Analisis exploratorio de dataSet ‘Toyota Corolla’

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.

Carga de Librerias

library(fastDummies) # libreria para encoding
library(car)

Loading required package: carData
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     

library(corrplot) # lbreria para ver la correlacion entre variables

corrplot 0.84 loaded

library(mctest) # libreria para calculo de TOF Y VIF
library(tidyverse) # libreria para limpieza de datos y formateo

Registered S3 method overwritten by 'dplyr':
  method           from
  print.rowwise_df     
-- Attaching packages --------------------------------------- tidyverse 1.2.1 --
v ggplot2 3.2.1     v purrr   0.3.2
v tibble  2.1.3     v dplyr   0.8.3
v tidyr   1.0.0     v stringr 1.4.0
v readr   1.3.1     v forcats 0.4.0
-- Conflicts ------------------------------------------ tidyverse_conflicts() --
x dplyr::filter() masks stats::filter()
x dplyr::lag()    masks stats::lag()
x dplyr::recode() masks car::recode()
x purrr::some()   masks car::some()

Lectura del DataSet

a_raw_data = read.csv("ToyotaCorolla.csv") 

DataSet

a_raw_data

Estructura del DataSet

str(a_raw_data)

'data.frame':   1436 obs. of  37 variables:
 $ Id              : int  1 2 3 4 5 6 7 8 9 10 ...
 $ Model           : Factor w/ 372 levels "?TOYOTA Corolla 1.3 16V HATCHB G6 2/3-Doors",..: 332 332 67 332 331 331 64 326 62 59 ...
 $ 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 ...

Resumen del DataSet

summary(a_raw_data)

       Id                                                         Model          Price      
 Min.   :   1.0   TOYOTA Corolla 1.6 16V HATCHB LINEA TERRA 2/3-Doors: 107   Min.   : 4350  
 1st Qu.: 361.8   TOYOTA Corolla 1.3 16V HATCHB LINEA TERRA 2/3-Doors:  83   1st Qu.: 8450  
 Median : 721.5   TOYOTA Corolla 1.6 16V LIFTB LINEA LUNA 4/5-Doors  :  79   Median : 9900  
 Mean   : 721.6   TOYOTA Corolla 1.6 16V LIFTB LINEA TERRA 4/5-Doors :  70   Mean   :10731  
 3rd Qu.:1081.2   TOYOTA Corolla 1.6 16V SEDAN LINEA TERRA 4/5-Doors :  43   3rd Qu.:11950  
 Max.   :1442.0   TOYOTA Corolla 1.4 16V VVT I HATCHB TERRA 2/3-Doors:  42   Max.   :32500  
                  (Other)                                            :1012                  
   Age_08_04       Mfg_Month         Mfg_Year          KM          Fuel_Type          HP       
 Min.   : 1.00   Min.   : 1.000   Min.   :1998   Min.   :     1   CNG   :  17   Min.   : 69.0  
 1st Qu.:44.00   1st Qu.: 3.000   1st Qu.:1998   1st Qu.: 43000   Diesel: 155   1st Qu.: 90.0  
 Median :61.00   Median : 5.000   Median :1999   Median : 63390   Petrol:1264   Median :110.0  
 Mean   :55.95   Mean   : 5.549   Mean   :2000   Mean   : 68533                 Mean   :101.5  
 3rd Qu.:70.00   3rd Qu.: 8.000   3rd Qu.:2001   3rd Qu.: 87021                 3rd Qu.:110.0  
 Max.   :80.00   Max.   :12.000   Max.   :2004   Max.   :243000                 Max.   :192.0  
                                                                                               
   Met_Color        Automatic             cc            Doors         Cylinders     Gears      
 Min.   :0.0000   Min.   :0.00000   Min.   : 1300   Min.   :2.000   Min.   :4   Min.   :3.000  
 1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.: 1400   1st Qu.:3.000   1st Qu.:4   1st Qu.:5.000  
 Median :1.0000   Median :0.00000   Median : 1600   Median :4.000   Median :4   Median :5.000  
 Mean   :0.6748   Mean   :0.05571   Mean   : 1577   Mean   :4.033   Mean   :4   Mean   :5.026  
 3rd Qu.:1.0000   3rd Qu.:0.00000   3rd Qu.: 1600   3rd Qu.:5.000   3rd Qu.:4   3rd Qu.:5.000  
 Max.   :1.0000   Max.   :1.00000   Max.   :16000   Max.   :5.000   Max.   :4   Max.   :6.000  
                                                                                               
 Quarterly_Tax        Weight     Mfr_Guarantee    BOVAG_Guarantee  Guarantee_Period      ABS        
 Min.   : 19.00   Min.   :1000   Min.   :0.0000   Min.   :0.0000   Min.   : 3.000   Min.   :0.0000  
 1st Qu.: 69.00   1st Qu.:1040   1st Qu.:0.0000   1st Qu.:1.0000   1st Qu.: 3.000   1st Qu.:1.0000  
 Median : 85.00   Median :1070   Median :0.0000   Median :1.0000   Median : 3.000   Median :1.0000  
 Mean   : 87.12   Mean   :1072   Mean   :0.4095   Mean   :0.8955   Mean   : 3.815   Mean   :0.8134  
 3rd Qu.: 85.00   3rd Qu.:1085   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.: 3.000   3rd Qu.:1.0000  
 Max.   :283.00   Max.   :1615   Max.   :1.0000   Max.   :1.0000   Max.   :36.000   Max.   :1.0000  
                                                                                                    
    Airbag_1         Airbag_2          Airco        Automatic_airco   Boardcomputer      CD_Player     
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:1.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :1.0000   Median :1.0000   Median :1.0000   Median :0.00000   Median :0.0000   Median :0.0000  
 Mean   :0.9708   Mean   :0.7228   Mean   :0.5084   Mean   :0.05641   Mean   :0.2946   Mean   :0.2187  
 3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.00000   3rd Qu.:1.0000   3rd Qu.:0.0000  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.0000   Max.   :1.0000  
                                                                                                       
  Central_Lock    Powered_Windows Power_Steering       Radio          Mistlamps      Sport_Model    
 Min.   :0.0000   Min.   :0.000   Min.   :0.0000   Min.   :0.0000   Min.   :0.000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.000   1st Qu.:1.0000   1st Qu.:0.0000   1st Qu.:0.000   1st Qu.:0.0000  
 Median :1.0000   Median :1.000   Median :1.0000   Median :0.0000   Median :0.000   Median :0.0000  
 Mean   :0.5801   Mean   :0.562   Mean   :0.9777   Mean   :0.1462   Mean   :0.257   Mean   :0.3001  
 3rd Qu.:1.0000   3rd Qu.:1.000   3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:1.000   3rd Qu.:1.0000  
 Max.   :1.0000   Max.   :1.000   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.

Análisis exploratorio

par(mfrow=c(1,1))
boxplot(a_raw_data$Price,main = "Precio Vehiculos Toyota Corolla",
        ylab = "Precio ($)", notch = TRUE)

• 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.
  ## Graficos Age_08_04 y Mfg_Year

par(mfrow=c(1,2))

boxplot(a_raw_data$Age_08_04,main = "Age_08_04")
boxplot(a_raw_data$Mfg_Year,main = "Año de Mfg_Year")

• El atributo “Age_08_04” presenta valores outliers correspondientes a vehiculos nuevos cuya antiguedad es 0.

Graficos KM y HP

par(mfrow=c(1,2))

boxplot(a_raw_data$KM,main = "KM",
        ylab = "KM", notch = TRUE)

boxplot(a_raw_data$HP,main = "HP",
        ylab = "HP", notch = FALSE)

• 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.

• El atributo “KM” presenta valores outliers. Destaco sobretodo un conjunto de valores superiores a los 200000.
  ## Grafico CC

boxplot(a_raw_data$cc,main = "Cilindrada",
        ylab = "CC", notch = FALSE)

• 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.

##Graficos Quarterly_Tax y Weight

par(mfrow=c(1,2))

boxplot(a_raw_data$Quarterly_Tax, main="Quarterly_Tax")
boxplot(a_raw_data$Weight, main="Peso(KG)")

• El atributo “Quarterly_Tax” presenta outliers para valores superiores a 150 y valores menores a 50, sobre una mediana de 70 aproximadamente.
  
• El atributo “Weight” presenta outliers para valores superiores a 1150 sobre una mediana de 1050 aproximadamente.

Graficos Fueltype y Radio Cassete

lbls <- c("0: No tiene", "1: Tiene")

par(mfrow=c(1,2)) 

barplot(table(as.factor(a_raw_data$Fuel_Type)), main="Fuel_Type")
pie(x = table(a_raw_data$Radio_cassette), labels = lbls, main="Radio Cassete")

Graficos Metallic Rim y Backseat Divider

par(mfrow=c(1,2)) 

pie(x = table(a_raw_data$Metallic_Rim), labels = lbls,  main="Metallic Rim")
pie(x = table(a_raw_data$Backseat_Divider) , labels = lbls,  main="Backseat_Divider")

Graficos Mistlamp, Radio y Sport Model

par(mfrow=c(1,3))

pie(x = table(a_raw_data$Mistlamps) , labels = lbls,  main="Mistlamps")
pie(x = table(a_raw_data$Radio), labels = lbls,  main="Radio")
pie(x = table(a_raw_data$Sport_Model), labels = lbls,  main="Sport_Model")

Graficos Central Lock, CD Player y BoardComputer

par(mfrow=c(1,3))

pie(x = table(a_raw_data$Central_Lock), labels = lbls, main="Central_Lock")
pie(x = table(a_raw_data$CD_Player), labels = lbls, main="CD_Player")
pie(x = table(a_raw_data$Boardcomputer), labels = lbls, main="Boardcomputer")

Graficos Airco, Airbag_2 y Airbag_1

par(mfrow=c(1,3))

pie(x = table(a_raw_data$Airco), labels = lbls,  main="Airco")
pie(x = table(a_raw_data$Airbag_2), labels = lbls,  main="Airbag_2")
pie(x = table(a_raw_data$Airbag_1), labels = lbls,main="Airbag_1")

Graficos Guarantee Period y Automatic Airco

par(mfrow=c(1,2))

barplot(table(as.factor(a_raw_data$Guarantee_Period)), main="Guarantee_Period") 
pie(x = table(a_raw_data$Automatic_airco), labels = lbls,  main="Automatic_airco")

Graficos MFR Guarantee, Gears y BOVAG Guarantee

par(mfrow=c(1,3))

pie(x = table(a_raw_data$Mfr_Guarantee), labels = lbls, main="Mfr_Guarantee")
barplot(table(as.factor(a_raw_data$Gears)), main="Gears")
pie(x = table(a_raw_data$BOVAG_Guarantee), labels = lbls, main="BOVAG_Guarantee")

Graficos Doors, Automatic y ABS

par(mfrow=c(1,3))

barplot(table(as.factor(a_raw_data$Doors)), main="Doors")
pie(x = table(a_raw_data$Automatic),labels = lbls, main="Automatic")
pie(x = table(a_raw_data$ABS),labels = lbls, main="ABS")

Estudio de Variable Objetivo “Price”

Distribucion de Price

hist(a_raw_data$Price, col="blue", breaks = 60, freq = F)
lines(density(a_raw_data$Price), col = "red", lwd=2)

rug(a_raw_data$Price)

Relacion Price vs .

plot(Price~., data=a_raw_data,col="blue")

Seleccion y modificacion de Variables

Seleccion de Atributos

data_set <- select(a_raw_data, -c("Model","Id"))

• 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.

