Seleccion de Variables: Dataset ‘Toyota Corolla’
Alvarez Ignacio Nicolas
Este ejercicio consiste en realizar un análisis exploratorio sobre un dataset de vehiculos Toyota Corolla con 1436 instancias y 37 atributos.
El objetivo es conseguir un modelo de regresión lineal con un resultado aceptable interpretando cada paso del razonamiento necesario para llegar al objetivo.
- El atributo objetivo es Price.
1: Carga de Librerias
library(fastDummies)
library(car)
library(corrplot)
library(mctest)
library(tidyverse)
library(leaps)
library(glmnet)
library(MASS)
library(reshape)
library(caret)
library(ggrepel)2: Lectura del DataSet
raw_data = read.csv("ToyotaCorolla.csv")
raw_data$Id = NULL
raw_data$Model = NULL
- El atributo ID no es representativo de cada instancia, decido no considerarlo en el modelo.
- El atributo Model no es representativo de cada instancia, decido no considerarlo en el modelo.
3: DataSet
raw_data4: Estructura del DataSet
str(raw_data)'data.frame': 1436 obs. of 35 variables:
$ Price : int 13500 13750 13950 14950 13750 12950 16900 18600 21500 12950 ...
$ Age_08_04 : int 23 23 24 26 30 32 27 30 27 23 ...
$ Mfg_Month : int 10 10 9 7 3 1 6 3 6 10 ...
$ Mfg_Year : int 2002 2002 2002 2002 2002 2002 2002 2002 2002 2002 ...
$ KM : int 46986 72937 41711 48000 38500 61000 94612 75889 19700 71138 ...
$ Fuel_Type : Factor w/ 3 levels "CNG","Diesel",..: 2 2 2 2 2 2 2 2 3 2 ...
$ HP : int 90 90 90 90 90 90 90 90 192 69 ...
$ Met_Color : int 1 1 1 0 0 0 1 1 0 0 ...
$ Automatic : int 0 0 0 0 0 0 0 0 0 0 ...
$ cc : int 2000 2000 2000 2000 2000 2000 2000 2000 1800 1900 ...
$ Doors : int 3 3 3 3 3 3 3 3 3 3 ...
$ Cylinders : int 4 4 4 4 4 4 4 4 4 4 ...
$ Gears : int 5 5 5 5 5 5 5 5 5 5 ...
$ Quarterly_Tax : int 210 210 210 210 210 210 210 210 100 185 ...
$ Weight : int 1165 1165 1165 1165 1170 1170 1245 1245 1185 1105 ...
$ Mfr_Guarantee : int 0 0 1 1 1 0 0 1 0 0 ...
$ BOVAG_Guarantee : int 1 1 1 1 1 1 1 1 1 1 ...
$ Guarantee_Period: int 3 3 3 3 3 3 3 3 3 3 ...
$ ABS : int 1 1 1 1 1 1 1 1 1 1 ...
$ Airbag_1 : int 1 1 1 1 1 1 1 1 1 1 ...
$ Airbag_2 : int 1 1 1 1 1 1 1 1 0 1 ...
$ Airco : int 0 1 0 0 1 1 1 1 1 1 ...
$ Automatic_airco : int 0 0 0 0 0 0 0 0 0 0 ...
$ Boardcomputer : int 1 1 1 1 1 1 1 1 0 1 ...
$ CD_Player : int 0 1 0 0 0 0 0 1 0 0 ...
$ Central_Lock : int 1 1 0 0 1 1 1 1 1 0 ...
$ Powered_Windows : int 1 0 0 0 1 1 1 1 1 0 ...
$ Power_Steering : int 1 1 1 1 1 1 1 1 1 1 ...
$ Radio : int 0 0 0 0 0 0 0 0 1 0 ...
$ Mistlamps : int 0 0 0 0 1 1 0 0 0 0 ...
$ Sport_Model : int 0 0 0 0 0 0 1 0 0 0 ...
$ Backseat_Divider: int 1 1 1 1 1 1 1 1 0 1 ...
$ Metallic_Rim : int 0 0 0 0 0 0 0 0 1 0 ...
$ Radio_cassette : int 0 0 0 0 0 0 0 0 1 0 ...
$ Tow_Bar : int 0 0 0 0 0 0 0 0 0 0 ...5: Resumen del DataSet
summary(raw_data) Price Age_08_04 Mfg_Month Mfg_Year KM
Min. : 4350 Min. : 1.00 Min. : 1.000 Min. :1998 Min. : 1
1st Qu.: 8450 1st Qu.:44.00 1st Qu.: 3.000 1st Qu.:1998 1st Qu.: 43000
Median : 9900 Median :61.00 Median : 5.000 Median :1999 Median : 63390
Mean :10731 Mean :55.95 Mean : 5.549 Mean :2000 Mean : 68533
3rd Qu.:11950 3rd Qu.:70.00 3rd Qu.: 8.000 3rd Qu.:2001 3rd Qu.: 87021
Max. :32500 Max. :80.00 Max. :12.000 Max. :2004 Max. :243000
Fuel_Type HP Met_Color Automatic cc
CNG : 17 Min. : 69.0 Min. :0.0000 Min. :0.00000 Min. : 1300
Diesel: 155 1st Qu.: 90.0 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.: 1400
Petrol:1264 Median :110.0 Median :1.0000 Median :0.00000 Median : 1600
Mean :101.5 Mean :0.6748 Mean :0.05571 Mean : 1577
3rd Qu.:110.0 3rd Qu.:1.0000 3rd Qu.:0.00000 3rd Qu.: 1600
Max. :192.0 Max. :1.0000 Max. :1.00000 Max. :16000
Doors Cylinders Gears Quarterly_Tax Weight
Min. :2.000 Min. :4 Min. :3.000 Min. : 19.00 Min. :1000
1st Qu.:3.000 1st Qu.:4 1st Qu.:5.000 1st Qu.: 69.00 1st Qu.:1040
Median :4.000 Median :4 Median :5.000 Median : 85.00 Median :1070
Mean :4.033 Mean :4 Mean :5.026 Mean : 87.12 Mean :1072
3rd Qu.:5.000 3rd Qu.:4 3rd Qu.:5.000 3rd Qu.: 85.00 3rd Qu.:1085
Max. :5.000 Max. :4 Max. :6.000 Max. :283.00 Max. :1615
Mfr_Guarantee BOVAG_Guarantee Guarantee_Period ABS
Min. :0.0000 Min. :0.0000 Min. : 3.000 Min. :0.0000
1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.: 3.000 1st Qu.:1.0000
Median :0.0000 Median :1.0000 Median : 3.000 Median :1.0000
Mean :0.4095 Mean :0.8955 Mean : 3.815 Mean :0.8134
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.: 3.000 3rd Qu.:1.0000
Max. :1.0000 Max. :1.0000 Max. :36.000 Max. :1.0000
Airbag_1 Airbag_2 Airco Automatic_airco
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.00000
1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
Median :1.0000 Median :1.0000 Median :1.0000 Median :0.00000
Mean :0.9708 Mean :0.7228 Mean :0.5084 Mean :0.05641
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.00000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.00000
Boardcomputer CD_Player Central_Lock Powered_Windows
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000
Median :0.0000 Median :0.0000 Median :1.0000 Median :1.000
Mean :0.2946 Mean :0.2187 Mean :0.5801 Mean :0.562
3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.000
Power_Steering Radio Mistlamps Sport_Model
Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.0000
1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
Median :1.0000 Median :0.0000 Median :0.000 Median :0.0000
Mean :0.9777 Mean :0.1462 Mean :0.257 Mean :0.3001
3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1.000 3rd Qu.:1.0000
Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.0000
Backseat_Divider Metallic_Rim Radio_cassette Tow_Bar
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :1.0000 Median :0.0000 Median :0.0000 Median :0.0000
Mean :0.7702 Mean :0.2047 Mean :0.1455 Mean :0.2779
3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:1.0000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000 Observaciones
* El valor maximo de cc es de 16000, demasiado alto considerando la media.
* El atributo Fuel_Type es de tipo char, requerira un proceso de encoding.
* El valor de Cylinder es constante.
6: Análisis exploratorio
6a: Price
par(mfrow=c(1,2))
boxplot(raw_data$Price,main = "Precio Vehiculos Toyota Corolla",
ylab = "Precio ($)", notch = TRUE)
hist(raw_data$Price,main = "Precio Vehiculos Toyota Corolla")
- Se observa que la mediana del precio de los vehiculos, ronda los $10000 aproximadamente.
- Se presentan valores atípicos con valores superiores a las $20000 y valores menores a $7000 aproximadamente.
6b: Mfg_Year
par(mfrow=c(1,2))
boxplot(raw_data$Age_08_04,main = "Age_08_04")
barplot(table(as.factor(raw_data$Age_08_04)),main = "Age_08_04")
- El atributo “Age_08_04” presenta valores outliers correspondientes a vehiculos nuevos cuya antiguedad es 0.
6c: Mfg_Year
par(mfrow=c(1,2))
boxplot(raw_data$Mfg_Year,main = "Año de Mfg_Year")
barplot(table(as.factor(raw_data$Mfg_Year)),main = "Mfg_Year")
6d: KM
par(mfrow=c(1,2))
boxplot(raw_data$KM,main = "KM",
ylab = "KM", notch = TRUE)
hist(raw_data$KM,main = "KM")
- El atributo “KM” presenta valores outliers. Destaco sobretodo un conjunto de valores superiores a los 200000.
6e: HP
par(mfrow=c(1,2))
boxplot(raw_data$HP,main = "HP",
ylab = "HP", notch = FALSE)
barplot(table(as.factor(raw_data$HP)),main = "HP")
- El atributo “HP” presenta un valor outlier superior a 180. Según una investigacion realizada en medios externos al dataset, el valor si corresponde a un modelo de Toyota Corolla.
6f: CC
par(mfrow=c(1,2))
boxplot(raw_data$cc,main = "Cilindrada",
ylab = "CC", notch = FALSE)
barplot(table(as.factor(raw_data$cc)),main = "Cilindrada")
- El atributo “CC” presenta un outlier notorio superior a 16000, este valor esta fuera del contexto de un vehiculo toyota corolla, donde los valores promedio rondan el 100.
6g: Quarterly_Tax
