age + sex_numeric + bmi + children + reg_numeric + smoker_numeric, data = train, hidden = c(5, 3), linear.output = TRUE)
# Plot the neural network
plot(nn_model)
# Hacer predicciones con el modelo de red neuronal en los datos de entrenamiento
nn_predictions <- predict(nn_model, train)
# Calcular los residuos
residuals <- nn_predictions - train$expenses
# Calcular el RMSE
rmsenn <- sqrt(mean(residuals^2))
# Lets do some diagnostic check of regression residuals
residuals<-train$expenses - nn_predictions
plot(residuals, xlab= "Dependent Variable", ylab = "Residuals", main = 'Neural Net Regression Residuals')
abline(0,0)
# Mostrar el valor del RMSE
print(rmsenn) #12201.58## [1] 12201.58Principales hallagazos encontrados durante el EDA:
A travez del EDA pudimos observar:
Al examinar los gráficos de dispersión, notamos que existe una tendencia clara: a medida que la edad aumenta, también lo hacen los gastos médicos.
Observamos que las personas que fuman y tienen un índice de masa corporal elevado tienden a registrar gastos médicos más altos.
Observamos que la base de datos no presenta NA’s.
Podemos observar que el gasto entre hombres y mujeres es casi el mismo porque sus medias se encuentran igual pero el grupo de los homres presenta una dispersion mayor
Podemos observar que la region southeast es la que genera mayor expenses,a traves del analisis del boxplot
Ademas que tambien podemos obversar que la region southeast es la que genera un BMI mas alto lo que puede ser un factor importante
RMSE de los diferentes modelos
# Datos
model_names <- c("OLS", "OLS Log", "XGBoost", "DT", "RF", "NN") # Nombres de los modelos
rmse_values <- c(0.7475, 7517,6.6629 , 0.4010, 8521.414, 12201.58) # Valores de RMSE correspondientes a cada modelo
# Crear un dataframe con los datos
rmse_data <- data.frame(Modelo = model_names, RMSE = rmse_values)
# Crear el gráfico de barras
barplot(rmse_data$RMSE, names.arg = rmse_data$Modelo, col = "skyblue",
main = "RMSE de Modelos Estimados", xlab = "Modelo", ylab = "RMSE")
# Seleccion del Modelo
El modelo que mejor se ajusta según el RMSE es el modelo de Decision Tree (DT) ya que tiene el valor de RMSE más bajo (0.4010).ya que un RMSE más bajo indica un mejor ajuste del modelo a los datos.otro modelo que pudiera ser buena opcion seria el ols ya que su rmse es bajo igaul pero presenta un aic alto, ademas de que hay evidencia de que presenta heterocedasticidad.
---
title: "Actividad 1 Concentracion"
author: "Luis Mendoza - A00829099"
date: "2024-03-5"
output: 
  html_document:
    toc: TRUE
    toc_float: TRUE
    code_download: TRUE
---

![](C:\\Users\\Luis Rodriguez\\Downloads\\inteligencia-artificial-1.jpg)  

# Instalar Librerias
```{r message=FALSE, warning=FALSE}
library(foreign)       
library(ggplot2)        
library(dplyr)          
library(mapview)        
library(naniar)         
library(tmap)           
library(RColorBrewer)   
library(dlookr)         
library(regclass)      
library(mctest)         
library(lmtest)        
library(spdep)          
library(sf)            
library(spData)         
library(spatialreg)     
library(caret)          
library(e1071)         
library(SparseM)       
library(Metrics)        
library(randomForest)   
library(jtools)        
library(xgboost)        
library(DiagrammeR)    
library(effects)        
library(shinyjs)
library(sp)
library(geoR)
library(gstat)
library(caret)
library(readtext)
library(kableExtra)
library(nortest) 
library(rpart.plot)
library(neuralnet)
```

# 1.Preguntas
#1)¿Qué es Supervised Machine Learning y cuáles son algunas de sus aplicaciones en Inteligencia de Negocios?
Un modelo de aprendizaje supervisado es aquel a el que se le entregan datos etiquetados, para realizar predicciones o clasificaciones de estos datos de manera precisa, algunas de sus principales aplicaciones son las investigaciones de mercado, para saber cual es el mejor publico, segmento, cual es la mejor ubicacion para tu producto e incluso cual es el mejor momento para vender tu producto, tambien ppueden ayudar a fijar precios dinamicos de vuelos o viajes, a travez de datos que estan en constante cambio como la epoca del año, clima, demanda, entre otros