Encoding de atributo Fuel_type

• El atributo Fuel_type es de tipo char, y representa una categoria con varios posibles valores, por lo tanto es necesario realizar un procedimiento de encoding. Tambien es recomendable eliminar una de los columnas producto del enconding para evitar problemas de colinealidad.

data_set <- dummy_cols(data_set, select_columns = "Fuel_Type")
data_set <- select(data_set, -c("Fuel_Type"))

Estudio de correlacion

corrplot(cor(data_set), type="upper", method="pie")

the standard deviation is zero

cor(data_set)

the standard deviation is zero

                       Price    Age_08_04    Mfg_Month     Mfg_Year           KM          HP    Met_Color
Price             1.00000000 -0.876590497 -0.018138222  0.885159220 -0.569960165  0.31498983  0.108904755
Age_08_04        -0.87659050  1.000000000 -0.123255398 -0.983661157  0.505672180 -0.15662202 -0.108149585
Mfg_Month        -0.01813822 -0.123255398  1.000000000 -0.057415518 -0.020629897 -0.03931242  0.030265828
Mfg_Year          0.88515922 -0.983661157 -0.057415518  1.000000000 -0.504974450  0.16469687  0.103310169
KM               -0.56996016  0.505672180 -0.020629897 -0.504974450  1.000000000 -0.33353795 -0.080502926
HP                0.31498983 -0.156622020 -0.039312420  0.164696875 -0.333537948  1.00000000  0.058711703
Met_Color         0.10890475 -0.108149585  0.030265828  0.103310169 -0.080502926  0.05871170  1.000000000
Automatic         0.03308069  0.031716772  0.009146095 -0.033566969 -0.081854083  0.01314403 -0.019335450
cc                0.12638920 -0.098083739  0.037386567  0.091891919  0.102682891  0.03585580  0.031812068
Doors             0.18532555 -0.148359215 -0.012068863  0.151441979 -0.036196614  0.09242450  0.085242826
Cylinders                 NA           NA           NA           NA           NA          NA           NA
Gears             0.06310386 -0.005363947 -0.013063024  0.007766049  0.015023328  0.20947715  0.018600646
Quarterly_Tax     0.21919691 -0.198430508  0.031372634  0.193933911  0.278164697 -0.29843172  0.011325559
Weight            0.58119759 -0.470253184 -0.002167494  0.473477930 -0.028598457  0.08961406  0.057928835
Mfr_Guarantee     0.19780199 -0.164658304 -0.005770789  0.166696657 -0.212850802  0.14002631  0.154849992
BOVAG_Guarantee   0.02813304  0.006864920 -0.003862534 -0.006205542  0.001437579  0.02270078  0.010783490
Guarantee_Period  0.14662661 -0.152562534  0.029009539  0.148218449 -0.138941822  0.07616270  0.009294540
ABS               0.30613784 -0.412887311  0.072532362  0.402215110 -0.177203384  0.05783181  0.022297508
Airbag_1          0.09358787 -0.105405927  0.003756160  0.105359191 -0.018012148  0.02513692  0.100054833
Airbag_2          0.24897390 -0.329017479  0.076749474  0.317075233 -0.139275138  0.01764356  0.038415730
Airco             0.42925943 -0.403600048  0.057088375  0.395673667 -0.133056812  0.24113427  0.114190482
Automatic_airco   0.58826200 -0.426259145 -0.049017448  0.437718185 -0.258221494  0.24495736  0.027977182
Boardcomputer     0.60129196 -0.719448710  0.017714587  0.720567067 -0.353862248  0.12971474  0.089885891
CD_Player         0.48137444 -0.510895187 -0.016735694  0.517007513 -0.266826156  0.10229988  0.198219962
Central_Lock      0.34345757 -0.279630639  0.010055129  0.279490247 -0.125177013  0.25012219  0.153307153
Powered_Windows   0.35651823 -0.283855826  0.025184550  0.280996200 -0.156241578  0.26559348  0.145147102
Power_Steering    0.06427537 -0.069191857 -0.055495374  0.079676069  0.007396622  0.04885045  0.086543865
                    Automatic            cc        Doors Cylinders        Gears Quarterly_Tax
Price             0.033080694  0.1263891974  0.185325550        NA  0.063103857   0.219196911
Age_08_04         0.031716772 -0.0980837391 -0.148359215        NA -0.005363947  -0.198430508
Mfg_Month         0.009146095  0.0373865668 -0.012068863        NA -0.013063024   0.031372634
Mfg_Year         -0.033566969  0.0918919186  0.151441979        NA  0.007766049   0.193933911
KM               -0.081854083  0.1026828910 -0.036196614        NA  0.015023328   0.278164697
HP                0.013144031  0.0358558027  0.092424496        NA  0.209477146  -0.298431717
Met_Color        -0.019335450  0.0318120676  0.085242826        NA  0.018600646   0.011325559
Automatic         1.000000000  0.0667403090 -0.027653817        NA -0.098555054  -0.055370791
cc                0.066740309  1.0000000000  0.079903296        NA  0.014629352   0.306995798
Doors            -0.027653817  0.0799032965  1.000000000        NA -0.160141430   0.109363225
Cylinders                  NA            NA           NA         1           NA            NA
Gears            -0.098555054  0.0146293521 -0.160141430        NA  1.000000000  -0.005451955
Quarterly_Tax    -0.055370791  0.3069957983  0.109363225        NA -0.005451955   1.000000000
Weight            0.057248510  0.3356373992  0.302617644        NA  0.020613284   0.626133733
Mfr_Guarantee     0.026193798 -0.0574065681  0.037689328        NA  0.010822444  -0.022150154
BOVAG_Guarantee   0.023393188 -0.0817250929 -0.014311384        NA  0.072123611   0.094330856
Guarantee_Period -0.002256229 -0.0176829456  0.053653901        NA -0.030677543  -0.163438345
ABS              -0.016128172  0.0378055951  0.063732629        NA  0.086234835   0.080287748
Airbag_1         -0.011895357  0.0226780779  0.053827968        NA  0.002443573   0.082340476
Airbag_2          0.001171485  0.0247384005  0.021733788        NA  0.095209774   0.200172594
Airco            -0.028352763  0.1198880518  0.170543978        NA  0.145489368   0.118225262
Automatic_airco   0.059056613  0.1626688293  0.054808873        NA  0.077791331   0.123125182
Boardcomputer    -0.037068561  0.0093119139  0.089606069        NA -0.025889315   0.141534096
CD_Player        -0.010967021  0.0577868309  0.094652527        NA -0.047466045   0.090868341
Central_Lock     -0.002501825  0.0726344348  0.132091580        NA  0.126963598   0.032084382
Powered_Windows  -0.005863832  0.0552988754  0.107625618        NA  0.131423084   0.003826656
Power_Steering   -0.004469112  0.0329326048  0.059791778        NA  0.021200029   0.047956107
                       Weight Mfr_Guarantee BOVAG_Guarantee Guarantee_Period         ABS      Airbag_1
Price             0.581197589   0.197801991     0.028133044      0.146626614  0.30613784  0.0935878711
Age_08_04        -0.470253184  -0.164658304     0.006864920     -0.152562534 -0.41288731 -0.1054059274
Mfg_Month        -0.002167494  -0.005770789    -0.003862534      0.029009539  0.07253236  0.0037561596
Mfg_Year          0.473477930   0.166696657    -0.006205542      0.148218449  0.40221511  0.1053591914
KM               -0.028598457  -0.212850802     0.001437579     -0.138941822 -0.17720338 -0.0180121479
HP                0.089614059   0.140026308     0.022700778      0.076162697  0.05783181  0.0251369203
Met_Color         0.057928835   0.154849992     0.010783490      0.009294540  0.02229751  0.1000548326
Automatic         0.057248510   0.026193798     0.023393188     -0.002256229 -0.01612817 -0.0118953566
cc                0.335637399  -0.057406568    -0.081725093     -0.017682946  0.03780560  0.0226780779
Doors             0.302617644   0.037689328    -0.014311384      0.053653901  0.06373263  0.0538279678
Cylinders                  NA            NA              NA               NA          NA            NA
Gears             0.020613284   0.010822444     0.072123611     -0.030677543  0.08623483  0.0024435733
Quarterly_Tax     0.626133733  -0.022150154     0.094330856     -0.163438345  0.08028775  0.0823404757
Weight            1.000000000  -0.008564636    -0.056076982     -0.012913462  0.10261557  0.0301817619
Mfr_Guarantee    -0.008564636   1.000000000     0.233458589     -0.098563061  0.11899626  0.0520891638
BOVAG_Guarantee  -0.056076982   0.233458589     1.000000000     -0.300062902  0.13444124  0.2244788766
Guarantee_Period -0.012913462  -0.098563061    -0.300062902      1.000000000 -0.06083998 -0.1424531130
ABS               0.102615574   0.118996262     0.134441245     -0.060839975  1.00000000  0.2775065414
Airbag_1          0.030181762   0.052089164     0.224478877     -0.142453113  0.27750654  1.0000000000
Airbag_2          0.078494306   0.202394935     0.287030993     -0.322769418  0.66176551  0.2803176212
Airco             0.310061953   0.051233618     0.005708771      0.026246244  0.22609484  0.0938356338
Automatic_airco   0.430478501   0.072634969    -0.015188469     -0.039162519  0.11711670  0.0424390956
Boardcomputer     0.274324106   0.198185513     0.115804372     -0.056305124  0.30953619  0.1121653509
CD_Player         0.247056066   0.155637001     0.059487871     -0.003948487  0.19286592  0.0718280455
Central_Lock      0.234644220   0.039915427    -0.023008433      0.058934226  0.09945414  0.1202756810
Powered_Windows   0.213356016   0.041550927    -0.012405873      0.040533587  0.09946502  0.1216410915