par(mfrow=c(1,2))
boxplot(raw_data$Quarterly_Tax, main="Quarterly_Tax")
hist(raw_data$Quarterly_Tax)
- El atributo “Quarterly_Tax” presenta outliers para valores superiores a 150 y valores menores a 50, sobre una mediana de 70 aproximadamente.
6h: Weight
par(mfrow=c(1,2))
boxplot(raw_data$Weight, main="Peso(KG)")
hist(raw_data$Weight)
- El atributo “Weight” presenta outliers para valores superiores a 1150 sobre una mediana de 1050 aproximadamente.
6i: Fueltype y Radio Cassete
lbls <- c("0: No tiene", "1: Tiene")
par(mfrow=c(1,2))
barplot(table(as.factor(raw_data$Fuel_Type)), main="Fuel_Type")
pie(x = table(raw_data$Radio_cassette), labels = lbls, main="Radio Cassete")
6j: Metallic Rim y Backseat Divider
par(mfrow=c(1,2))
pie(x = table(raw_data$Metallic_Rim), labels = lbls, main="Metallic Rim")
pie(x = table(raw_data$Backseat_Divider) , labels = lbls, main="Backseat_Divider")
6k: Mistlamp, Radio y Sport Model
par(mfrow=c(1,3))
pie(x = table(raw_data$Mistlamps) , labels = lbls, main="Mistlamps")
pie(x = table(raw_data$Radio), labels = lbls, main="Radio")
pie(x = table(raw_data$Sport_Model), labels = lbls, main="Sport_Model")6l: Central Lock, CD Player y BoardComputer
par(mfrow=c(1,3))
pie(x = table(raw_data$Central_Lock), labels = lbls, main="Central_Lock")
pie(x = table(raw_data$CD_Player), labels = lbls, main="CD_Player")
pie(x = table(raw_data$Boardcomputer), labels = lbls, main="Boardcomputer")
6m: Airco, Airbag_2 y Airbag_1
par(mfrow=c(1,3))
pie(x = table(raw_data$Airco), labels = lbls, main="Airco")
pie(x = table(raw_data$Airbag_2), labels = lbls, main="Airbag_2")
pie(x = table(raw_data$Airbag_1), labels = lbls,main="Airbag_1")
6n: Guarantee Period y Automatic Airco
par(mfrow=c(1,2))
barplot(table(as.factor(raw_data$Guarantee_Period)), main="Guarantee_Period")
pie(x = table(raw_data$Automatic_airco), labels = lbls, main="Automatic_airco")
6o: MFR Guarantee, Gears y BOVAG Guarantee
par(mfrow=c(1,3))
pie(x = table(raw_data$Mfr_Guarantee), labels = lbls, main="Mfr_Guarantee")
barplot(table(as.factor(raw_data$Gears)), main="Gears")
pie(x = table(raw_data$BOVAG_Guarantee), labels = lbls, main="BOVAG_Guarantee")6p: Doors, Automatic y ABS
par(mfrow=c(1,3))
barplot(table(as.factor(raw_data$Doors)), main="Doors")
pie(x = table(raw_data$Automatic),labels = lbls, main="Automatic")
pie(x = table(raw_data$ABS),labels = lbls, main="ABS")7: Estudio de Variable Objetivo “Price”
7a: Distribucion de Price
hist(raw_data$Price, col="blue", breaks = 60, freq = F)
lines(density(raw_data$Price), col = "red", lwd=2)rug(raw_data$Price)
7b: Relacion Price vs Resto de Predictores
plot(Price~., data=raw_data,col="blue")
8: Seleccion y modificacion de Variables
8a: Estudio de correlacion
corrplot(cor(dplyr::select(raw_data, -c("Fuel_Type"))), type="upper", method="pie")the standard deviation is zero
8b: Indicadores de Colinealidad
imcdiag(dplyr::select(raw_data, -c("Price", "Fuel_Type")), raw_data$Price)
Call:
imcdiag(x = dplyr::select(raw_data, -c("Price", "Fuel_Type")),
y = raw_data$Price)
All Individual Multicollinearity Diagnostics Result
VIF TOL Wi Fi Leamer CVIF Klein
Age_08_04 Inf 0.0000 Inf Inf 0.0000 -Inf 1
Mfg_Month Inf 0.0000 Inf Inf 0.0000 -Inf 1
Mfg_Year Inf 0.0000 Inf Inf 0.0000 -Inf 1
KM 1.8647 0.5363 37.9120 39.1629 0.7323 -0.0556 0
HP 1.6023 0.6241 26.4092 27.2805 0.7900 -0.0478 0
Met_Color 1.1398 0.8773 6.1308 6.3331 0.9367 -0.0340 0
Automatic 1.0805 0.9255 3.5309 3.6474 0.9620 -0.0322 0
cc 1.2170 0.8217 9.5136 9.8275 0.9065 -0.0363 0
Doors 1.2554 0.7966 11.1979 11.5674 0.8925 -0.0374 0
Cylinders 2.0001 0.5000 43.8472 45.2939 NA -0.0596 0
Gears 1.2599 0.7937 11.3958 11.7718 0.8909 -0.0376 0
Quarterly_Tax 2.7801 0.3597 78.0447 80.6197 0.5998 -0.0829 0
Weight 3.2137 0.3112 97.0581 100.2604 0.5578 -0.0958 0
Mfr_Guarantee 1.1983 0.8345 8.6960 8.9830 0.9135 -0.0357 0
BOVAG_Guarantee 1.3712 0.7293 16.2736 16.8105 0.8540 -0.0409 0
Guarantee_Period 1.5381 0.6502 23.5907 24.3691 0.8063 -0.0458 0
ABS 2.2232 0.4498 53.6282 55.3976 0.6707 -0.0663 0
Airbag_1 1.5989 0.6254 26.2590 27.1253 0.7908 -0.0477 0
Airbag_2 3.0894 0.3237 91.6074 94.6299 0.5689 -0.0921 0
Airco 1.8361 0.5446 36.6558 37.8652 0.7380 -0.0547 0
Automatic_airco 1.7419 0.5741 32.5257 33.5988 0.7577 -0.0519 0
Boardcomputer 2.6305 0.3802 71.4869 73.8455 0.6166 -0.0784 0
CD_Player 1.5503 0.6450 24.1291 24.9253 0.8031 -0.0462 0
Central_Lock 4.5886 0.2179 157.3372 162.5283 0.4668 -0.1368 0
Powered_Windows 4.6078 0.2170 158.1800 163.3990 0.4659 -0.1373 0
Power_Steering 1.5557 0.6428 24.3626 25.1664 0.8018 -0.0464 0
Radio 62.3090 0.0160 2688.0184 2776.7064 0.1267 -1.8572 1
Mistlamps 2.0750 0.4819 47.1335 48.6886 0.6942 -0.0618 0
Sport_Model 1.4606 0.6846 20.1946 20.8609 0.8274 -0.0435 0
Backseat_Divider 2.5379 0.3940 67.4257 69.6504 0.6277 -0.0756 0
Metallic_Rim 1.3400 0.7463 14.9077 15.3995 0.8639 -0.0399 0
Radio_cassette 62.1291 0.0161 2680.1284 2768.5561 0.1269 -1.8518 1
Tow_Bar 1.1445 0.8738 6.3348 6.5438 0.9347 -0.0341 0
1 --> COLLINEARITY is detected by the test
0 --> COLLINEARITY is not detected by the test
HP , Automatic , Doors , Guarantee_Period , ABS , Boardcomputer , Central_Lock , Powered_Windows , Power_Steering , Mistlamps , Backseat_Divider , coefficient(s) are non-significant may be due to multicollinearity
R-square of y on all x: 0.9058
* use method argument to check which regressors may be the reason of collinearity
===================================- Mediante el calculo de VIF y haciendo principal hincapíe en los atributos cuyo valor de VIF es muy superior a 5, es posible que exista colinealidad vinculado con los atributos Age_08_04,Mfg_Month, Mfg_Year, Radio y Radio_cassette
9: Limpieza de Datos
9a: Tratamiento de Outliers
- El atributo CC presenta un outlier(valor atípico) de CC = 16000. No es un valor coherente con el contexto de un vehiculo Toyota Corolla. Considero que probablemente fue un error y supongo que se agrego un cero de más, siendo el valor correcto 1600.
- El atributo Guarantee_Period presenta un outlier de Guarantee_Period = 13.Considero que probablemente fue un error y decido imputar el valor 12.
- El atributo KM presenta outliers para valores superiores a 150000 y valores menos a 10000. Si bien son valores coherentes dentro del contexto de vehiculos, al estar la mayor concentracion de los vehiculos dentro del intervalo (10000,120000), decido recortar el dataSet, reduciendo su tamaño un 12%.
- El atributo Age_08_04 presenta outliers para instancias cuyo Age_08_04 es menor a 25.
- El atributo HP presenta outliers para valores superiores a 120 y valores menores a 80. Si bien son valores coherentes para algunos modelos de Toyota Corrolla, son casos particulares no representativos del conjunto de vehiculos.
- Tras realizar estas operaciones, el dataset restante posee un 80% de las instancias del dataset original.
- El atributo Price posee outliers para valores menores a 6500 y valores superiores a 15000. Por este motivo considero el intervalo (6500,14500), dado que los valores excluidos no son representativos de la mayoria del conjunto.
clean_data <- raw_data
clean_data = clean_data %>% mutate(cc = ifelse(cc == 16000, 1600, cc))
clean_data = clean_data %>% mutate(Guarantee_Period = ifelse(Guarantee_Period == 13, 12, Guarantee_Period))
clean_data = clean_data %>% filter((KM > 20000 & KM < 130000))
clean_data = clean_data %>% filter(Weight < 1075 & Weight > 1010)
clean_data$Cylinders = NULL
- El dataset restante posee un 72% de las instancias del dataset original.
10: Selección de Variables
10a: Best SubSet Selection
bss.model <- regsubsets(Price~., data = clean_data, nvmax = dim(clean_data)[2])2 linear dependencies foundReordering variables and trying again:summary(bss.model)Subset selection object