#3) ¿Qué es la R2 Ajustada? ¿Qué es la métrica RMSE? ¿Cuál es la diferencia entre la R2 Ajustada y la métrica RMSE? 
La R2 y el RMSE son medidas o metodos de evaluacion, pero se centran en cosas distintas, la R2 evalua la calidad del modelo atraves de la varianza de las variables, nos ayuda a ver que variables no son significantes para el modelo, mientras que el RMSE evalua la precision del modelo ya que se centra en la diferencia entre los valores observados y los valores predichos por el modelo

#Obtener Base de datos
```{r}
df <- read.csv("C:\\Users\\Luis Rodriguez\\Downloads\\health_insurance.csv")
#df

df[ , c("sex", "smoker", "region")] <- 
  lapply(df[ , c("sex", "smoker", "region")], as.factor) #Es necesario cambiar variables de tipo factor a una escala adecuada para poder manejar los datos de dichas variable.

```

# 2. Analisis Exploratorio de los datos (EDA):

Identificacion de NA’s:
```{r}
# Identificación de NA's por columna
nas <- colSums(is.na(df))
nas
```

Remplazo de NA’s:  En este caso no tenemos NA’s por lo cual no es necesario realizar un reemplazo

# Medidas Descriptivas:
```{r}
# Medidas descriptivas para todas las columnas numéricas
summary(df)
```
# Medidas de Dispersion: 
```{r message=FALSE, warning=FALSE}
varianza <- apply(df,2,var)
varianza

desviacion <- apply(df,2,sd)
desviacion
```
# Identifiacion de patrones y/o tendencias
Ejemplos de gráficos
```{r}
boxplot(expenses ~ sex, data = df, col = c("red","green","blue","purple", main = "Expenses por sexo"))
# Diagrama de caja para la variable 'bmi' por género
boxplot(bmi ~ region, data = df, col = c("blue","purple", "cyan", "lightpink"), main = "BMI por Region", xlab = "Region", ylab = "BMI")
boxplot(expenses ~ region, data = df, col = c("blue","purple", "cyan", "lightpink"), main = "Expenses por Region", xlab = "Region", ylab = "Expenses")
# Gráfico de dispersión para la relación entre 'age' y 'expenses'
plot(df$children, df$expenses, main = "Children vs. Gastos Médicos", xlab = "Children", ylab = "Gastos Médicos", col = "blue")
# Gráfico de dispersión para la relación entre 'smoke' y 'expenses'
plot(df$age, df$expenses, main = "Edad vs. Gastos Médicos", xlab = "Edad", ylab = "Gastos Médicos", col = "darkgreen")
# Gráfico de dispersión para la relación entre 'bmi' y 'expenses' tomando en cuenta 'Expenses'
ggplot(df, aes(x=bmi, y=expenses, shape=smoker, color=smoker)) +
  geom_point() +
  theme_minimal() +
  scale_color_brewer(palette = "Greens")
```

# 3.Apartir de los resultados de EDA describir la especificación del modelo de regresión lineal  a estimar. Brevemente, describir cómo es el posible impacto de cada una de las variables  explicativas sobre la principal variable de estudio.

Basándonos en los resultados del Análisis Exploratorio de Datos (EDA), identificamos que las variables más relevantes para predecir los gastos médicos (expenses) son el índice de masa corporal (bmi), la edad (age) y si la persona es fumadora (smoker).

Al examinar los gráficos de dispersión, notamos que existe una tendencia clara: a medida que la edad aumenta, también lo hacen los gastos médicos. Además, observamos que las personas que fuman y tienen un índice de masa corporal elevado tienden a registrar gastos médicos más altos.