Power_Steering    0.047848786   0.029771454     0.164391857     -0.118973564  0.25462559  0.5617703725
                     Airbag_2        Airco Automatic_airco Boardcomputer     CD_Player Central_Lock
Price             0.248973897  0.429259430      0.58826200  0.6012919565  0.4813744379  0.343457572
Age_08_04        -0.329017479 -0.403600048     -0.42625915 -0.7194487099 -0.5108951869 -0.279630639
Mfg_Month         0.076749474  0.057088375     -0.04901745  0.0177145869 -0.0167356937  0.010055129
Mfg_Year          0.317075233  0.395673667      0.43771818  0.7205670674  0.5170075127  0.279490247
KM               -0.139275138 -0.133056812     -0.25822149 -0.3538622479 -0.2668261563 -0.125177013
HP                0.017643556  0.241134272      0.24495736  0.1297147413  0.1022998776  0.250122190
Met_Color         0.038415730  0.114190482      0.02797718  0.0898858909  0.1982199624  0.153307153
Automatic         0.001171485 -0.028352763      0.05905661 -0.0370685613 -0.0109670214 -0.002501825
cc                0.024738401  0.119888052      0.16266883  0.0093119139  0.0577868309  0.072634435
Doors             0.021733788  0.170543978      0.05480887  0.0896060689  0.0946525275  0.132091580
Cylinders                  NA           NA              NA            NA            NA           NA
Gears             0.095209774  0.145489368      0.07779133 -0.0258893149 -0.0474660452  0.126963598
Quarterly_Tax     0.200172594  0.118225262      0.12312518  0.1415340959  0.0908683412  0.032084382
Weight            0.078494306  0.310061953      0.43047850  0.2743241058  0.2470560657  0.234644220
Mfr_Guarantee     0.202394935  0.051233618      0.07263497  0.1981855134  0.1556370005  0.039915427
BOVAG_Guarantee   0.287030993  0.005708771     -0.01518847  0.1158043718  0.0594878710 -0.023008433
Guarantee_Period -0.322769418  0.026246244     -0.03916252 -0.0563051243 -0.0039484870  0.058934226
ABS               0.661765511  0.226094835      0.11711670  0.3095361928  0.1928659238  0.099454144
Airbag_1          0.280317621  0.093835634      0.04243910  0.1121653509  0.0718280455  0.120275681
Airbag_2          1.000000000  0.184626833      0.09070263  0.3762454725  0.2372386822  0.024819190
Airco             0.184626833  1.000000000      0.24044391  0.2932442060  0.2573869774  0.540588387
Automatic_airco   0.090702625  0.240443910      1.00000000  0.2724152210  0.2503957737  0.195790059
Boardcomputer     0.376245473  0.293244206      0.27241522  1.0000000000  0.4897251626  0.203125940
CD_Player         0.237238682  0.257386977      0.25039577  0.4897251626  1.0000000000  0.194075729
Central_Lock      0.024819190  0.540588387      0.19579006  0.2031259404  0.1940757289  1.000000000
Powered_Windows   0.049129417  0.543981749      0.20368691  0.2133274783  0.1953859749  0.875552474
Power_Steering    0.212187253  0.096893133      0.03691172  0.0872071153  0.0684516980  0.129646282
                 Powered_Windows Power_Steering         Radio    Mistlamps   Sport_Model Backseat_Divider
Price               0.3565182258    0.064275368 -0.0418873522  0.222082519  0.1641209622       0.10256915
Age_08_04          -0.2838558256   -0.069191857  0.0137914024 -0.126894569 -0.1109883188      -0.11675106
Mfg_Month           0.0251845496   -0.055495374  0.0316014980 -0.033503771  0.0527892029       0.02324544
Mfg_Year            0.2809961995    0.079676069 -0.0196073695  0.133736662  0.1020799610       0.11323703
KM                 -0.1562415784    0.007396622  0.0136611034 -0.074326655 -0.0447838761      -0.04565758
HP                  0.2655934848    0.048850452  0.0209981381  0.210571265 -0.0060266503       0.01090798
Met_Color           0.1451471025    0.086543865  0.0727564442  0.023821349  0.0037788003       0.03774104
Automatic          -0.0058638318   -0.004469112 -0.0146002437  0.003077421  0.0131753360      -0.01887627
cc                  0.0552988754    0.032932605 -0.0003610891  0.017326122 -0.0351951669      -0.05571083
Doors               0.1076256182    0.059791778 -0.0083180738  0.064704827 -0.1298805666      -0.02254186
Cylinders                     NA             NA            NA           NA            NA               NA
Gears               0.1314230843    0.021200029  0.0150902447  0.238788846  0.1741171356       0.07670513
Quarterly_Tax       0.0038266562    0.047956107 -0.0318162601  0.024024007  0.0675251905       0.19841873
Weight              0.2133560160    0.047848786 -0.0384073722  0.135235745  0.1259738904       0.03644617
Mfr_Guarantee       0.0415509270    0.029771454 -0.0520575752  0.083957782  0.0541294147       0.25624925
BOVAG_Guarantee    -0.0124058729    0.164391857 -0.0390748594  0.117472133  0.1739778084       0.45746808
Guarantee_Period    0.0405335874   -0.118973564  0.1988855994 -0.118021352 -0.1728737542      -0.48442685
ABS                 0.0994650204    0.254625594 -0.0546698668  0.179432532  0.2005960321       0.25665879
Airbag_1            0.1216410915    0.561770372 -0.0100345937  0.092618058  0.1136707859       0.30794725
Airbag_2            0.0491294169    0.212187253 -0.2236631719  0.228843121  0.3002735426       0.58998743
Airco               0.5439817486    0.096893133 -0.0305710644  0.466750824  0.0027302616       0.10514887
Automatic_airco     0.2036869067    0.036911721 -0.0926473776  0.312140517  0.2152873511       0.01875632
Boardcomputer       0.2133274783    0.087207115 -0.1290936057  0.147900225  0.0368018520       0.28761493
CD_Player           0.1953859749    0.068451698 -0.1855677207  0.124589102  0.0579195080       0.14880586
Central_Lock        0.8755524744    0.129646282 -0.0112509667  0.487425901 -0.0031278972       0.05844882
Powered_Windows     1.0000000000    0.123457779 -0.0358111799  0.496696773 -0.0006504532       0.07824375
Power_Steering      0.1234577794    1.000000000  0.0090747860  0.077984550  0.0988660173       0.26516943
                 Metallic_Rim Radio_cassette      Tow_Bar Fuel_Type_CNG Fuel_Type_Diesel Fuel_Type_Petrol
Price              0.10856398   -0.043178988 -0.172368602 -0.0395362811     0.0540842283    -0.0385164095
Age_08_04         -0.04004538    0.012857260  0.188719528  0.0023892110    -0.0977404115     0.0926105871
Mfg_Month          0.02350647    0.032576240 -0.042169981  0.0012890926     0.0515007047    -0.0496464779
Mfg_Year           0.03602212   -0.018844434 -0.182205679 -0.0026374554     0.0889860345    -0.0841617029
KM                -0.01359877    0.015770423  0.084153196  0.1440158195     0.4030599249    -0.4331596083
HP                 0.20678416    0.019919200  0.068271274  0.0621088646    -0.5334531033     0.4891102880
Met_Color          0.05382944    0.071529685  0.148536237  0.0210086689    -0.0124203059     0.0048715287
Automatic         -0.07809465   -0.014149521  0.018785917  0.0014856725    -0.0844902184     0.0802489005
cc                 0.00323562   -0.000469534  0.002724607  0.0059408788     0.3277228757    -0.3151700204
Doors             -0.03955479   -0.008265241  0.102291795  0.0096796305     0.0254947130    -0.0275885443
Cylinders                  NA             NA           NA            NA               NA               NA
Gears              0.29507704    0.015397437 -0.029356649 -0.0495366325    -0.0488468198     0.0631816471
Quarterly_Tax     -0.01196455   -0.031008861 -0.004987518  0.2337906099     0.7927262329    -0.8354516723
Weight             0.05384674   -0.037265380 -0.074931667  0.0527564752     0.5680868663    -0.5604702648
Mfr_Guarantee      0.02672792   -0.054532147 -0.023328109 -0.0125827868    -0.1527413987     0.1501599491
BOVAG_Guarantee    0.06043430   -0.039826683 -0.006718221 -0.0257713458    -0.0499624245     0.0563315074
Guarantee_Period  -0.04400287    0.193910054  0.008590048 -0.0104018096    -0.0651612322     0.0657367438
ABS                0.07915186   -0.055724076 -0.065976495 -0.0301966909     0.0341430554    -0.0225705022
Airbag_1           0.05734470   -0.022116573  0.052311749 -0.0574221897     0.0204230626    -0.0003899949
Airbag_2           0.07512782   -0.220917181 -0.063955554 -0.0185317254     0.0198530039    -0.0127997246
Airco              0.23316610   -0.036523590 -0.024361999  0.0174886051     0.0323421048    -0.0367335003
Automatic_airco    0.10036278   -0.092348095 -0.117966859 -0.0267612333     0.0511371894    -0.0399554476
Boardcomputer     -0.02499875   -0.128073275 -0.128001147 -0.0001081937     0.0213757390    -0.0203918636
CD_Player          0.04473025   -0.189668131 -0.079910736  0.0355575671     0.0005822628    -0.0124007590
Central_Lock       0.28133382   -0.016954462 -0.007727796  0.0018078245    -0.0496221000     0.0468195828
Powered_Windows    0.29141941   -0.037625504 -0.013251510 -0.0071843814    -0.0909472155     0.0893076003
Power_Steering     0.05321656   -0.004583647  0.030452502  0.0165243619     0.0221070879    -0.0266311292
 [ reached getOption("max.print") -- omitted 10 rows ]