Call: regsubsets.formula(Price ~ ., data = clean_data, nvmax = dim(clean_data)[2])
34 Variables (and intercept)
Forced in Forced out
Age_08_04 FALSE FALSE
Mfg_Month FALSE FALSE
KM FALSE FALSE
Fuel_TypePetrol FALSE FALSE
HP FALSE FALSE
Met_Color FALSE FALSE
Automatic FALSE FALSE
cc FALSE FALSE
Doors FALSE FALSE
Gears FALSE FALSE
Quarterly_Tax FALSE FALSE
Weight FALSE FALSE
Mfr_Guarantee FALSE FALSE
BOVAG_Guarantee FALSE FALSE
Guarantee_Period FALSE FALSE
ABS FALSE FALSE
Airbag_1 FALSE FALSE
Airbag_2 FALSE FALSE
Airco FALSE FALSE
Automatic_airco FALSE FALSE
Boardcomputer FALSE FALSE
CD_Player FALSE FALSE
Central_Lock FALSE FALSE
Powered_Windows FALSE FALSE
Power_Steering FALSE FALSE
Radio FALSE FALSE
Mistlamps FALSE FALSE
Sport_Model FALSE FALSE
Backseat_Divider FALSE FALSE
Metallic_Rim FALSE FALSE
Radio_cassette FALSE FALSE
Tow_Bar FALSE FALSE
Mfg_Year FALSE FALSE
Fuel_TypeDiesel FALSE FALSE
1 subsets of each size up to 32
Selection Algorithm: exhaustive
Age_08_04 Mfg_Month Mfg_Year KM Fuel_TypeDiesel Fuel_TypePetrol HP
1 ( 1 ) " " " " "*" " " " " " " " "
2 ( 1 ) " " " " "*" " " " " " " " "
3 ( 1 ) " " " " "*" "*" " " " " " "
4 ( 1 ) " " " " "*" "*" " " " " " "
5 ( 1 ) " " " " "*" "*" " " " " " "
6 ( 1 ) " " " " "*" "*" " " " " " "
7 ( 1 ) " " " " "*" "*" " " " " " "
8 ( 1 ) " " " " "*" "*" " " " " " "
9 ( 1 ) " " " " "*" "*" " " " " " "
10 ( 1 ) " " " " "*" "*" " " "*" " "
11 ( 1 ) " " " " "*" "*" " " "*" " "
12 ( 1 ) " " " " "*" "*" " " "*" " "
13 ( 1 ) " " " " "*" "*" " " "*" " "
14 ( 1 ) " " " " "*" "*" " " "*" "*"
15 ( 1 ) " " " " "*" "*" " " "*" "*"
16 ( 1 ) " " " " "*" "*" " " "*" "*"
17 ( 1 ) " " " " "*" "*" " " "*" "*"
18 ( 1 ) " " " " "*" "*" " " "*" "*"
19 ( 1 ) " " " " "*" "*" " " "*" "*"
20 ( 1 ) " " " " "*" "*" " " "*" "*"
21 ( 1 ) " " " " "*" "*" " " "*" "*"
22 ( 1 ) " " " " "*" "*" " " "*" "*"
23 ( 1 ) " " " " "*" "*" " " "*" "*"
24 ( 1 ) " " " " "*" "*" " " "*" "*"
25 ( 1 ) " " "*" "*" "*" " " "*" "*"
26 ( 1 ) " " "*" "*" "*" " " "*" "*"
27 ( 1 ) " " "*" "*" "*" " " "*" "*"
28 ( 1 ) " " "*" "*" "*" " " "*" "*"
29 ( 1 ) "*" " " "*" "*" " " "*" "*"
Met_Color Automatic cc Doors Gears Quarterly_Tax Weight Mfr_Guarantee
1 ( 1 ) " " " " " " " " " " " " " " " "
2 ( 1 ) " " " " " " " " " " " " "*" " "
3 ( 1 ) " " " " " " " " " " " " "*" " "
4 ( 1 ) " " " " " " " " " " " " "*" " "
5 ( 1 ) " " " " " " " " " " " " "*" " "
6 ( 1 ) " " " " " " " " " " " " "*" " "
7 ( 1 ) " " " " " " " " " " " " "*" "*"
8 ( 1 ) " " "*" " " " " " " " " "*" "*"
9 ( 1 ) " " "*" " " " " " " " " "*" "*"
10 ( 1 ) " " "*" " " " " " " " " "*" "*"
11 ( 1 ) " " "*" " " " " " " " " "*" "*"
12 ( 1 ) " " "*" " " " " " " " " "*" "*"
13 ( 1 ) " " "*" " " " " " " " " "*" "*"
14 ( 1 ) " " " " "*" " " "*" " " "*" "*"
15 ( 1 ) " " " " "*" " " "*" " " "*" "*"
16 ( 1 ) " " " " "*" " " "*" " " "*" "*"
17 ( 1 ) " " " " "*" " " "*" " " "*" "*"
18 ( 1 ) " " "*" "*" " " "*" " " "*" "*"
19 ( 1 ) " " "*" "*" " " "*" "*" "*" "*"
20 ( 1 ) " " "*" "*" " " "*" "*" "*" "*"
21 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*"
22 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*"
23 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*"
24 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*"
25 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*"
26 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*"
27 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*"
28 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*"
29 ( 1 ) "*" "*" "*" " " "*" "*" "*" "*"
BOVAG_Guarantee Guarantee_Period ABS Airbag_1 Airbag_2 Airco
1 ( 1 ) " " " " " " " " " " " "
2 ( 1 ) " " " " " " " " " " " "
3 ( 1 ) " " " " " " " " " " " "
4 ( 1 ) " " " " " " " " " " "*"
5 ( 1 ) " " " " " " " " " " "*"
6 ( 1 ) " " "*" " " " " " " "*"
7 ( 1 ) " " "*" " " " " " " "*"
8 ( 1 ) " " "*" " " " " " " "*"
9 ( 1 ) " " "*" " " " " " " "*"
10 ( 1 ) " " "*" " " " " " " "*"
11 ( 1 ) " " "*" " " " " " " "*"
12 ( 1 ) "*" "*" " " " " " " "*"
13 ( 1 ) "*" "*" " " " " "*" "*"
14 ( 1 ) "*" "*" " " " " " " "*"
15 ( 1 ) "*" "*" " " " " " " "*"
16 ( 1 ) "*" "*" " " " " " " "*"
17 ( 1 ) "*" "*" " " " " "*" "*"
18 ( 1 ) "*" "*" " " " " "*" "*"
19 ( 1 ) "*" "*" " " " " "*" "*"
20 ( 1 ) "*" "*" " " " " "*" "*"
21 ( 1 ) "*" "*" " " " " "*" "*"
22 ( 1 ) "*" "*" " " " " "*" "*"
23 ( 1 ) "*" "*" " " " " "*" "*"
24 ( 1 ) "*" "*" " " " " "*" "*"
25 ( 1 ) "*" "*" " " " " "*" "*"
26 ( 1 ) "*" "*" " " " " "*" "*"
27 ( 1 ) "*" "*" "*" " " "*" "*"
28 ( 1 ) "*" "*" "*" "*" "*" "*"
29 ( 1 ) "*" "*" "*" "*" "*" "*"
Automatic_airco Boardcomputer CD_Player Central_Lock Powered_Windows
1 ( 1 ) " " " " " " " " " "
2 ( 1 ) " " " " " " " " " "
3 ( 1 ) " " " " " " " " " "
4 ( 1 ) " " " " " " " " " "
5 ( 1 ) " " " " " " "*" " "
6 ( 1 ) " " " " " " " " " "
7 ( 1 ) " " " " " " " " " "
8 ( 1 ) " " " " " " " " " "
9 ( 1 ) " " " " " " "*" " "
10 ( 1 ) " " " " " " "*" " "
11 ( 1 ) " " " " " " "*" " "
12 ( 1 ) " " " " " " "*" " "
13 ( 1 ) " " " " " " " " "*"
14 ( 1 ) " " " " " " "*" " "
15 ( 1 ) "*" " " " " "*" " "
16 ( 1 ) "*" " " " " "*" " "
17 ( 1 ) "*" " " " " "*" " "
18 ( 1 ) "*" " " " " "*" " "
19 ( 1 ) "*" " " " " "*" " "
20 ( 1 ) "*" "*" " " "*" " "
21 ( 1 ) "*" " " "*" "*" " "
22 ( 1 ) "*" "*" "*" "*" " "
23 ( 1 ) "*" "*" "*" "*" " "
24 ( 1 ) "*" "*" "*" "*" " "
25 ( 1 ) "*" "*" "*" "*" " "
26 ( 1 ) "*" "*" "*" "*" "*"
27 ( 1 ) "*" "*" "*" "*" "*"
28 ( 1 ) "*" "*" "*" "*" "*"
29 ( 1 ) "*" "*" "*" "*" "*"
Power_Steering Radio Mistlamps Sport_Model Backseat_Divider Metallic_Rim
1 ( 1 ) " " " " " " " " " " " "
2 ( 1 ) " " " " " " " " " " " "
3 ( 1 ) " " " " " " " " " " " "
4 ( 1 ) " " " " " " " " " " " "
5 ( 1 ) " " " " " " " " " " " "
6 ( 1 ) " " " " "*" " " " " " "
7 ( 1 ) " " " " "*" " " " " " "
8 ( 1 ) " " " " "*" " " " " " "
9 ( 1 ) " " " " "*" " " " " " "
10 ( 1 ) " " " " "*" " " " " " "
11 ( 1 ) " " " " "*" " " " " " "
12 ( 1 ) " " " " "*" " " " " " "
13 ( 1 ) " " " " "*" " " " " " "
14 ( 1 ) " " " " " " "*" " " " "
15 ( 1 ) " " " " " " "*" " " " "
16 ( 1 ) " " " " " " "*" " " " "
17 ( 1 ) " " " " " " "*" " " " "
18 ( 1 ) " " " " " " "*" " " " "
19 ( 1 ) " " " " " " "*" " " " "
20 ( 1 ) " " " " " " "*" " " " "
21 ( 1 ) " " " " " " "*" " " " "
22 ( 1 ) " " " " " " "*" " " " "
23 ( 1 ) "*" " " " " "*" " " " "
24 ( 1 ) "*" " " "*" "*" " " " "
25 ( 1 ) "*" " " "*" "*" " " " "
26 ( 1 ) "*" " " "*" "*" " " " "
27 ( 1 ) "*" " " "*" "*" " " " "
28 ( 1 ) "*" " " "*" "*" " " " "
29 ( 1 ) "*" "*" "*" "*" " " " "
Radio_cassette Tow_Bar
1 ( 1 ) " " " "
2 ( 1 ) " " " "
3 ( 1 ) " " " "
4 ( 1 ) " " " "
5 ( 1 ) " " " "
6 ( 1 ) " " " "
7 ( 1 ) " " " "
8 ( 1 ) " " " "
9 ( 1 ) " " " "
10 ( 1 ) " " " "
11 ( 1 ) " " "*"
12 ( 1 ) " " "*"
13 ( 1 ) " " "*"
14 ( 1 ) " " "*"
15 ( 1 ) " " "*"
16 ( 1 ) "*" "*"
17 ( 1 ) "*" "*"
18 ( 1 ) "*" "*"
19 ( 1 ) "*" "*"
20 ( 1 ) "*" "*"
21 ( 1 ) "*" "*"
22 ( 1 ) "*" "*"
23 ( 1 ) "*" "*"
24 ( 1 ) "*" "*"
25 ( 1 ) "*" "*"
26 ( 1 ) "*" "*"
27 ( 1 ) "*" "*"
28 ( 1 ) "*" "*"
29 ( 1 ) "*" "*"
[ reached getOption("max.print") -- omitted 3 rows ]- Mediante Best Subset se definen todos los modelos posibles para los 34 predictores del modelo mediante combinaciones de los mismos y comparando su valor de RSS obtenido.
10a.1: Cantidad de Variables propuestas por el modelo
which.max(summary(bss.model)$adjr2)[1] 24- El modelo con un mejor valor de R ajustado utiliza 24 predictores.
10a.2: R Ajustado vs Cant. Predictores
p <- ggplot(data = data.frame(n_predictores = 1:32,
R_ajustado = summary(bss.model)$adjr2),
aes(x = n_predictores, y = R_ajustado)) +
geom_line() +
geom_point()
p <- p + geom_point(aes(
x = n_predictores[which.max(summary(bss.model)$adjr2)],
y = R_ajustado[which.max(summary(bss.model)$adjr2)]),
colour = "red", size = 3)
p <- p + scale_x_continuous(breaks = c(0:34)) +
theme_bw() +