# 4.  Estimación de cada uno de los siguientes modelos de Supervised Machine Learning (SML): 
# a.OLS Regresión

lets split data into training and test sets the training set is used to build the model and the test set to evaluate its predictive accuracy.
```{r}
set.seed(123)
partition <- createDataPartition(y = df$expenses, p=0.8, list=F)
train = df[partition, ]
test  = df[-partition, ]
```

```{r}
ols_model <- lm(expenses ~ age + bmi + smoker, data = df)
summary(ols_model)

log_ols_model <- lm(log(expenses) ~ log(age) + log(bmi) + smoker, data = df)
summary(log_ols_model)

AIC(ols_model)      # AIC = 27123.76
AIC(log_ols_model)  # AIC = 1717.374

RMSE_ols_model     <- sqrt(mean(ols_model$residuals^2)) #RMSE = 0.7475
RMSE_log_ols_model <- sqrt(mean(log_ols_model$residuals^2)) #RMSE = 7517

#Modelo OLS ABSOLUTO
residuos_ols <- resid(ols_model)
residuos_ols
valores_ajustados_ols <- fitted(ols_model)

plot(valores_ajustados_ols, residuos_ols, main = "Residuos vs. Ajustes", xlab = "Valores Ajustados", ylab = "Residuos")

#Modelo LOG_OLS
residuos_log_ols <- resid(log_ols_model)
residuos_log_ols
valores_ajustados_log_ols <- fitted(ols_model)

plot(valores_ajustados_log_ols, residuos_log_ols, main = "Residuos vs. Ajustes del LOG", xlab = "Valores Ajustados", ylab = "Residuos")
```
# Pruebas del modelo ols y ols log
```{r}
# Prueba de multicolinealidad
vif_result <- car::vif(ols_model)# Factor de inflación de la varianza
vif_result

#No hay multicolinealidad entre la variable predictora y el resto de las variables predictoras.

# Prueba de heterocedasticidad (Test de Breusch-Pagan)
bp_test <- bptest(ols_model)
bp_test

#El valor p es menor que el nivel de significancia (p < 0.05), hay evidencia de heterocedasticidad y se rechaza la hipótesis nula de homocedasticidad.

# Prueba de autocorrelación serial (Test de Durbin-Watson)
dw_test <- dwtest(ols_model)
dw_test

#El valor del estadístico de prueba está cerca de 2, lo que sugiere que los residuos del modelo de regresión no muestran una autocorrelación serial significativa. Un valor de DW cercano a 2 indica que no hay autocorrelación serial.

# Prueba de normalidad de los residuos (Anderson-Darling)
ad_test <- ad.test(ols_model$residuals)
ad_test

#Dado que el valor p es extremadamente bajo, se rechaza la hipótesis nula de que los residuos siguen una distribución normal. Los residuos del modelo de regresión no se ajustan a una distribución normal según el test de Anderson-Darling. 

# Imprimir resultados
print("Prueba de Multicolinealidad (VIF):")
print(vif_result)
print("Prueba de Heterocedasticidad (Breusch-Pagan):")
print(bp_test)
print("Prueba de Autocorrelación Serial (Durbin-Watson):")
print(dw_test)
#print("Prueba de Autocorrelación Espacial (Moran's I):")
#print(moran_test)
print("Prueba de Normalidad de los Residuos (Anderson-Darling):")
print(ad_test)

# Prueba de multicolinealidad
vif_result <- car::vif(log_ols_model)# Factor de inflación de la varianza
vif_result

#Los valores de VIF cercanos a 1 para todas las variables indican que no hay evidencia sustancial de multicolinealidad entre las variables incluidas en el modelo. 

# Prueba de heterocedasticidad (Test de Breusch-Pagan)
bp_test <- bptest(log_ols_model)
bp_test

#Dado que el valor p es muy pequeño, se rechaza la hipótesis nula de que no hay heterocedasticidad en los residuos. En otras palabras, hay evidencia de heterocedasticidad en los residuos del modelo de regresión. Podriamos utilizar métodos de ponderación para dar más peso a las observaciones con menor varianza y menos peso a las observaciones con mayor varianza. Esto puede ayudar a compensar la heterocedasticidad y mejorar la precisión de las estimaciones.

# Prueba de autocorrelación serial (Test de Durbin-Watson)
dw_test <- dwtest(log_ols_model)
dw_test

#El valor del estadístico de prueba está cerca de 2, lo que sugiere que los residuos del modelo de regresión no muestran una autocorrelación serial significativa. Un valor de DW cercano a 2 indica que no hay autocorrelación serial.

# Prueba de normalidad de los residuos (Anderson-Darling)
ad_test <- ad.test(log_ols_model$residuals)
ad_test

#Dado que el valor p es mayor que el nivel de significancia, no hay suficiente evidencia para rechazar la hipótesis nula de que no hay autocorrelación serial en los residuos del modelo. En este caso, la hipótesis nula sugiere que no hay autocorrelación positiva en los residuos del modelo.

# Imprimir resultados
print("Prueba de Multicolinealidad (VIF):")
print(vif_result)
print("Prueba de Heterocedasticidad (Breusch-Pagan):")
print(bp_test)
print("Prueba de Autocorrelación Serial (Durbin-Watson):")
print(dw_test)
#print("Prueba de Autocorrelación Espacial (Moran's I):")
#print(moran_test)
print("Prueba de Normalidad de los Residuos (Anderson-Darling):")
print(ad_test)
```