Busqueda de posible Colinealidad

imcdiag(select(data_set, -c("Price")), data_set$Price)

Call:
imcdiag(x = select(data_set, -c("Price")), y = data_set$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                2.0862 0.4793   43.4499   44.7598 0.6923 -0.0602     0
HP                2.5533 0.3916   62.1333   64.0064 0.6258 -0.0736     0
Met_Color         1.1438 0.8743    5.7511    5.9245 0.9350 -0.0330     0
Automatic         1.1161 0.8960    4.6423    4.7822 0.9466 -0.0322     0
cc                1.2567 0.7957   10.2682   10.5777 0.8920 -0.0362     0
Doors             1.3512 0.7401   14.0483   14.4718 0.8603 -0.0390     0
Cylinders         2.0000 0.5000   39.9983   41.2041     NA -0.0577     0
Gears             1.2711 0.7867   10.8445   11.1715 0.8870 -0.0367     0
Quarterly_Tax     5.2040 0.1922  168.1594  173.2289 0.4384 -0.1501     0
Weight            4.2108 0.2375  128.4331  132.3049 0.4873 -0.1214     0
Mfr_Guarantee     1.2005 0.8330    8.0215    8.2634 0.9127 -0.0346     0
BOVAG_Guarantee   1.3737 0.7280   14.9466   15.3972 0.8532 -0.0396     0
Guarantee_Period  1.5401 0.6493   21.6051   22.2564 0.8058 -0.0444     0
ABS               2.2675 0.4410   50.6996   52.2280 0.6641 -0.0654     0
Airbag_1          1.6124 0.6202   24.4970   25.2355 0.7875 -0.0465     0
Airbag_2          3.1059 0.3220   84.2375   86.7770 0.5674 -0.0896     0
Airco             1.8382 0.5440   33.5291   34.5399 0.7376 -0.0530     0
Automatic_airco   1.7455 0.5729   29.8215   30.7206 0.7569 -0.0503     0
Boardcomputer     2.6347 0.3796   65.3876   67.3588 0.6161 -0.0760     0
CD_Player         1.5582 0.6418   22.3288   23.0020 0.8011 -0.0449     0
Central_Lock      4.5916 0.2178  143.6625  147.9935 0.4667 -0.1324     0
Powered_Windows   4.6403 0.2155  145.6129  150.0027 0.4642 -0.1338     0
Power_Steering    1.5828 0.6318   23.3118   24.0146 0.7949 -0.0456     0
Radio            62.3145 0.0160 2452.5793 2526.5173 0.1267 -1.7969     1
Mistlamps         2.0764 0.4816   43.0577   44.3558 0.6940 -0.0599     0
Sport_Model       1.4939 0.6694   19.7557   20.3513 0.8182 -0.0431     0
Backseat_Divider  2.6918 0.3715   67.6718   69.7119 0.6095 -0.0776     0
Metallic_Rim      1.3439 0.7441   13.7553   14.1700 0.8626 -0.0388     0
Radio_cassette   62.1305 0.0161 2445.2194 2518.9356 0.1269 -1.7916     1
Tow_Bar           1.1468 0.8720    5.8734    6.0505 0.9338 -0.0331     0
Fuel_Type_CNG        Inf 0.0000       Inf       Inf 0.0000    -Inf     1
Fuel_Type_Diesel     Inf 0.0000       Inf       Inf 0.0000    -Inf     1
Fuel_Type_Petrol     Inf 0.0000       Inf       Inf 0.0000    -Inf     1

1 --> COLLINEARITY is detected by the test 
0 --> COLLINEARITY is not detected by the test

HP , Automatic , cc , Doors , Guarantee_Period , ABS , Boardcomputer , Central_Lock , Powered_Windows , Power_Steering , Backseat_Divider , coefficient(s) are non-significant may be due to multicollinearity

R-square of y on all x: 0.9087 

* 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, Fuel_Type_CNG, Fuel_Type_Diesel, Fuel_Type_Petrol

Modelo: Regresion Lineal

linearMod <- lm(formula = Price ~ ., data=data_set)
summary(linearMod)

Call:
lm(formula = Price ~ ., data = data_set)

Residuals:
    Min      1Q  Median      3Q     Max 
-8047.3  -645.4   -35.0   641.4  5528.8 

Coefficients: (3 not defined because of singularities)
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       2.668e+03  1.445e+03   1.847 0.065014 .  
Age_08_04        -1.190e+02  3.475e+00 -34.236  < 2e-16 ***
Mfg_Month        -9.553e+01  9.079e+00 -10.522  < 2e-16 ***
Mfg_Year                 NA         NA      NA       NA    
KM               -1.638e-02  1.127e-03 -14.528  < 2e-16 ***
HP                1.910e+01  3.122e+00   6.119 1.22e-09 ***
Met_Color        -1.686e+00  6.680e+01  -0.025 0.979865    
Automatic         3.460e+02  1.348e+02   2.567 0.010354 *  
cc               -1.136e-01  7.731e-02  -1.470 0.141829    
Doors             3.779e+01  3.571e+01   1.058 0.290110    
Cylinders                NA         NA      NA       NA    
Gears             1.539e+02  1.750e+02   0.879 0.379433    
Quarterly_Tax     1.442e+01  1.623e+00   8.882  < 2e-16 ***
Weight            1.095e+01  1.141e+00   9.598  < 2e-16 ***
Mfr_Guarantee     2.258e+02  6.519e+01   3.464 0.000548 ***
BOVAG_Guarantee   4.914e+02  1.121e+02   4.383 1.26e-05 ***
Guarantee_Period  6.602e+01  1.206e+01   5.473 5.25e-08 ***
ABS              -2.686e+02  1.131e+02  -2.376 0.017650 *  
Airbag_1          1.187e+02  2.205e+02   0.538 0.590485    
Airbag_2         -7.726e+01  1.152e+02  -0.671 0.502527    
Airco             1.984e+02  7.935e+01   2.501 0.012499 *  
Automatic_airco   2.441e+03  1.676e+02  14.571  < 2e-16 ***
Boardcomputer    -2.670e+02  1.042e+02  -2.563 0.010474 *  
CD_Player         2.091e+02  8.836e+01   2.367 0.018087 *  
Central_Lock     -8.865e+01  1.270e+02  -0.698 0.485364    
Powered_Windows   4.189e+02  1.270e+02   3.297 0.001000 ***
Power_Steering   -4.368e+01  2.494e+02  -0.175 0.860981    
Radio             5.382e+02  6.536e+02   0.823 0.410384    
Mistlamps        -5.027e+01  9.649e+01  -0.521 0.602447    
Sport_Model       3.046e+02  7.803e+01   3.904 9.92e-05 ***
Backseat_Divider -2.649e+02  1.141e+02  -2.321 0.020410 *  
Metallic_Rim      2.060e+02  8.406e+01   2.451 0.014368 *  
Radio_cassette   -6.395e+02  6.540e+02  -0.978 0.328314    
Tow_Bar          -2.035e+02  6.995e+01  -2.909 0.003677 ** 
Fuel_Type_CNG    -2.122e+03  3.299e+02  -6.431 1.74e-10 ***
Fuel_Type_Diesel -1.163e+03  2.665e+02  -4.364 1.37e-05 ***
Fuel_Type_Petrol         NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1109 on 1402 degrees of freedom
Multiple R-squared:  0.9087,    Adjusted R-squared:  0.9066 
F-statistic: 422.9 on 33 and 1402 DF,  p-value: < 2.2e-16

A partir de este modelo de regresión lineal, obtengo las siguientes consideraciones:
* Las variables con un alto T Value (posibles variables más significativas) son: Age_08_04, Mfg_Month, KM, Weight, Automatic_airco, entre otras.
* Algunas variables presentan un T Value muy cercano a cero, posiblemente no son muy relevantes para el modelo: Met_Color, Doors, Gears, Airbag_1, Airbag_2, Central_Lock, Power_Steering, Mistlamps, Radio_cassette.
* El precio base de un vehiculo es de 2.668e+03.
* El modelo tiene una exactitud de 0.90, el cual es un buen valor. Sin embargo, existen problemas de colinealidad.
* Es necesario tomar acciones sobre Mfg_Year y Fuel_Type_Petrol por los problemas de colinealidad.

Plot Residuos

par(mfrow=c(2,2))
plot(linearMod)

A partir de este modelo de regresión lineal, observo lo siguiente:

• En el grafico Residuals vs Fitted se observa una curva, casi recta, que tiende a cero, que es lo deseable. Pero se manifiesta la presencia de puntos que tiran de la curva, como es el caso del punto 110 y 222. Es necesario un retrabajo.
  
• En el grafico Normal Q-Q se observa que la mayoria de los puntos se adecuan a la recta, pero existen puntos como el 222 y el 81, que estan tirando la forma de la recta, es necesario un retrabajo.
  
• En el grafico Scale-Location se observa una curva abonbada que posiblemente esta siendo influia por la gran concentracion de puntos alrrededor de 10000.
  
• En el grafico Residuals vs Leverage se oberva que hay valores que se encuentran fuera de la distancia de Cook, como el punto 81 o 222. Es necesario un retrabajo.