labs(title = 'R2_ajustado vs número de predictores',
x = 'número predictores')
p
10a.3: Coeficientes: Predictores propuestos por el modelo
coef(object = bss.model, id = which.max(summary(bss.model)$adjr2)) (Intercept) KM Fuel_TypePetrol Met_Color
-2.529947e+06 -1.179339e-02 -2.636556e+03 -1.288967e+02
Automatic cc Doors Gears
5.137662e+02 2.755593e-01 7.045670e+01 4.497871e+02
Weight Mfr_Guarantee BOVAG_Guarantee Guarantee_Period
1.073410e+01 2.288838e+02 3.509444e+02 5.796841e+01
ABS Airbag_1 Automatic_airco Boardcomputer
-1.306206e+02 -1.155433e+02 9.962195e+02 1.253951e+00
CD_Player Central_Lock Powered_Windows Power_Steering
1.386529e+02 1.808711e+02 1.862831e+02 -2.503139e+02
Mistlamps Backseat_Divider Metallic_Rim Mfg_Year
3.676494e+02 -3.742877e+01 5.032722e+01 1.264728e+03
Fuel_TypeDiesel
0.000000e+00 - El modelo obtenido mediante el uso del metodo Best Subset propone usar los predictores expuestos en el recuadro superior.
10a.4: R Ajustado: Predictores propuestos por el modelo
summary(bss.model)$adjr2[24][1] 0.774939- El valor de R Ajustado obtenido para el uso de 24 predictores es de 0.77. Pero, el uso de demasiados predictores añade complejidad al modelo.
10a.5: R Ajustado: Cant. de Predictores Alternativas
summary(bss.model)$adjr2[9][1] 0.7579834summary(bss.model)$adjr2[6][1] 0.7469467- Reduciendo la cantidad predictores, disminuye el valor de R ajustado, pero disminuye la complejidad del modelo lo que permite una respuesta más general frente a nuevos datos de entrada.
10a.6: CP, AIC Y BIC
bss.model.sum = summary(bss.model)
par(mfrow = c(2, 2))
plot(bss.model.sum$rss, xlab = "Numero de Predictores", ylab = "RSS", type = "b")
plot(bss.model.sum$adjr2, xlab = "Numero de Predictores", ylab = "R Ajustada", type = "b")best_adj_r2 = which.max(bss.model.sum$adjr2)
points(best_adj_r2, bss.model.sum$adjr2[best_adj_r2],
col = "red",cex = 2, pch = 20)
plot(bss.model.sum$cp, xlab = "Numero de Predictores", ylab = "Cp", type = 'b')best_cp = which.min(bss.model.sum$cp)
points(best_cp, bss.model.sum$cp[best_cp],
col = "red", cex = 2, pch = 20)
plot(bss.model.sum$bic, xlab = "Numero de Predictores", ylab = "BIC", type = 'b')best_bic = which.min(bss.model.sum$bic)
points(best_bic, bss.model.sum$bic[best_bic],
col = "red", cex = 2, pch = 20)
En las gráficas anteriores BIC, CP, R ajustada se observan los puntos cuyo valores son mínimos y que no concordancia entre ellos para seleccionar ubivocamente la cantidad de predictores a emplear en un modelo. Sin embargo, puede observarse puntualmente en cada grafico, que existen sutiles mejoras (casi imperceptibles) entre algunas cantidades de predictores.
Se destaca que no tiene importancia destacar el punto minimo de RSS, dado que al por la naturaleza del modelo, a mayor cantidad de variable, menor será su valor.
10a.7: Coeficientes: Modelo Seleccionado
coef(object = bss.model, id = 7) (Intercept) KM Fuel_TypePetrol BOVAG_Guarantee
1.309274e+04 -2.326143e-02 -4.063483e+03 4.683116e+02
Guarantee_Period Airbag_1 Boardcomputer Backseat_Divider
1.697532e+02 2.091082e+02 1.959851e+03 3.807397e+02 - Mediante la comparación de las graficas, se opta por un modelo con 7 predictores.
10a.8: Validacion Cruzada
set.seed(10)
index <- createDataPartition(clean_data$Price, p = 0.7, list = FALSE)
data.train <- clean_data[index, ]
data.test <- clean_data[-index, ]set.seed(10)
model.fwd <- regsubsets(Price ~., data = data.train, nvmax = 7)3 linear dependencies foundReordering variables and trying again:summary(model.fwd)Subset selection object
Call: regsubsets.formula(Price ~ ., data = data.train, nvmax = 7)
34 Variables (and intercept)
Forced in Forced out
Age_08_04 FALSE FALSE
Mfg_Month FALSE FALSE
KM FALSE FALSE
Fuel_TypePetrol FALSE FALSE
HP FALSE FALSE
Met_Color FALSE FALSE
Automatic FALSE FALSE
cc FALSE FALSE
Doors FALSE FALSE
Gears FALSE FALSE
Quarterly_Tax FALSE FALSE
Weight FALSE FALSE
Mfr_Guarantee FALSE FALSE
BOVAG_Guarantee FALSE FALSE
Guarantee_Period FALSE FALSE
ABS FALSE FALSE
Airbag_1 FALSE FALSE
Airbag_2 FALSE FALSE
Airco FALSE FALSE
Automatic_airco FALSE FALSE
Boardcomputer FALSE FALSE
CD_Player FALSE FALSE
Central_Lock FALSE FALSE
Powered_Windows FALSE FALSE
Power_Steering FALSE FALSE
Radio FALSE FALSE
Mistlamps FALSE FALSE
Sport_Model FALSE FALSE
Backseat_Divider FALSE FALSE
Metallic_Rim FALSE FALSE
Tow_Bar FALSE FALSE
Mfg_Year FALSE FALSE
Fuel_TypeDiesel FALSE FALSE
Radio_cassette FALSE FALSE
1 subsets of each size up to 8
Selection Algorithm: exhaustive
Age_08_04 Mfg_Month Mfg_Year KM Fuel_TypeDiesel Fuel_TypePetrol HP
1 ( 1 ) " " " " "*" " " " " " " " "
2 ( 1 ) " " " " "*" " " " " " " " "
3 ( 1 ) " " " " "*" "*" " " " " " "
4 ( 1 ) " " " " "*" "*" " " " " " "
5 ( 1 ) " " " " "*" "*" " " " " " "
6 ( 1 ) " " " " "*" "*" " " " " " "
7 ( 1 ) " " " " "*" "*" " " " " " "
8 ( 1 ) " " " " "*" "*" " " " " " "
Met_Color Automatic cc Doors Gears Quarterly_Tax Weight Mfr_Guarantee
1 ( 1 ) " " " " " " " " " " " " " " " "
2 ( 1 ) " " " " " " " " " " " " "*" " "
3 ( 1 ) " " " " " " " " " " " " "*" " "
4 ( 1 ) " " " " " " " " " " " " "*" " "
5 ( 1 ) " " " " " " " " " " " " "*" " "
6 ( 1 ) " " " " " " " " " " " " "*" "*"
7 ( 1 ) " " " " " " " " " " " " "*" "*"
8 ( 1 ) " " " " " " " " " " " " "*" "*"
BOVAG_Guarantee Guarantee_Period ABS Airbag_1 Airbag_2 Airco
1 ( 1 ) " " " " " " " " " " " "
2 ( 1 ) " " " " " " " " " " " "
3 ( 1 ) " " " " " " " " " " " "
4 ( 1 ) " " " " " " " " " " " "
5 ( 1 ) " " " " " " " " " " "*"
6 ( 1 ) " " " " " " " " " " "*"
7 ( 1 ) " " "*" " " " " " " "*"
8 ( 1 ) " " "*" " " " " " " "*"
Automatic_airco Boardcomputer CD_Player Central_Lock Powered_Windows
1 ( 1 ) " " " " " " " " " "
2 ( 1 ) " " " " " " " " " "
3 ( 1 ) " " " " " " " " " "
4 ( 1 ) " " " " " " " " "*"
5 ( 1 ) " " " " " " " " "*"
6 ( 1 ) " " " " " " " " "*"
7 ( 1 ) " " " " " " " " "*"
8 ( 1 ) " " " " " " " " "*"
Power_Steering Radio Mistlamps Sport_Model Backseat_Divider Metallic_Rim
1 ( 1 ) " " " " " " " " " " " "
2 ( 1 ) " " " " " " " " " " " "
3 ( 1 ) " " " " " " " " " " " "
4 ( 1 ) " " " " " " " " " " " "
5 ( 1 ) " " " " " " " " " " " "
6 ( 1 ) " " " " " " " " " " " "
7 ( 1 ) " " " " " " " " " " " "
8 ( 1 ) " " " " " " " " " " " "
Radio_cassette Tow_Bar
1 ( 1 ) " " " "
2 ( 1 ) " " " "
3 ( 1 ) " " " "
4 ( 1 ) " " " "
5 ( 1 ) " " " "
6 ( 1 ) " " " "
7 ( 1 ) " " " "
8 ( 1 ) " " "*" 10a.9: RMSE
val.errors = rep(NA,7)
x.test <- model.matrix(Price ~., data = data.test)
for(i in 1:7)
{
coeficientes <- coef(model.fwd, id = i)
predictions <- x.test[,names(coeficientes)] %*% coeficientes
val.errors[i] <- mean((data.test$Price - predictions)^2)
}
rmse <- sqrt(mean(val.errors))
rmse[1] 1407.842- Tras una validación cruzada se obtiene un valor de RMSE de 1408.
10b: Ridge
- Mediante Ridge se obtiene un modelo a partir de los 34 predictores iniciales, ponderando la influencia de cada predictor pero sin eliminar ninguno de los mismos del modelo.
set.seed(10)
index <- createDataPartition(clean_data$Price, p = 0.7, list = FALSE)
data.train <- clean_data[index, ]
data.test <- clean_data[-index, ]- Se produce en conjunto de entrenamiento y de prueba.
10b.1: Modelo
x = model.matrix(Price ~ . , data.train)[, -1]
y = as.matrix(data.train$Price)
ridge.model = glmnet(x, y, alpha = 0)
beta=coef(ridge.model)
tmp <- as.data.frame(as.matrix(beta))
tmp$coef <- row.names(tmp)
tmp <- reshape::melt(tmp, id = "coef")
tmp$variable <- as.numeric(gsub("s", "", tmp$variable))
tmp$lambda <- ridge.model$lambda[tmp$variable+1]
tmp$norm <- apply(abs(beta[-1,]), 2, sum)[tmp$variable+1]
ggplot(tmp[tmp$coef != "(Intercept)",], aes(lambda, value, color = coef, group = coef, )) +
geom_line() +
scale_x_log10() +
xlab("Lambda (log scale)") +
guides(color = guide_legend(title = ""),
linetype = guide_legend(title = "")) +
theme_bw() +