# b.SAR
No podemos realizar este modelo

# c.SEM
No podemos realizar este modelo

# d.XGBoost Regresión 
```{r}
df_alt <- df %>% select(age,bmi,smoker,expenses,children,sex, region)

df_alt$bmi <- as.numeric(df_alt$bmi)
df_alt$expenses <- as.numeric(df_alt$expenses)
df_alt$smoker_numeric <- as.numeric(df_alt$smoker == "yes")
df_alt$sex_numeric <- as.numeric(df_alt$sex == "yes")
df_alt$reg_numeric <- as.numeric(df_alt$region == "yes")

df_alt$age     <- log(df_alt$age)
df_alt$bmi <- log(df_alt$bmi)
df_alt$smoker_numeric <- log(df_alt$smoker_numeric) 
df_alt$expenses <- log(df_alt$expenses)
df_alt$children <- log(df_alt$children + 0.01)
df_alt$sex_numeric <- log(df_alt$sex_numeric) 
df_alt$reg_numeric     <- log(df_alt$reg_numeric)

summary(df_alt)


set.seed(123) # What is set.seed()? We want to make sure that we get the same results for randomization each time you run the script.   
cv_data   <- createDataPartition(y = df$expenses, p=0.7, list=F)
cv_train = df_alt[cv_data, ]
cv_test = df_alt[-cv_data, ]

# define explanatory variables (X's) and dependent variable (Y) in training set
train_x = data.matrix(cv_train[, -7])
train_y = cv_train[,7]

# define explanatory variables (X's) and dependent variable (Y) in testing set
test_x = data.matrix(cv_test[, -7])
test_y = cv_test[, 7]

any(is.infinite(test_y))
train_x[is.infinite(train_x)] <- NA
test_x[is.infinite(test_x)] <- NA

# Calcular la media de cada columna
means <- colMeans(train_x, na.rm = TRUE)

# Imputar los valores NA con la media de cada columna
for (i in 1:ncol(train_x)) {
  train_x[is.na(train_x[, i]), i] <- means[i]
}

# Calcular la media de cada columna
means2 <- colMeans(test_x, na.rm = TRUE)

# Imputar los valores NA con la media de cada columna
for (i in 1:ncol(test_x)) {
  test_x[is.na(test_x[, i]), i] <- means2[i]
}

any(is.na(train_x))
any(is.infinite(train_x))
any(is.na(train_y))
any(is.infinite(train_y))
any(is.na(test_x))
any(is.infinite(test_x))
any(is.na(test_y))

# define final training and testing sets
xgb_train = xgb.DMatrix(data = train_x, label = train_y)
xgb_test  = xgb.DMatrix(data = test_x, label = test_y)

# Lets fit XGBoost regression model and display RMSE for both training and testing data at each round
watchlist = list(train=xgb_train, test=xgb_test)
model_xgb = xgb.train(data=xgb_train, max.depth=3, watchlist=watchlist, nrounds=70) # the more the number of rounds selected, the longer the time to display the results. 

# Looks like the lowest RMSE for both training and test dataset is achieved at 59 round. 
# Lets estimate our final regression model
reg_xgb = xgboost(data = xgb_train, max.depth = 3, nrounds = 59, verbose = 0) # setting verbose = 0 avoids to display the training and testing error for each round. 
prediction_xgb_test<-predict(reg_xgb, xgb_test)
rmse(prediction_xgb_test, cv_test$expenses)

# Lets do some diagnostic check of regression residuals 
xgb_reg_residuals<-cv_test$expenses - prediction_xgb_test
plot(xgb_reg_residuals, xlab= "Dependent Variable", ylab = "Residuals", main = 'XGBoost Regression Residuals')
abline(0,0)

# Plot first 3 trees of model
xgb.plot.tree(model=reg_xgb, trees=0:2)
importance_matrix <- xgb.importance(model = reg_xgb)
xgb.plot.importance(importance_matrix, xlab = "Explanatory Variables X's Importance")
```

# e.Decision Trees
```{r}
decision_tree_model <- rpart(log(expenses) ~ log(bmi) + log(age) + log(children + 0.01) + smoker , data = train)

# summary(decision_tree_regression)
plot(decision_tree_model, compress = TRUE)
text(decision_tree_model, use.n = TRUE)
rpart.plot(decision_tree_model)

# Hacer predicciones con el modelo de árbol de decisión en los datos de entrenamiento
decision_tree_predictions <- predict(decision_tree_model, train)

# Calcular los residuos
residuals <- decision_tree_predictions - log(train$expenses)

# Calcular el RMSE
rmsedt <- sqrt(mean(residuals^2))

# Mostrar el valor del RMSE
print(rmsedt) #0.4010