Plot Residuos: Histograma

residuos = resid(linearMod)
hist(residuos, col="blue", breaks = 60, freq = F)
lines(density(residuos), col = "red", lwd=2)

rug(residuos)

• Los residuos del modelo de regresión lineal aplicado sobre el dataSet original, sin consideración de los valores atípicos, presenta una distribución similar a una distribución normal, con un sesgo hacia la izquierda.

• El modelo de regresión lineal aplicado sobre el dataSet original, presenta una exactitud de 0.90. Sin embargo, el conjunto de datos original presenta problemas de colinealidad.

Seleccion de Variables 1°

• Se elimina el atributo cylinders porque es un valor constante que no es significativo.
  
• Se eliminan los atributos cd player y radio cassete, por ser considerados como derivados del atributo radio.
  
• Se eliminan los atributos Met_Color, Doors, Gears, Airbag_1, Airbag_2, Central_Lock, Power_Steering, Mistlamps y Radio_cassette debido a la poca relevancia que tienen sobre el modelo, basado en su T Value.
  
• Se elimina el atributo Fuel_Type_Diesel como resultado del proceso previo de encoding.

data_set_1 <- select(data_set, -c("Mfg_Month", 
                                  "Cylinders", 
                                  "CD_Player", "Mfg_Year", "Met_Color", "Doors", "Gears", "Airbag_1", "Airbag_2", "Central_Lock", "Power_Steering", "Mistlamps", "Radio_cassette", "Fuel_Type_Diesel"))

summary(data_set_1)

     Price         Age_08_04           KM               HP          Automatic             cc       
 Min.   : 4350   Min.   : 1.00   Min.   :     1   Min.   : 69.0   Min.   :0.00000   Min.   : 1300  
 1st Qu.: 8450   1st Qu.:44.00   1st Qu.: 43000   1st Qu.: 90.0   1st Qu.:0.00000   1st Qu.: 1400  
 Median : 9900   Median :61.00   Median : 63390   Median :110.0   Median :0.00000   Median : 1600  
 Mean   :10731   Mean   :55.95   Mean   : 68533   Mean   :101.5   Mean   :0.05571   Mean   : 1577  
 3rd Qu.:11950   3rd Qu.:70.00   3rd Qu.: 87021   3rd Qu.:110.0   3rd Qu.:0.00000   3rd Qu.: 1600  
 Max.   :32500   Max.   :80.00   Max.   :243000   Max.   :192.0   Max.   :1.00000   Max.   :16000  
 Quarterly_Tax        Weight     Mfr_Guarantee    BOVAG_Guarantee  Guarantee_Period      ABS        
 Min.   : 19.00   Min.   :1000   Min.   :0.0000   Min.   :0.0000   Min.   : 3.000   Min.   :0.0000  
 1st Qu.: 69.00   1st Qu.:1040   1st Qu.:0.0000   1st Qu.:1.0000   1st Qu.: 3.000   1st Qu.:1.0000  
 Median : 85.00   Median :1070   Median :0.0000   Median :1.0000   Median : 3.000   Median :1.0000  
 Mean   : 87.12   Mean   :1072   Mean   :0.4095   Mean   :0.8955   Mean   : 3.815   Mean   :0.8134  
 3rd Qu.: 85.00   3rd Qu.:1085   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.: 3.000   3rd Qu.:1.0000  
 Max.   :283.00   Max.   :1615   Max.   :1.0000   Max.   :1.0000   Max.   :36.000   Max.   :1.0000  
     Airco        Automatic_airco   Boardcomputer    Powered_Windows     Radio         Sport_Model    
 Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Min.   :0.000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :1.0000   Median :0.00000   Median :0.0000   Median :1.000   Median :0.0000   Median :0.0000  
 Mean   :0.5084   Mean   :0.05641   Mean   :0.2946   Mean   :0.562   Mean   :0.1462   Mean   :0.3001  
 3rd Qu.:1.0000   3rd Qu.:0.00000   3rd Qu.:1.0000   3rd Qu.:1.000   3rd Qu.:0.0000   3rd Qu.:1.0000  
 Max.   :1.0000   Max.   :1.00000   Max.   :1.0000   Max.   :1.000   Max.   :1.0000   Max.   :1.0000  
 Backseat_Divider  Metallic_Rim       Tow_Bar       Fuel_Type_CNG     Fuel_Type_Petrol
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000  
 1st Qu.:1.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:1.0000  
 Median :1.0000   Median :0.0000   Median :0.0000   Median :0.00000   Median :1.0000  
 Mean   :0.7702   Mean   :0.2047   Mean   :0.2779   Mean   :0.01184   Mean   :0.8802  
 3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:0.00000   3rd Qu.:1.0000  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.0000  

Estudio de correlacion

corrplot(cor(data_set_1), type="upper", method="pie")

cor(data_set_1)

                       Price    Age_08_04           KM          HP    Automatic            cc
Price             1.00000000 -0.876590497 -0.569960165  0.31498983  0.033080694  0.1263891974
Age_08_04        -0.87659050  1.000000000  0.505672180 -0.15662202  0.031716772 -0.0980837391
KM               -0.56996016  0.505672180  1.000000000 -0.33353795 -0.081854083  0.1026828910
HP                0.31498983 -0.156622020 -0.333537948  1.00000000  0.013144031  0.0358558027
Automatic         0.03308069  0.031716772 -0.081854083  0.01314403  1.000000000  0.0667403090
cc                0.12638920 -0.098083739  0.102682891  0.03585580  0.066740309  1.0000000000
Quarterly_Tax     0.21919691 -0.198430508  0.278164697 -0.29843172 -0.055370791  0.3069957983
Weight            0.58119759 -0.470253184 -0.028598457  0.08961406  0.057248510  0.3356373992
Mfr_Guarantee     0.19780199 -0.164658304 -0.212850802  0.14002631  0.026193798 -0.0574065681
BOVAG_Guarantee   0.02813304  0.006864920  0.001437579  0.02270078  0.023393188 -0.0817250929
Guarantee_Period  0.14662661 -0.152562534 -0.138941822  0.07616270 -0.002256229 -0.0176829456
ABS               0.30613784 -0.412887311 -0.177203384  0.05783181 -0.016128172  0.0378055951
Airco             0.42925943 -0.403600048 -0.133056812  0.24113427 -0.028352763  0.1198880518
Automatic_airco   0.58826200 -0.426259145 -0.258221494  0.24495736  0.059056613  0.1626688293
Boardcomputer     0.60129196 -0.719448710 -0.353862248  0.12971474 -0.037068561  0.0093119139
Powered_Windows   0.35651823 -0.283855826 -0.156241578  0.26559348 -0.005863832  0.0552988754
Radio            -0.04188735  0.013791402  0.013661103  0.02099814 -0.014600244 -0.0003610891
Sport_Model       0.16412096 -0.110988319 -0.044783876 -0.00602665  0.013175336 -0.0351951669
Backseat_Divider  0.10256915 -0.116751059 -0.045657583  0.01090798 -0.018876271 -0.0557108268
Metallic_Rim      0.10856398 -0.040045378 -0.013598770  0.20678416 -0.078094651  0.0032356199
Tow_Bar          -0.17236860  0.188719528  0.084153196  0.06827127  0.018785917  0.0027246074
Fuel_Type_CNG    -0.03953628  0.002389211  0.144015820  0.06210886  0.001485673  0.0059408788
Fuel_Type_Petrol -0.03851641  0.092610587 -0.433159608  0.48911029  0.080248901 -0.3151700204
                 Quarterly_Tax       Weight Mfr_Guarantee BOVAG_Guarantee Guarantee_Period         ABS
Price              0.219196911  0.581197589   0.197801991     0.028133044      0.146626614  0.30613784
Age_08_04         -0.198430508 -0.470253184  -0.164658304     0.006864920     -0.152562534 -0.41288731
KM                 0.278164697 -0.028598457  -0.212850802     0.001437579     -0.138941822 -0.17720338
HP                -0.298431717  0.089614059   0.140026308     0.022700778      0.076162697  0.05783181
Automatic         -0.055370791  0.057248510   0.026193798     0.023393188     -0.002256229 -0.01612817
cc                 0.306995798  0.335637399  -0.057406568    -0.081725093     -0.017682946  0.03780560
Quarterly_Tax      1.000000000  0.626133733  -0.022150154     0.094330856     -0.163438345  0.08028775
Weight             0.626133733  1.000000000  -0.008564636    -0.056076982     -0.012913462  0.10261557
Mfr_Guarantee     -0.022150154 -0.008564636   1.000000000     0.233458589     -0.098563061  0.11899626
BOVAG_Guarantee    0.094330856 -0.056076982   0.233458589     1.000000000     -0.300062902  0.13444124
Guarantee_Period  -0.163438345 -0.012913462  -0.098563061    -0.300062902      1.000000000 -0.06083998
ABS                0.080287748  0.102615574   0.118996262     0.134441245     -0.060839975  1.00000000
Airco              0.118225262  0.310061953   0.051233618     0.005708771      0.026246244  0.22609484
Automatic_airco    0.123125182  0.430478501   0.072634969    -0.015188469     -0.039162519  0.11711670
Boardcomputer      0.141534096  0.274324106   0.198185513     0.115804372     -0.056305124  0.30953619
Powered_Windows    0.003826656  0.213356016   0.041550927    -0.012405873      0.040533587  0.09946502
Radio             -0.031816260 -0.038407372  -0.052057575    -0.039074859      0.198885599 -0.05466987
Sport_Model        0.067525190  0.125973890   0.054129415     0.173977808     -0.172873754  0.20059603
Backseat_Divider   0.198418730  0.036446167   0.256249254     0.457468081     -0.484426852  0.25665879
Metallic_Rim      -0.011964548  0.053846741   0.026727922     0.060434301     -0.044002874  0.07915186
Tow_Bar           -0.004987518 -0.074931667  -0.023328109    -0.006718221      0.008590048 -0.06597649
Fuel_Type_CNG      0.233790610  0.052756475  -0.012582787    -0.025771346     -0.010401810 -0.03019669
Fuel_Type_Petrol  -0.835451672 -0.560470265   0.150159949     0.056331507      0.065736744 -0.02257050
                        Airco Automatic_airco Boardcomputer Powered_Windows         Radio   Sport_Model
Price             0.429259430      0.58826200  0.6012919565    0.3565182258 -0.0418873522  0.1641209622
Age_08_04        -0.403600048     -0.42625915 -0.7194487099   -0.2838558256  0.0137914024 -0.1109883188
KM               -0.133056812     -0.25822149 -0.3538622479   -0.1562415784  0.0136611034 -0.0447838761
HP                0.241134272      0.24495736  0.1297147413    0.2655934848  0.0209981381 -0.0060266503
Automatic        -0.028352763      0.05905661 -0.0370685613   -0.0058638318 -0.0146002437  0.0131753360
cc                0.119888052      0.16266883  0.0093119139    0.0552988754 -0.0003610891 -0.0351951669
Quarterly_Tax     0.118225262      0.12312518  0.1415340959    0.0038266562 -0.0318162601  0.0675251905
Weight            0.310061953      0.43047850  0.2743241058    0.2133560160 -0.0384073722  0.1259738904
Mfr_Guarantee     0.051233618      0.07263497  0.1981855134    0.0415509270 -0.0520575752  0.0541294147
BOVAG_Guarantee   0.005708771     -0.01518847  0.1158043718   -0.0124058729 -0.0390748594  0.1739778084
Guarantee_Period  0.026246244     -0.03916252 -0.0563051243    0.0405335874  0.1988855994 -0.1728737542
ABS               0.226094835      0.11711670  0.3095361928    0.0994650204 -0.0546698668  0.2005960321
Airco             1.000000000      0.24044391  0.2932442060    0.5439817486 -0.0305710644  0.0027302616
Automatic_airco   0.240443910      1.00000000  0.2724152210    0.2036869067 -0.0926473776  0.2152873511
Boardcomputer     0.293244206      0.27241522  1.0000000000    0.2133274783 -0.1290936057  0.0368018520
Powered_Windows   0.543981749      0.20368691  0.2133274783    1.0000000000 -0.0358111799 -0.0006504532
Radio            -0.030571064     -0.09264738 -0.1290936057   -0.0358111799  1.0000000000 -0.1377287584
Sport_Model       0.002730262      0.21528735  0.0368018520   -0.0006504532 -0.1377287584  1.0000000000
Backseat_Divider  0.105148873      0.01875632  0.2876149262    0.0782437522 -0.2095898260  0.3577132365
Metallic_Rim      0.233166104      0.10036278 -0.0249987520    0.2914194137 -0.0341621429  0.0518101200
Tow_Bar          -0.024361999     -0.11796686 -0.1280011466   -0.0132515099  0.1436522639 -0.0941471363
Fuel_Type_CNG     0.017488605     -0.02676123 -0.0001081937   -0.0071843814  0.0093645265 -0.0576304085
Fuel_Type_Petrol -0.036733500     -0.03995545 -0.0203918636    0.0893076003 -0.0051397374  0.0309964827
                 Backseat_Divider Metallic_Rim      Tow_Bar Fuel_Type_CNG Fuel_Type_Petrol
Price                  0.10256915   0.10856398 -0.172368602 -0.0395362811     -0.038516409
Age_08_04             -0.11675106  -0.04004538  0.188719528  0.0023892110      0.092610587
KM                    -0.04565758  -0.01359877  0.084153196  0.1440158195     -0.433159608
HP                     0.01090798   0.20678416  0.068271274  0.0621088646      0.489110288
Automatic             -0.01887627  -0.07809465  0.018785917  0.0014856725      0.080248901
cc                    -0.05571083   0.00323562  0.002724607  0.0059408788     -0.315170020
Quarterly_Tax          0.19841873  -0.01196455 -0.004987518  0.2337906099     -0.835451672
Weight                 0.03644617   0.05384674 -0.074931667  0.0527564752     -0.560470265
Mfr_Guarantee          0.25624925   0.02672792 -0.023328109 -0.0125827868      0.150159949
BOVAG_Guarantee        0.45746808   0.06043430 -0.006718221 -0.0257713458      0.056331507
Guarantee_Period      -0.48442685  -0.04400287  0.008590048 -0.0104018096      0.065736744
ABS                    0.25665879   0.07915186 -0.065976495 -0.0301966909     -0.022570502
Airco                  0.10514887   0.23316610 -0.024361999  0.0174886051     -0.036733500
Automatic_airco        0.01875632   0.10036278 -0.117966859 -0.0267612333     -0.039955448
Boardcomputer          0.28761493  -0.02499875 -0.128001147 -0.0001081937     -0.020391864
Powered_Windows        0.07824375   0.29141941 -0.013251510 -0.0071843814      0.089307600
Radio                 -0.20958983  -0.03416214  0.143652264  0.0093645265     -0.005139737
Sport_Model            0.35771324   0.05181012 -0.094147136 -0.0576304085      0.030996483
Backseat_Divider       1.00000000   0.10486232 -0.049175675 -0.0473400119      0.053391920
Metallic_Rim           0.10486232   1.00000000 -0.037330986  0.0402018637      0.059605905
Tow_Bar               -0.04917567  -0.03733099  1.000000000  0.0327207640      0.042090434
Fuel_Type_CNG         -0.04734001   0.04020186  0.032720764  1.0000000000     -0.296717101
Fuel_Type_Petrol       0.05339192   0.05960590  0.042090434 -0.2967171005      1.000000000