theme(legend.key.width = unit(3,"lines")) 
plot(ridge.model, xvar = "lambda", label = TRUE)
- Mediante los dos graficos anteriores se puede observar que los predictores mas significativos son aquellos que, durante el procesamiento del modelo, demoran mas en acercarse a valores cercanos a cero.
indices <- sample(c(TRUE,FALSE), nrow(data.train), replace = TRUE)
cv.out <- cv.glmnet(x[indices,], y[indices], alpha = 0)
plot(cv.out)
coef(cv.out)35 x 1 sparse Matrix of class "dgCMatrix"
1
(Intercept) -9.276178e+05
Age_08_04 -3.403398e+01
Mfg_Month -1.675292e+01
Mfg_Year 4.666735e+02
KM -8.205862e-03
Fuel_TypeDiesel .
Fuel_TypePetrol .
HP 4.510978e+00
Met_Color -4.077869e+01
Automatic 5.819668e+02
cc 3.425118e-01
Doors 3.215659e+01
Gears 1.800406e+02
Quarterly_Tax 8.492749e+00
Weight 4.057818e+00
Mfr_Guarantee 2.013134e+02
BOVAG_Guarantee 3.643001e+02
Guarantee_Period 4.918492e+01
ABS 1.136664e+02
Airbag_1 -1.506483e+02
Airbag_2 -4.032492e-01
Airco 2.930682e+02
Automatic_airco 7.676041e+02
Boardcomputer 2.717277e+02
CD_Player 1.082930e+02
Central_Lock 2.059698e+02
Powered_Windows 6.839280e+01
Power_Steering -7.009734e+02
Radio -3.066674e+01
Mistlamps 5.970154e+01
Sport_Model -2.479769e+02
Backseat_Divider 3.448104e+00
Metallic_Rim 5.100967e+01
Radio_cassette -3.071270e+01
Tow_Bar -2.591923e+02- La grafica anterior representa como el error incrementa a mayores valores de log(lambda).
- Las lineas punteadas indican, el valor minimo de mse obtenido en la validacion cruzada y el valor de la derecha representa el error estandar.
bestlam = cv.out$lambda.min
bestlam[1] 137.6734- Se emplea el menor lambda obtenido de la validacion cruzada propia del modelo.
ridge.pred <- predict(ridge.model, s = bestlam, newx = x[-indices,])
sqrt(mean((ridge.pred - y[-indices])^2))[1] 807.2642- Se obtiene un valor de rmse de 807 obtenido mediante los datos de entrenamiento.
10b.2: Validacion Cruzada
x = model.matrix(Price ~ . , data.test)[, -1]
y = as.matrix(data.test$Price)
ridge.model = glmnet(x, y, alpha = 0)
indices <- sample(c(TRUE,FALSE), nrow(data.test), replace = TRUE)
cv.out <- cv.glmnet(x[indices,], y[indices], alpha = 0)
plot(cv.out)
coef(cv.out)35 x 1 sparse Matrix of class "dgCMatrix"
1
(Intercept) -5.107223e+05
Age_08_04 -1.990590e+01
Mfg_Month -1.156697e+01
Mfg_Year 2.572843e+02
KM -9.166624e-03
Fuel_TypeDiesel .
Fuel_TypePetrol .
HP 1.018606e-01
Met_Color -3.050419e+01
Automatic -3.058052e+02
cc -7.618709e-02
Doors 8.384777e+01
Gears 4.417662e+02
Quarterly_Tax 4.467208e+00
Weight 4.256372e+00
Mfr_Guarantee 2.180984e+02
BOVAG_Guarantee 5.903780e+01
Guarantee_Period 2.742444e+01
ABS 1.886358e+02
Airbag_1 -2.687474e+01
Airbag_2 6.792561e+01
Airco 1.990458e+02
Automatic_airco .
Boardcomputer 4.884786e+02
CD_Player 3.181346e+02
Central_Lock 8.770576e+01
Powered_Windows 2.707806e+01
Power_Steering 9.958717e-01
Radio -7.240374e+01
Mistlamps 2.673791e+02
Sport_Model -3.403362e+02
Backseat_Divider 6.955809e+01
Metallic_Rim 3.906290e+00
Radio_cassette -7.238457e+01
Tow_Bar -8.097683e+01- El valor minimo de MSE y el error estandar, son similares a los obtenidos mediante datos de entrenamiento.
bestlam = cv.out$lambda.min
bestlam[1] 489.783- Se emplea el menor lambda obtenido de la validacion cruzada propia del modelo.
ridge.pred <- predict(ridge.model, s = bestlam, newx = x[-indices,])
sqrt(mean((ridge.pred - y[-indices])^2))[1] 775.3981- Se obtiene un valor de rmse de 775 datos de prueba.
10c: Lasso
- Mediante Lasso se obtiene un modelo a partir de los 34 predictores iniciales, ponderando la influencia de cada predictor. A diferencia de Ridge, usando Lasso si se realiza una seleccion de variables.
set.seed(10)
index <- createDataPartition(clean_data$Price, p = 0.7, list = FALSE)
data.train <- clean_data[index, ]
data.test <- clean_data[-index, ]- Se produce en conjunto de entrenamiento y de prueba.
10c.1: Modelo
x = model.matrix(Price ~ . , data.train)[, -1]
y = as.matrix(data.train$Price)
lasso.model = glmnet(x, y, alpha = 1)
beta=coef(lasso.model)
tmp <- as.data.frame(as.matrix(beta))
tmp$coef <- row.names(tmp)
tmp <- reshape::melt(tmp, id = "coef")
tmp$variable <- as.numeric(gsub("s", "", tmp$variable))
tmp$lambda <- lasso.model$lambda[tmp$variable+1]
tmp$norm <- apply(abs(beta[-1,]), 2, sum)[tmp$variable+1]
ggplot(tmp[tmp$coef != "(Intercept)",], aes(lambda, value, color = coef, group = coef, )) +
geom_line() +
scale_x_log10() +
xlab("Lambda (log scale)") +
guides(color = guide_legend(title = ""),
linetype = guide_legend(title = "")) +
theme_bw() +
theme(legend.key.width = unit(3,"lines")) 
plot(lasso.model, xvar = "lambda", label = TRUE)
- Mediante los dos graficos anteriores se puede observar que los predictores mas significativos son aquellos que, durante el procesamiento del modelo, demoran mas en acercarse a valores cercanos a cero.
indices <- sample(c(TRUE,FALSE), nrow(data.train), replace = TRUE)
cv.out <- cv.glmnet(x[indices,], y[indices], alpha = 1)
plot(cv.out)
coef(cv.out)35 x 1 sparse Matrix of class "dgCMatrix"
1
(Intercept) -2.152194e+06
Age_08_04 -9.617712e+00
Mfg_Month .
Mfg_Year 1.077728e+03
KM -6.654090e-03
Fuel_TypeDiesel .
Fuel_TypePetrol .
HP .
Met_Color .
Automatic 3.858173e+02
cc 2.490596e-01
Doors .
Gears .
Quarterly_Tax 3.041571e+00
Weight 7.261598e+00
Mfr_Guarantee 1.032277e+02
BOVAG_Guarantee 1.922574e+02
Guarantee_Period 9.119164e+00
ABS .
Airbag_1 .
Airbag_2 .
Airco 2.308151e+02
Automatic_airco .
Boardcomputer .
CD_Player .
Central_Lock 2.433077e+02
Powered_Windows .
Power_Steering -4.338181e+02
Radio .
Mistlamps .
Sport_Model -6.242317e+01
Backseat_Divider .
Metallic_Rim .
Radio_cassette .
Tow_Bar -1.144862e+02- El valor minimo de MSE y el error estandar, son similares a los obtenidos mediante datos de entrenamiento.
bestlam = cv.out$lambda.min
bestlam[1] 27.66179- Se emplea el menor lambda obtenido de la validacion cruzada propia del modelo.
lasso.pred <- predict(lasso.model, s = bestlam, newx = x[-indices,])
sqrt(mean((lasso.pred - y[-indices])^2))[1] 812.298- Se obtiene un valor de rmse de 813 datos de entrenamiento.
10c.2: Validacion Cruzada
x = model.matrix(Price ~ . , data.test)[, -1]
y = as.matrix(data.test$Price)
lasso.model = glmnet(x, y, alpha = 1)
indices <- sample(c(TRUE,FALSE), nrow(data.test), replace = TRUE)
cv.out <- cv.glmnet(x[indices,], y[indices], alpha = 1)
plot(cv.out)
coef(cv.out)35 x 1 sparse Matrix of class "dgCMatrix"
1
(Intercept) -2.083003e+06
Age_08_04 .
Mfg_Month .
Mfg_Year 1.045326e+03
KM -6.128349e-03
Fuel_TypeDiesel .
Fuel_TypePetrol .
HP .
Met_Color .
Automatic .
cc .
Doors 6.359957e+01
Gears 2.868344e+01
Quarterly_Tax .
Weight 2.598188e+00
Mfr_Guarantee .
BOVAG_Guarantee .
Guarantee_Period .
ABS .
Airbag_1 .
Airbag_2 .
Airco 2.077925e+02
Automatic_airco .
Boardcomputer 6.818690e+01
CD_Player .
Central_Lock .
Powered_Windows .
Power_Steering .
Radio .
Mistlamps 2.173762e+02
Sport_Model -5.946130e+01
Backseat_Divider .
Metallic_Rim .
Radio_cassette .
Tow_Bar .
bestlam = cv.out$lambda.min
bestlam[1] 81.70072
lasso.pred <- predict(lasso.model, s = bestlam, newx = x[-indices,])
sqrt(mean((lasso.pred - y[-indices])^2))[1] 813.2023- Se obtiene un valor de rmse de 813 datos de prueba.
11: Conclusión
Dado que es un dataset con una cantidad baja de instancias (1500 aprox), y que mediante el uso de Lasso se obtuvo un resultado aceptable comparado a los rmse calculados con otros métodos (Best Subset y Ridge), se opta por usar ese metodo para seleccion de variables.
---
title: "Seleccion de Variables: Dataset 'Toyota Corolla'"
author: "Alvarez Ignacio Nicolas"
output:
  html_notebook:
    df_print: paged
    fig:height: 4
    fig:width: 6
    theme: readable
    toc: yes
    toc_float: yes
  pdf_document:
    toc: yes
fig:height: 4
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