```

# f.Random Forest 
```{r}
rf_model <- randomForest(expenses ~ age + bmi  +  children + smoker + sex + region, data = train, proximity=TRUE)

print(rf_model)

# Prediction & Confusion Matrix – test data
rf_prediction <- predict(rf_model,cv_test)

# confusionMatrix(rf_prediction_train_data, train$MEDV) # a confusion matrix is essentially a table that categorizes predictions against actual values.
RMSE_rf <- rmse(rf_prediction, cv_test$expenses)
RMSE_rf #8521.414

# Evalute Variables' Importance
# How to interpret varImpPlot()? The higher the value of mean decrease accuracy, the higher the importance of the variable in the model. 
# In other words, mean decrease accuracy represents how much removing each variable reduces the accuracy of the model.
varImpPlot(rf_model, n.var = 5, main = "Top 5 - Variable") # It displays a variable importance plot from the random forest model. 
importance(rf_model)                                        # It is worth mentioning that IncNodePurity by how much the model error increases by dropping each of the specified explanatory variables. 
                                                            # Briefly, varImpPlot() indicates each variable's importance in explaining the performance of the dependent variable (Y).

```


# g.Neural Networks Regresión 
```{r}
# Lets estimate a Neural Network Regression
summary(train)
train$bmi <- as.numeric(train$bmi)
train$expenses <- as.numeric(train$expenses)
train$smoker_numeric <- as.numeric(train$smoker == "yes")
train$sex_numeric <- as.numeric(train$sex == "yes")
train$reg_numeric <- as.numeric(train$region == "yes")

nn_model <- neuralnet(expenses ~ age + sex_numeric + bmi + children + reg_numeric + smoker_numeric, data = train, hidden = c(5, 3), linear.output = TRUE) 

# Plot the neural network 
plot(nn_model)

# Hacer predicciones con el modelo de red neuronal en los datos de entrenamiento
nn_predictions <- predict(nn_model, train)

# Calcular los residuos
residuals <- nn_predictions - train$expenses

# Calcular el RMSE
rmsenn <- sqrt(mean(residuals^2))

# Lets do some diagnostic check of regression residuals 
residuals<-train$expenses - nn_predictions
plot(residuals, xlab= "Dependent Variable", ylab = "Residuals", main = 'Neural Net Regression Residuals')
abline(0,0)

# Mostrar el valor del RMSE
print(rmsenn) #12201.58
```
# Principales hallagazos encontrados durante el EDA:

A travez del EDA pudimos observar:  

* Al examinar los gráficos de dispersión, notamos que existe una tendencia clara: a medida que la edad aumenta, también lo hacen los gastos médicos.  

* Observamos que las personas que fuman y tienen un índice de masa corporal elevado tienden a registrar gastos médicos más altos.  

* Observamos que la base de datos no presenta NA's.  

* Podemos observar que el gasto entre hombres y mujeres es casi el mismo porque sus medias se encuentran igual pero el grupo de los homres presenta una dispersion mayor 

* Podemos observar que la region southeast es la que genera mayor expenses,a traves del analisis del boxplot  

* Ademas que tambien podemos obversar que la region southeast es la que genera un BMI mas alto lo que puede ser un factor importante  

# RMSE de los diferentes modelos
```{r}
# Datos 
model_names <- c("OLS", "OLS Log", "XGBoost", "DT", "RF", "NN")  # Nombres de los modelos
rmse_values <- c(0.7475, 7517,6.6629 , 0.4010, 8521.414, 12201.58)  # Valores de RMSE correspondientes a cada modelo

# Crear un dataframe con los datos
rmse_data <- data.frame(Modelo = model_names, RMSE = rmse_values)

# Crear el gráfico de barras
barplot(rmse_data$RMSE, names.arg = rmse_data$Modelo, col = "skyblue", 
        main = "RMSE de Modelos Estimados", xlab = "Modelo", ylab = "RMSE")
```
# Seleccion del Modelo

El modelo que mejor se ajusta según el RMSE es el modelo de Decision Tree (DT) ya que tiene el valor de RMSE más bajo (0.4010).ya que un RMSE más bajo indica un mejor ajuste del modelo a los datos.otro modelo que pudiera ser buena opcion seria el ols ya que su rmse es bajo igaul pero presenta un aic alto, ademas de que hay evidencia de que presenta heterocedasticidad.