Busqueda de posible Colinealidad

imcdiag(select(data_set_1, -c("Price")), data_set_1$Price)

Call:
imcdiag(x = select(data_set_1, -c("Price")), y = data_set_1$Price)


All Individual Multicollinearity Diagnostics Result

                    VIF    TOL       Wi       Fi Leamer    CVIF Klein
Age_08_04        4.3590 0.2294 226.1754 237.6521 0.4790 -0.2340     0
KM               2.0563 0.4863  71.1230  74.7319 0.6974 -0.1104     0
HP               2.3954 0.4175  93.9552  98.7227 0.6461 -0.1286     0
Automatic        1.0877 0.9194   5.9040   6.2035 0.9588 -0.0584     0
cc               1.2468 0.8021  16.6180  17.4612 0.8956 -0.0669     0
Quarterly_Tax    4.9128 0.2036 263.4604 276.8290 0.4512 -0.2637     0
Weight           3.5150 0.2845 169.3437 177.9366 0.5334 -0.1887     0
Mfr_Guarantee    1.1665 0.8573  11.2120  11.7810 0.9259 -0.0626     0
BOVAG_Guarantee  1.3502 0.7406  23.5826  24.7792 0.8606 -0.0725     0
Guarantee_Period 1.5054 0.6643  34.0311  35.7579 0.8150 -0.0808     0
ABS              1.3685 0.7307  24.8104  26.0694 0.8548 -0.0734     0
Airco            1.6779 0.5960  45.6446  47.9607 0.7720 -0.0901     0
Automatic_airco  1.5320 0.6527  35.8214  37.6391 0.8079 -0.0822     0
Boardcomputer    2.5231 0.3963 102.5527 107.7565 0.6296 -0.1354     0
Powered_Windows  1.5612 0.6405  37.7894  39.7069 0.8003 -0.0838     0
Radio            1.1215 0.8917   8.1779   8.5929 0.9443 -0.0602     0
Sport_Model      1.3315 0.7510  22.3216  23.4542 0.8666 -0.0715     0
Backseat_Divider 2.2185 0.4508  82.0467  86.2099 0.6714 -0.1191     0
Metallic_Rim     1.1816 0.8463  12.2252  12.8455 0.9200 -0.0634     0
Tow_Bar          1.0956 0.9128   6.4349   6.7614 0.9554 -0.0588     0
Fuel_Type_CNG    1.3667 0.7317  24.6919  25.9448 0.8554 -0.0734     0
Fuel_Type_Petrol 7.8849 0.1268 463.5805 487.1037 0.3561 -0.4232     0

1 --> COLLINEARITY is detected by the test 
0 --> COLLINEARITY is not detected by the test

Automatic , cc , Boardcomputer , Radio , coefficient(s) are non-significant may be due to multicollinearity

R-square of y on all x: 0.9005 

* use method argument to check which regressors may be the reason of collinearity
===================================

Tras la selección de atributos, aparentemente se resolvio el problema de colinealidad sobre el dataSet 1.

Outliers

Visualizacion de Outliers

par(mfrow=c(1,2))
boxplot(data_set_1$Price, main="price")
boxplot(data_set_1$KM, main="KM")

par(mfrow=c(1,2))
boxplot(data_set_1$Weight, main="Weight")
boxplot(data_set_1$HP, main="HP")

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.

data_set_1[which(data_set_1$cc == 16000), "cc"] <- 1600
data_set_1[which(data_set_1$Guarantee_Period == 13), "Guarantee_Period"] <- 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%.

data_set_1 = data_set_1 %>% filter((data_set_1$KM > 10000 & data_set_1$KM < 120000))
data_set_1 = data_set_1 %>% filter(data_set_1$Weight < 1150)

• 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.

data_set_1 = data_set_1 %>% filter(data_set_1$Age_08_04 > 25)
data_set_1 = data_set_1 %>% filter(data_set_1$HP < 120 & data_set_1$HP > 80)

• 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.
  