Este ejercicio consiste en realizar un análisis exploratorio sobre un dataset de vehiculos Toyota Corolla con 1436 instancias y 37 atributos. 

El objetivo es conseguir un modelo de regresión lineal con un resultado aceptable interpretando cada paso del razonamiento necesario para llegar al objetivo.

* El atributo objetivo es Price.   

# 1: Carga de Librerias
```{r Carga de Librerias, eval=FALSE}
library(fastDummies) 
library(car)
library(corrplot) 
library(mctest) 
library(tidyverse) 
library(leaps)
library(glmnet)
library(MASS)
library(reshape)
library(caret)
library(ggrepel)
```

# 2: Lectura del DataSet

```{r Lectura del DataSet}
raw_data = read.csv("ToyotaCorolla.csv") 
raw_data$Id = NULL
raw_data$Model = NULL

```

* El atributo **ID** no es representativo de cada instancia, decido no considerarlo en el modelo.     
* El atributo **Model** no es representativo de cada instancia, decido no considerarlo en el modelo. 


# 3: DataSet

```{r Visualizacion del DataSet}
raw_data
```

# 4: Estructura del DataSet

```{r Estructura del DataSet}
str(raw_data)
```

# 5: Resumen del DataSet

```{r Resumen del DataSet}
summary(raw_data)
```

**Observaciones**   
* El valor maximo de cc es de 16000, demasiado alto considerando la media.    
* El atributo Fuel_Type es de tipo char, requerira un proceso de encoding.    
* El valor de Cylinder es constante. 

# 6: Análisis exploratorio    

## 6a: Price 

```{r Price}
par(mfrow=c(1,2))
boxplot(raw_data$Price,main = "Precio Vehiculos Toyota Corolla",
        ylab = "Precio ($)", notch = TRUE)

hist(raw_data$Price,main = "Precio Vehiculos Toyota Corolla")
```
* Se observa que la mediana del precio de los vehiculos, ronda los $10000 aproximadamente. 
* Se presentan valores atípicos con valores superiores a las $20000 y valores menores a $7000 aproximadamente.  

## 6b: Mfg_Year
     
```{r Age_08_04}
par(mfrow=c(1,2))

boxplot(raw_data$Age_08_04,main = "Age_08_04")
barplot(table(as.factor(raw_data$Age_08_04)),main = "Age_08_04")

```
* El atributo "Age_08_04" presenta valores outliers correspondientes a vehiculos nuevos cuya antiguedad es 0.  

## 6c: Mfg_Year

```{r Mfg_Year}
par(mfrow=c(1,2))

boxplot(raw_data$Mfg_Year,main = "Año de Mfg_Year")
barplot(table(as.factor(raw_data$Mfg_Year)),main = "Mfg_Year")
```

## 6d: KM

```{r Boxplot KM}
par(mfrow=c(1,2))

boxplot(raw_data$KM,main = "KM",
        ylab = "KM", notch = TRUE)

hist(raw_data$KM,main = "KM")

```
* El atributo "KM" presenta valores outliers. Destaco sobretodo un conjunto de valores superiores a los 200000. 


## 6e: HP
```{r HP}
par(mfrow=c(1,2))

boxplot(raw_data$HP,main = "HP",
        ylab = "HP", notch = FALSE)

barplot(table(as.factor(raw_data$HP)),main = "HP")
```

* El atributo "HP" presenta un valor outlier superior a 180. Según una investigacion realizada en medios externos al dataset, el valor si corresponde a un modelo de Toyota Corolla.    


## 6f: CC
  
```{r Boxplot CC}
par(mfrow=c(1,2))

boxplot(raw_data$cc,main = "Cilindrada",
        ylab = "CC", notch = FALSE)

barplot(table(as.factor(raw_data$cc)),main = "Cilindrada")
```

* El atributo "CC" presenta un outlier notorio superior a 16000, este valor esta fuera del contexto de un vehiculo toyota corolla, donde los valores promedio rondan el 100.    