• El dataset restante posee un 72% de las instancias del dataset original.

data_set_1 = data_set_1 %>% filter(data_set_1$Price > 6500 & data_set_1$Price < 14500)

Visualizacion post tratamiento de outliers

par(mfrow=c(1,2))
boxplot(data_set_1$Price, main="price")
boxplot(data_set_1$KM, main="KM")

par(mfrow=c(1,2))
boxplot(data_set_1$Weight, main="Weight")
boxplot(data_set_1$HP, main="HP")

Estudio de correlacion post selección de atributos 1°

corrplot(cor(data_set_1), type="upper", method="pie")

cor(data_set_1)

                        Price   Age_08_04           KM           HP     Automatic           cc
Price             1.000000000 -0.81086438 -0.435235606  0.239783342  0.0237901939  0.210977921
Age_08_04        -0.810864381  1.00000000  0.397917080 -0.126926355  0.0712622678 -0.083829576
KM               -0.435235606  0.39791708  1.000000000  0.028951107 -0.0544686728  0.049562785
HP                0.239783342 -0.12692636  0.028951107  1.000000000 -0.0650888935  0.994410006
Automatic         0.023790194  0.07126227 -0.054468673 -0.065088893  1.0000000000 -0.033880839
cc                0.210977921 -0.08382958  0.049562785  0.994410006 -0.0338808390  1.000000000
Quarterly_Tax     0.173941104 -0.11326464  0.046061595  0.232331268 -0.0054740273  0.230926217
Weight            0.307188125 -0.12668928  0.024109991  0.680511130  0.1857467403  0.685818658
Mfr_Guarantee     0.209950366 -0.16307255 -0.048186377  0.035914774  0.0170620003  0.033505374
BOVAG_Guarantee   0.095236152 -0.05372062 -0.017835157 -0.005639483  0.0138840169 -0.009814461
Guarantee_Period  0.074821866 -0.02608321 -0.028775942  0.021439871  0.0282380708  0.019553773
ABS               0.342044231 -0.43348939 -0.119286718  0.068129936 -0.0196186920  0.051396197
Airco             0.386881506 -0.27148013 -0.004902131  0.321174563 -0.0438821897  0.317986513
Automatic_airco  -0.001912387  0.02333268  0.006127251  0.033721110  0.0327451085  0.031109680
Boardcomputer     0.550072533 -0.65778398 -0.267149783  0.103867288 -0.0795007521  0.061005976
Powered_Windows   0.214774868 -0.07853545  0.050774834  0.237633841 -0.0119825576  0.243497709
Radio             0.031718411 -0.05495276  0.007948905  0.043575090  0.0004786372  0.038732273
Sport_Model      -0.250139747  0.22645226  0.119482811 -0.101201424  0.0091588378 -0.077899171
Backseat_Divider  0.137403685 -0.15616546 -0.033824004  0.013955368 -0.0495385171  0.010900605
Metallic_Rim      0.047770538  0.02854947  0.049458769  0.105356647 -0.0787599589  0.109304126
Tow_Bar          -0.062610185  0.07429896  0.045145220  0.143090217  0.0119462953  0.147782724
Fuel_Type_CNG     0.026799745 -0.05117355  0.080712160  0.058240636  0.0226909697  0.058867811
Fuel_Type_Petrol -0.026799745  0.05117355 -0.080712160 -0.058240636 -0.0226909697 -0.058867811
                 Quarterly_Tax      Weight Mfr_Guarantee BOVAG_Guarantee Guarantee_Period         ABS
Price              0.173941104  0.30718812   0.209950366    0.0952361518       0.07482187  0.34204423
Age_08_04         -0.113264643 -0.12668928  -0.163072546   -0.0537206180      -0.02608321 -0.43348939
KM                 0.046061595  0.02410999  -0.048186377   -0.0178351571      -0.02877594 -0.11928672
HP                 0.232331268  0.68051113   0.035914774   -0.0056394828       0.02143987  0.06812994
Automatic         -0.005474027  0.18574674   0.017062000    0.0138840169       0.02823807 -0.01961869
cc                 0.230926217  0.68581866   0.033505374   -0.0098144607       0.01955377  0.05139620
Quarterly_Tax      1.000000000  0.32848864   0.175256650    0.1603729376      -0.16520159  0.07077024
Weight             0.328488641  1.00000000   0.030339916   -0.0273485931       0.00397248  0.07342586
Mfr_Guarantee      0.175256650  0.03033992   1.000000000    0.2251127899      -0.07943866  0.11808102
BOVAG_Guarantee    0.160372938 -0.02734859   0.225112790    1.0000000000      -0.29857430  0.13094973
Guarantee_Period  -0.165201593  0.00397248  -0.079438656   -0.2985742987       1.00000000 -0.14787809
ABS                0.070770239  0.07342586   0.118081020    0.1309497298      -0.14787809  1.00000000
Airco              0.099036881  0.32482993   0.022658162    0.0104244215      -0.03614292  0.20488068
Automatic_airco   -0.238162545  0.06933205  -0.068155096   -0.0195238487       0.02646674  0.03817055
Boardcomputer      0.137186814  0.07200263   0.162696204    0.1051130583      -0.15057739  0.26559356
Powered_Windows    0.095237718  0.26654767  -0.026077572   -0.0002696174      -0.02657053  0.06950573
Radio             -0.057094414  0.02689977  -0.046382255   -0.0211878890       0.23932909 -0.02765671
Sport_Model        0.003388081 -0.07721750  -0.002711477    0.1277471579      -0.17828211  0.15465659
Backseat_Divider   0.332765087  0.08129328   0.230440807    0.3980766666      -0.58692617  0.28544272
Metallic_Rim       0.114696229  0.11499733   0.012205084    0.0671345412      -0.07408261  0.09823569
Tow_Bar            0.085564984  0.10877411  -0.008820041   -0.0469709756       0.06247537 -0.03141409
Fuel_Type_CNG      0.528301627  0.18852759   0.032082482   -0.0098909747      -0.01384006  0.01659740
Fuel_Type_Petrol  -0.528301627 -0.18852759  -0.032082482    0.0098909747       0.01384006 -0.01659740
                        Airco Automatic_airco Boardcomputer Powered_Windows         Radio  Sport_Model
Price             0.386881506    -0.001912387   0.550072533    0.2147748682  0.0317184108 -0.250139747
Age_08_04        -0.271480134     0.023332684  -0.657783975   -0.0785354480 -0.0549527641  0.226452262
KM               -0.004902131     0.006127251  -0.267149783    0.0507748340  0.0079489050  0.119482811
HP                0.321174563     0.033721110   0.103867288    0.2376338410  0.0435750903 -0.101201424
Automatic        -0.043882190     0.032745108  -0.079500752   -0.0119825576  0.0004786372  0.009158838
cc                0.317986513     0.031109680   0.061005976    0.2434977092  0.0387322731 -0.077899171
Quarterly_Tax     0.099036881    -0.238162545   0.137186814    0.0952377179 -0.0570944140  0.003388081
Weight            0.324829931     0.069332045   0.072002628    0.2665476676  0.0268997746 -0.077217496
Mfr_Guarantee     0.022658162    -0.068155096   0.162696204   -0.0260775725 -0.0463822553 -0.002711477
BOVAG_Guarantee   0.010424422    -0.019523849   0.105113058   -0.0002696174 -0.0211878890  0.127747158
Guarantee_Period -0.036142923     0.026466740  -0.150577387   -0.0265705336  0.2393290909 -0.178282113
ABS               0.204880681     0.038170548   0.265593557    0.0695057285 -0.0276567128  0.154656588
Airco             1.000000000     0.083659806   0.175476309    0.5195104818 -0.0115375896 -0.109702801
Automatic_airco   0.083659806     1.000000000  -0.040453927    0.0462194895 -0.0324294737 -0.041815756
Boardcomputer     0.175476309    -0.040453927   1.000000000    0.0791329013 -0.0512018641 -0.246803158
Powered_Windows   0.519510482     0.046219490   0.079132901    1.0000000000 -0.0343132382 -0.111716998
Radio            -0.011537590    -0.032429474  -0.051201864   -0.0343132382  1.0000000000 -0.068285872
Sport_Model      -0.109702801    -0.041815756  -0.246803158   -0.1117169977 -0.0682858722  1.000000000
Backseat_Divider  0.101972512    -0.140561686   0.260042283    0.0749633565 -0.1841207075  0.297490425
Metallic_Rim      0.259695833    -0.006077912  -0.059793611    0.2983940303 -0.0640819666  0.053682400
Tow_Bar           0.015445477    -0.051941036  -0.056341978    0.0388232637  0.1414457236 -0.054361558
Fuel_Type_CNG    -0.013941585    -0.006719890   0.006459918   -0.0054442252 -0.0068953966 -0.048331531
Fuel_Type_Petrol  0.013941585     0.006719890  -0.006459918    0.0054442252  0.0068953966  0.048331531
                 Backseat_Divider Metallic_Rim      Tow_Bar Fuel_Type_CNG Fuel_Type_Petrol
Price                  0.13740368  0.047770538 -0.062610185   0.026799745     -0.026799745
Age_08_04             -0.15616546  0.028549466  0.074298962  -0.051173550      0.051173550
KM                    -0.03382400  0.049458769  0.045145220   0.080712160     -0.080712160
HP                     0.01395537  0.105356647  0.143090217   0.058240636     -0.058240636
Automatic             -0.04953852 -0.078759959  0.011946295   0.022690970     -0.022690970
cc                     0.01090061  0.109304126  0.147782724   0.058867811     -0.058867811
Quarterly_Tax          0.33276509  0.114696229  0.085564984   0.528301627     -0.528301627
Weight                 0.08129328  0.114997327  0.108774110   0.188527589     -0.188527589
Mfr_Guarantee          0.23044081  0.012205084 -0.008820041   0.032082482     -0.032082482
BOVAG_Guarantee        0.39807667  0.067134541 -0.046970976  -0.009890975      0.009890975
Guarantee_Period      -0.58692617 -0.074082614  0.062475366  -0.013840061      0.013840061
ABS                    0.28544272  0.098235694 -0.031414086   0.016597398     -0.016597398
Airco                  0.10197251  0.259695833  0.015445477  -0.013941585      0.013941585
Automatic_airco       -0.14056169 -0.006077912 -0.051941036  -0.006719890      0.006719890
Boardcomputer          0.26004228 -0.059793611 -0.056341978   0.006459918     -0.006459918
Powered_Windows        0.07496336  0.298394030  0.038823264  -0.005444225      0.005444225
Radio                 -0.18412071 -0.064081967  0.141445724  -0.006895397      0.006895397
Sport_Model            0.29749043  0.053682400 -0.054361558  -0.048331531      0.048331531
Backseat_Divider       1.00000000  0.143134542 -0.070141379  -0.057328375      0.057328375
Metallic_Rim           0.14313454  1.000000000 -0.048242624   0.011388982     -0.011388982
Tow_Bar               -0.07014138 -0.048242624  1.000000000   0.010994168     -0.010994168
Fuel_Type_CNG         -0.05732837  0.011388982  0.010994168   1.000000000     -1.000000000
Fuel_Type_Petrol       0.05732837 -0.011388982 -0.010994168  -1.000000000      1.000000000