## 6g: Quarterly_Tax

```{r Boxplot Quarterly_Tax}
par(mfrow=c(1,2))

boxplot(raw_data$Quarterly_Tax, main="Quarterly_Tax")

hist(raw_data$Quarterly_Tax)
```

* El atributo "Quarterly_Tax" presenta outliers para valores superiores a 150 y valores menores a 50, sobre una mediana de 70 aproximadamente. 

## 6h: Weight

```{r Weight}
par(mfrow=c(1,2))

boxplot(raw_data$Weight, main="Peso(KG)")
hist(raw_data$Weight)
```

* El atributo "Weight" presenta outliers para valores superiores a 1150 sobre una mediana de 1050 aproximadamente.

## 6i: Fueltype y Radio Cassete

```{r Plot Fueltype y Radio Cassete}
lbls <- c("0: No tiene", "1: Tiene")

par(mfrow=c(1,2)) 

barplot(table(as.factor(raw_data$Fuel_Type)), main="Fuel_Type")
pie(x = table(raw_data$Radio_cassette), labels = lbls, main="Radio Cassete")
```

## 6j: Metallic Rim y Backseat Divider

```{r Plot Metallic Rim y Backseat Divider}

par(mfrow=c(1,2)) 

pie(x = table(raw_data$Metallic_Rim), labels = lbls,  main="Metallic Rim")
pie(x = table(raw_data$Backseat_Divider) , labels = lbls,  main="Backseat_Divider")
```

## 6k: Mistlamp, Radio y Sport Model

```{r Plot Mistlamp, Radio y Sport Model}
par(mfrow=c(1,3))

pie(x = table(raw_data$Mistlamps) , labels = lbls,  main="Mistlamps")
pie(x = table(raw_data$Radio), labels = lbls,  main="Radio")
pie(x = table(raw_data$Sport_Model), labels = lbls,  main="Sport_Model")
```

## 6l: Central Lock, CD Player y BoardComputer

```{r Plot Central Lock, CD Player y BoardComputer}

par(mfrow=c(1,3))

pie(x = table(raw_data$Central_Lock), labels = lbls, main="Central_Lock")
pie(x = table(raw_data$CD_Player), labels = lbls, main="CD_Player")
pie(x = table(raw_data$Boardcomputer), labels = lbls, main="Boardcomputer")

```

## 6m: Airco, Airbag_2 y Airbag_1

```{r Plot Airco, Airbag_2 y Airbag_1}
par(mfrow=c(1,3))

pie(x = table(raw_data$Airco), labels = lbls,  main="Airco")
pie(x = table(raw_data$Airbag_2), labels = lbls,  main="Airbag_2")
pie(x = table(raw_data$Airbag_1), labels = lbls,main="Airbag_1")

```

## 6n: Guarantee Period y Automatic Airco

```{r Plot Guarantee Period y Automatic Airco}

par(mfrow=c(1,2))

barplot(table(as.factor(raw_data$Guarantee_Period)), main="Guarantee_Period") 
pie(x = table(raw_data$Automatic_airco), labels = lbls,  main="Automatic_airco")

```

## 6o: MFR Guarantee, Gears y BOVAG Guarantee

```{r Plot MFR Guarantee, Gears y BOVAG Guarantee}

par(mfrow=c(1,3))

pie(x = table(raw_data$Mfr_Guarantee), labels = lbls, main="Mfr_Guarantee")
barplot(table(as.factor(raw_data$Gears)), main="Gears")
pie(x = table(raw_data$BOVAG_Guarantee), labels = lbls, main="BOVAG_Guarantee")
```

## 6p: Doors, Automatic y ABS

```{r Plot Doors, Automatic y ABS}
par(mfrow=c(1,3))

barplot(table(as.factor(raw_data$Doors)), main="Doors")
pie(x = table(raw_data$Automatic),labels = lbls, main="Automatic")
pie(x = table(raw_data$ABS),labels = lbls, main="ABS")
```

# 7: Estudio de Variable Objetivo "Price"

## 7a: Distribucion de Price
```{r Histograma de Price}
hist(raw_data$Price, col="blue", breaks = 60, freq = F)
lines(density(raw_data$Price), col = "red", lwd=2)
rug(raw_data$Price)
```

## 7b: Relacion Price vs Resto de Predictores
```{r Graficos de Dispersion: Price vs Todos}
plot(Price~., data=raw_data,col="blue")
```

# 8: Seleccion y modificacion de Variables    

## 8a: Estudio de correlacion
```{r Estudio de correlacion}
corrplot(cor(dplyr::select(raw_data, -c("Fuel_Type"))), type="upper", method="pie")
```


## 8b: Indicadores de Colinealidad

```{r Calculo de VIF y TOL sobre DataSet}
imcdiag(dplyr::select(raw_data, -c("Price", "Fuel_Type")), raw_data$Price)
```
* Mediante el calculo de VIF y haciendo principal hincapíe en los atributos cuyo valor de VIF es muy superior a 5, es posible que exista colinealidad vinculado con los atributos **Age_08_04,Mfg_Month, Mfg_Year, Radio y  Radio_cassette**

# 9: Limpieza de Datos   

## 9a: Tratamiento de Outliers 

* El atributo CC presenta un outlier(valor atípico) de CC = 16000. No es un valor coherente con el contexto de un vehiculo Toyota Corolla. Considero que probablemente fue un error y supongo que se agrego un cero de más, siendo el valor correcto 1600.   
* El atributo Guarantee_Period presenta un outlier de Guarantee_Period = 13.Considero que probablemente fue un error y decido imputar el valor 12.   
* El atributo KM presenta outliers para valores superiores a 150000 y valores menos a 10000. Si bien son valores coherentes dentro del contexto de vehiculos, al estar la mayor concentracion de los vehiculos dentro del **intervalo (10000,120000)**, decido recortar el dataSet, reduciendo su tamaño un 12%.     
* El atributo Age_08_04 presenta outliers para instancias cuyo Age_08_04 es menor a 25.   
* El atributo HP presenta outliers para valores superiores a 120 y valores menores a 80. Si bien son valores coherentes para algunos modelos de Toyota Corrolla, son casos particulares no representativos del conjunto de vehiculos.    
* Tras realizar estas operaciones, el dataset restante posee un 80% de las instancias del dataset original.     
* El atributo Price posee outliers para valores menores a 6500 y valores superiores a 15000. Por este motivo considero el **intervalo (6500,14500)**, dado que los valores excluidos no son representativos de la mayoria del conjunto.    


```{r Limpieza de Datos}

clean_data <- raw_data

clean_data = clean_data %>%  mutate(cc = ifelse(cc == 16000, 1600, cc))
clean_data = clean_data %>%  mutate(Guarantee_Period = ifelse(Guarantee_Period == 13, 12, Guarantee_Period))

clean_data = clean_data %>% filter((KM > 20000 & KM < 130000))
clean_data = clean_data %>% filter(Weight < 1075 & Weight > 1010)

clean_data$Cylinders = NULL

```

* El dataset restante posee un 72% de las instancias del dataset original.   


# 10: Selección de Variables  

## 10a: Best SubSet Selection


```{r Modelo Best SubSet Selection}
bss.model <- regsubsets(Price~., data = clean_data, nvmax = dim(clean_data)[2])
summary(bss.model)
```

* Mediante Best Subset se definen todos los modelos posibles para los 34 predictores del modelo mediante combinaciones de los mismos y comparando su valor de RSS obtenido.

### 10a.1: Cantidad de Variables propuestas por el modelo

```{r Modelo Best SubSet Selection 2 }
which.max(summary(bss.model)$adjr2)
```

* El modelo con un mejor valor de R ajustado utiliza 24 predictores. 

### 10a.2: R Ajustado vs Cant. Predictores

```{r BSS: R^2 ajustado vs Numero de Predictores}
p <- ggplot(data = data.frame(n_predictores = 1:32,
                              R_ajustado = summary(bss.model)$adjr2),
            aes(x = n_predictores, y = R_ajustado)) +
    geom_line() +
    geom_point()

p <- p + geom_point(aes(
                    x = n_predictores[which.max(summary(bss.model)$adjr2)],
                    y = R_ajustado[which.max(summary(bss.model)$adjr2)]),
                    colour = "red", size = 3)
p <- p +  scale_x_continuous(breaks = c(0:34)) + 
          theme_bw() +
          labs(title = 'R2_ajustado vs número de predictores', 
               x =  'número predictores')
p
```

### 10a.3: Coeficientes: Predictores propuestos por el modelo

```{r Coeficientes Max}
coef(object = bss.model, id = which.max(summary(bss.model)$adjr2))
```

* El modelo obtenido mediante el uso del metodo Best Subset propone usar los predictores expuestos en el recuadro superior.     

### 10a.4: R Ajustado: Predictores propuestos por el modelo

```{r Valor R^2 Ajustado: Metodo}
summary(bss.model)$adjr2[24]
```

* El valor de R Ajustado obtenido para el uso de 24 predictores es de 0.77. Pero, el uso de demasiados predictores añade complejidad al modelo.     

### 10a.5: R Ajustado: Cant. de Predictores Alternativas

```{r Valor R^2 Ajustado: Alternativas}
summary(bss.model)$adjr2[9]
```

```{r Valor R^2 Ajustado: Alternativas 2}
summary(bss.model)$adjr2[6]
```

* Reduciendo la cantidad predictores, disminuye el valor de R ajustado, pero disminuye la complejidad del modelo lo que permite una respuesta más general frente a nuevos datos de entrada.

### 10a.6: CP, AIC Y BIC

```{r BSS: AIC y BIC}
bss.model.sum = summary(bss.model)

par(mfrow = c(2, 2))
plot(bss.model.sum$rss, xlab = "Numero de Predictores", ylab = "RSS", type = "b")

plot(bss.model.sum$adjr2, xlab = "Numero de Predictores", ylab = "R Ajustada", type = "b")
best_adj_r2 = which.max(bss.model.sum$adjr2)
points(best_adj_r2, bss.model.sum$adjr2[best_adj_r2],
       col = "red",cex = 2, pch = 20)

plot(bss.model.sum$cp, xlab = "Numero de Predictores", ylab = "Cp", type = 'b')
best_cp = which.min(bss.model.sum$cp)
points(best_cp, bss.model.sum$cp[best_cp], 
       col = "red", cex = 2, pch = 20)

plot(bss.model.sum$bic, xlab = "Numero de Predictores", ylab = "BIC", type = 'b')
best_bic = which.min(bss.model.sum$bic)
points(best_bic, bss.model.sum$bic[best_bic], 
       col = "red", cex = 2, pch = 20)
```

* En las gráficas anteriores *BIC, CP, R ajustada* se observan los puntos cuyo valores son mínimos y que no concordancia entre ellos para seleccionar ubivocamente la cantidad de predictores a emplear en un modelo. Sin embargo, puede observarse puntualmente en cada grafico, que existen sutiles mejoras (casi imperceptibles) entre algunas cantidades de predictores.     

* Se destaca que no tiene importancia destacar el punto minimo de RSS, dado que al por la naturaleza del modelo, a mayor cantidad de variable, menor será su valor.   

### 10a.7: Coeficientes: Modelo Seleccionado

```{r Modelo 7 predictores}
coef(object = bss.model, id = 7)
```

* Mediante la comparación de las graficas, se opta por un modelo con 7 predictores.    

### 10a.8: Validacion Cruzada

```{r CV Modelo BSS}
set.seed(10)

index <- createDataPartition(clean_data$Price, p = 0.7, list = FALSE)

data.train <- clean_data[index, ]
data.test <- clean_data[-index, ]
```


```{r CV Modelo BSS 2}
set.seed(10)
model.fwd <- regsubsets(Price ~., data = data.train, nvmax = 7)
summary(model.fwd)
```

### 10a.9: RMSE

```{r Calculo de RMSE BSS}
val.errors = rep(NA,7)
x.test <- model.matrix(Price ~., data = data.test)

for(i in 1:7) 
{
  coeficientes <- coef(model.fwd, id = i)
  predictions <- x.test[,names(coeficientes)] %*% coeficientes
  val.errors[i] <- mean((data.test$Price - predictions)^2)
}

rmse <- sqrt(mean(val.errors))
rmse
```

* Tras una validación cruzada se obtiene un valor de RMSE de 1408.    


## 10b: Ridge

* Mediante Ridge se obtiene un modelo a partir de los 34 predictores iniciales, ponderando la influencia de cada predictor pero sin eliminar ninguno de los mismos del modelo.

```{r}
set.seed(10)

index <- createDataPartition(clean_data$Price, p = 0.7, list = FALSE)

data.train <- clean_data[index, ]
data.test <- clean_data[-index, ]
```

* Se produce en conjunto de entrenamiento y de prueba.    

## 10b.1: Modelo

```{r}

x = model.matrix(Price ~ . , data.train)[, -1]
y = as.matrix(data.train$Price)

ridge.model = glmnet(x, y, alpha = 0)

```


```{r}
beta=coef(ridge.model)

tmp <- as.data.frame(as.matrix(beta))
tmp$coef <- row.names(tmp)
tmp <- reshape::melt(tmp, id = "coef")
tmp$variable <- as.numeric(gsub("s", "", tmp$variable))
tmp$lambda <- ridge.model$lambda[tmp$variable+1]
tmp$norm <- apply(abs(beta[-1,]), 2, sum)[tmp$variable+1]

ggplot(tmp[tmp$coef != "(Intercept)",], aes(lambda, value, color = coef, group = coef, )) + 
  geom_line() + 
    scale_x_log10() + 
    xlab("Lambda (log scale)") + 
    guides(color = guide_legend(title = ""), 
           linetype = guide_legend(title = "")) +
    theme_bw() + 
    theme(legend.key.width = unit(3,"lines")) 
```


```{r}
plot(ridge.model, xvar = "lambda", label = TRUE)
```

* Mediante los dos graficos anteriores se puede observar que los predictores mas significativos son aquellos que, durante el procesamiento del modelo, demoran mas en acercarse a valores cercanos a cero.    

```{r}

indices <- sample(c(TRUE,FALSE), nrow(data.train), replace = TRUE)

cv.out <- cv.glmnet(x[indices,], y[indices], alpha = 0)

plot(cv.out)
coef(cv.out)
```


* La grafica anterior representa como el error incrementa a mayores valores de log(lambda).    
* Las lineas punteadas indican, el valor minimo de mse obtenido en la validacion cruzada y el valor de la derecha representa el error estandar.     


```{r}

bestlam = cv.out$lambda.min
bestlam

```

* Se emplea el menor lambda obtenido de la validacion cruzada propia del modelo.    

```{r}

ridge.pred <- predict(ridge.model, s = bestlam, newx = x[-indices,])
sqrt(mean((ridge.pred - y[-indices])^2))

```

* Se obtiene un valor de rmse de 807 obtenido mediante los datos de entrenamiento.    

## 10b.2: Validacion Cruzada   

```{r}

x = model.matrix(Price ~ . , data.test)[, -1]
y = as.matrix(data.test$Price)

ridge.model = glmnet(x, y, alpha = 0)

```


```{r}

indices <- sample(c(TRUE,FALSE), nrow(data.test), replace = TRUE)

cv.out <- cv.glmnet(x[indices,], y[indices], alpha = 0)

plot(cv.out)
coef(cv.out)
```

* El valor minimo de MSE y el error estandar, son similares a los obtenidos mediante datos de entrenamiento.   


```{r}

bestlam = cv.out$lambda.min
bestlam

```

* Se emplea el menor lambda obtenido de la validacion cruzada propia del modelo.    

```{r}

ridge.pred <- predict(ridge.model, s = bestlam, newx = x[-indices,])
sqrt(mean((ridge.pred - y[-indices])^2))

```

* Se obtiene un valor de rmse de 775 datos de prueba.



## 10c: Lasso      

* Mediante Lasso se obtiene un modelo a partir de los 34 predictores iniciales, ponderando la influencia de cada predictor. A diferencia de Ridge, usando Lasso si se realiza una seleccion de variables.     

```{r}
set.seed(10)

index <- createDataPartition(clean_data$Price, p = 0.7, list = FALSE)

data.train <- clean_data[index, ]
data.test <- clean_data[-index, ]
```

* Se produce en conjunto de entrenamiento y de prueba.    

## 10c.1: Modelo

```{r}

x = model.matrix(Price ~ . , data.train)[, -1]
y = as.matrix(data.train$Price)

lasso.model = glmnet(x, y, alpha = 1)

```


```{r}
beta=coef(lasso.model)

tmp <- as.data.frame(as.matrix(beta))
tmp$coef <- row.names(tmp)
tmp <- reshape::melt(tmp, id = "coef")
tmp$variable <- as.numeric(gsub("s", "", tmp$variable))
tmp$lambda <- lasso.model$lambda[tmp$variable+1]
tmp$norm <- apply(abs(beta[-1,]), 2, sum)[tmp$variable+1]

ggplot(tmp[tmp$coef != "(Intercept)",], aes(lambda, value, color = coef, group = coef, )) + 
  geom_line() + 
    scale_x_log10() + 
    xlab("Lambda (log scale)") + 
    guides(color = guide_legend(title = ""), 
           linetype = guide_legend(title = "")) +
    theme_bw() + 
    theme(legend.key.width = unit(3,"lines")) 
```


```{r}
plot(lasso.model, xvar = "lambda", label = TRUE)
```


* Mediante los dos graficos anteriores se puede observar que los predictores mas significativos son aquellos que, durante el procesamiento del modelo, demoran mas en acercarse a valores cercanos a cero.    


```{r}

indices <- sample(c(TRUE,FALSE), nrow(data.train), replace = TRUE)

cv.out <- cv.glmnet(x[indices,], y[indices], alpha = 1)

plot(cv.out)
coef(cv.out)
```

* El valor minimo de MSE y el error estandar, son similares a los obtenidos mediante datos de entrenamiento.   



```{r}

bestlam = cv.out$lambda.min
bestlam

```

* Se emplea el menor lambda obtenido de la validacion cruzada propia del modelo.    


```{r}

lasso.pred <- predict(lasso.model, s = bestlam, newx = x[-indices,])
sqrt(mean((lasso.pred - y[-indices])^2))

```

* Se obtiene un valor de rmse de 813 datos de entrenamiento.

## 10c.2: Validacion Cruzada 

```{r}

x = model.matrix(Price ~ . , data.test)[, -1]
y = as.matrix(data.test$Price)

lasso.model = glmnet(x, y, alpha = 1)

```

```{r}

indices <- sample(c(TRUE,FALSE), nrow(data.test), replace = TRUE)

cv.out <- cv.glmnet(x[indices,], y[indices], alpha = 1)

plot(cv.out)
coef(cv.out)
```

```{r}

bestlam = cv.out$lambda.min
bestlam

```

```{r}

lasso.pred <- predict(lasso.model, s = bestlam, newx = x[-indices,])
sqrt(mean((lasso.pred - y[-indices])^2))

```

* Se obtiene un valor de rmse de 813 datos de prueba.   


# 11: Conclusión

Dado que es un dataset con una cantidad baja de instancias (1500 aprox), y que mediante el uso de Lasso se obtuvo un resultado aceptable comparado a los rmse calculados con otros métodos (Best Subset y Ridge), se opta por usar ese metodo para seleccion de variables.    