Busqueda de posible Colinealidad post selección de atributos 1°

imcdiag(select(data_set_1, -c("Price")), data_set_1$Price)

Call:
imcdiag(x = select(data_set_1, -c("Price")), y = data_set_1$Price)


All Individual Multicollinearity Diagnostics Result

                      VIF    TOL        Wi        Fi Leamer     CVIF Klein
Age_08_04          2.6390 0.3789   79.2976   83.3444 0.6156  -0.7420     0
KM                 1.2469 0.8020   11.9448   12.5544 0.8955  -0.3506     0
HP               129.7755 0.0077 6230.2792 6548.2319 0.0878 -36.4900     1
Automatic          1.2580 0.7949   12.4844   13.1215 0.8916  -0.3537     0
cc               128.6272 0.0078 6174.7277 6489.8455 0.0882 -36.1671     1
Quarterly_Tax      2.0672 0.4837   51.6322   54.2671 0.6955  -0.5813     0
Weight             2.3868 0.4190   67.0938   70.5179 0.6473  -0.6711     0
Mfr_Guarantee      1.1312 0.8840    6.3459    6.6698 0.9402  -0.3181     0
BOVAG_Guarantee    1.2600 0.7937   12.5771   13.2189 0.8909  -0.3543     0
Guarantee_Period   1.6754 0.5969   32.6776   34.3453 0.7726  -0.4711     0
ABS                1.4314 0.6986   20.8739   21.9392 0.8358  -0.4025     0
Airco              1.6383 0.6104   30.8836   32.4597 0.7813  -0.4607     0
Automatic_airco    1.1419 0.8758    6.8630    7.2132 0.9358  -0.3211     0
Boardcomputer      2.0898 0.4785   52.7273   55.4182 0.6917  -0.5876     0
Powered_Windows    1.4851 0.6734   23.4685   24.6661 0.8206  -0.4176     0
Radio              1.1107 0.9003    5.3574    5.6308 0.9488  -0.3123     0
Sport_Model        1.3852 0.7219   18.6381   19.5893 0.8496  -0.3895     0
Backseat_Divider   2.4211 0.4130   68.7544   72.2632 0.6427  -0.6808     0
Metallic_Rim       1.1840 0.8446    8.8999    9.3541 0.9190  -0.3329     0
Tow_Bar            1.0760 0.9293    3.6781    3.8658 0.9640  -0.3026     0
Fuel_Type_CNG         Inf 0.0000       Inf       Inf 0.0000     -Inf     1
Fuel_Type_Petrol      Inf 0.0000       Inf       Inf 0.0000     -Inf     1

1 --> COLLINEARITY is detected by the test 
0 --> COLLINEARITY is not detected by the test

Automatic , ABS , Automatic_airco , Boardcomputer , Radio , Backseat_Divider , Metallic_Rim , coefficient(s) are non-significant may be due to multicollinearity

R-square of y on all x: 0.7643 

* use method argument to check which regressors may be the reason of collinearity
===================================

Modelo de Regresión Lineal post selección de atributos 1°

linearMod_1 <- lm(formula = Price ~ ., data=data_set_1)
summary(linearMod_1)

Call:
lm(formula = Price ~ ., data = data_set_1)

Residuals:
    Min      1Q  Median      3Q     Max 
-2603.7  -535.6   -20.1   524.1  3341.5 

Coefficients: (1 not defined because of singularities)
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       1.344e+03  1.551e+03   0.867  0.38622    
Age_08_04        -8.830e+01  3.328e+00 -26.536  < 2e-16 ***
KM               -1.188e-02  1.246e-03  -9.534  < 2e-16 ***
HP               -7.426e+01  3.009e+01  -2.468  0.01376 *  
Automatic         1.582e+02  1.212e+02   1.305  0.19224    
cc                5.497e+00  2.333e+00   2.356  0.01868 *  
Quarterly_Tax     6.516e+00  2.114e+00   3.082  0.00211 ** 
Weight            1.194e+01  1.647e+00   7.251 8.20e-13 ***
Mfr_Guarantee     2.396e+02  5.605e+01   4.275 2.09e-05 ***
BOVAG_Guarantee   3.981e+02  1.014e+02   3.924 9.28e-05 ***
Guarantee_Period  6.801e+01  1.519e+01   4.478 8.40e-06 ***
ABS              -5.034e+00  7.826e+01  -0.064  0.94873    
Airco             3.860e+02  6.732e+01   5.734 1.29e-08 ***
Automatic_airco   1.406e+02  3.691e+02   0.381  0.70334    
Boardcomputer     1.521e+02  9.143e+01   1.663  0.09655 .  
Powered_Windows   2.034e+02  6.394e+01   3.182  0.00151 ** 
Radio            -6.234e+01  7.662e+01  -0.814  0.41603    
Sport_Model      -1.919e+02  7.309e+01  -2.625  0.00879 ** 
Backseat_Divider -6.167e+01  9.720e+01  -0.634  0.52596    
Metallic_Rim      4.031e+01  7.143e+01   0.564  0.57266    
Tow_Bar          -1.257e+02  5.837e+01  -2.153  0.03154 *  
Fuel_Type_CNG    -1.232e+03  3.819e+02  -3.225  0.00130 ** 
Fuel_Type_Petrol         NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 843.6 on 1016 degrees of freedom
Multiple R-squared:  0.7643,    Adjusted R-squared:  0.7594 
F-statistic: 156.9 on 21 and 1016 DF,  p-value: < 2.2e-16

Plot Residuos

par(mfrow=c(2,2))
plot(linearMod_1)

Plot Residuos: Histograma

residuos = resid(linearMod_1)
hist(residuos, col = "blue", freq = F)
lines(density(residuos), col = "red", lwd=2)

rug(residuos)

Seleccion de Variables 2°

• Se eliminan los atributos “Fuel_Type_Petrol”, “Fuel_Type_CNG”, “Automatic” , “Quarterly_Tax” , “ABS” , “Automatic_airco” , “Boardcomputer” , “Radio” , “Backseat_Divider” , “Metallic_Rim”, “HP”, “cc”, “Tow_Bar”, “Sport_Model”, “BOVAG_Guarantee”, “Guarantee_Period” debido a la poca relevancia que tienen sobre el modelo, basado en su T Value.

data_set_2 <- select(data_set_1, -c("Fuel_Type_Petrol", "Fuel_Type_CNG", "Automatic" , "Quarterly_Tax" , "ABS" , "Automatic_airco" , "Boardcomputer" , "Radio" , "Backseat_Divider" , "Metallic_Rim", "HP", "cc", "Tow_Bar", "Sport_Model", "BOVAG_Guarantee", "Guarantee_Period"))

Estudio de correlacion post selección de atributos 2°

corrplot(cor(data_set_2), type="upper", method="pie")

cor(data_set_2)

                     Price   Age_08_04           KM      Weight Mfr_Guarantee        Airco
Price            1.0000000 -0.81086438 -0.435235606  0.30718812    0.20995037  0.386881506
Age_08_04       -0.8108644  1.00000000  0.397917080 -0.12668928   -0.16307255 -0.271480134
KM              -0.4352356  0.39791708  1.000000000  0.02410999   -0.04818638 -0.004902131
Weight           0.3071881 -0.12668928  0.024109991  1.00000000    0.03033992  0.324829931
Mfr_Guarantee    0.2099504 -0.16307255 -0.048186377  0.03033992    1.00000000  0.022658162
Airco            0.3868815 -0.27148013 -0.004902131  0.32482993    0.02265816  1.000000000
Powered_Windows  0.2147749 -0.07853545  0.050774834  0.26654767   -0.02607757  0.519510482
                Powered_Windows
Price                0.21477487
Age_08_04           -0.07853545
KM                   0.05077483
Weight               0.26654767
Mfr_Guarantee       -0.02607757
Airco                0.51951048
Powered_Windows      1.00000000

Busqueda de posible Colinealidad post selección de atributos 2°

imcdiag(select(data_set_2, -c("Price")), data_set_2$Price)

Call:
imcdiag(x = select(data_set_2, -c("Price")), y = data_set_2$Price)


All Individual Multicollinearity Diagnostics Result

                   VIF    TOL       Wi       Fi Leamer    CVIF Klein
Age_08_04       1.3418 0.7453  70.5517  88.2751 0.8633 -1.8736     0
KM              1.2090 0.8271  43.1341  53.9699 0.9095 -1.6881     0
Weight          1.1405 0.8768  28.9939  36.2775 0.9364 -1.5924     0
Mfr_Guarantee   1.0299 0.9710   6.1715   7.7218 0.9854 -1.4380     0
Airco           1.5512 0.6447 113.7681 142.3479 0.8029 -2.1659     0
Powered_Windows 1.4023 0.7131  83.0291 103.8869 0.8445 -1.9580     0

1 --> COLLINEARITY is detected by the test 
0 --> COLLINEARITY is not detected by the test

* all coefficients have significant t-ratios

R-square of y on all x: 0.747 

* use method argument to check which regressors may be the reason of collinearity
===================================

Modelo de Regresión Lineal post selección de atributos 2°

linearMod_2 <- lm(formula = Price ~ ., data=data_set_2)
summary(linearMod_2)

Call:
lm(formula = Price ~ ., data = data_set_2)

Residuals:
    Min      1Q  Median      3Q     Max 
-2917.3  -567.6    -3.0   569.4  3284.0 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)      3.231e+03  1.237e+03   2.611 0.009167 ** 
Age_08_04       -9.037e+01  2.440e+00 -37.034  < 2e-16 ***
KM              -1.252e-02  1.262e-03  -9.917  < 2e-16 ***
Weight           1.182e+01  1.171e+00  10.100  < 2e-16 ***
Mfr_Guarantee    2.988e+02  5.500e+01   5.433 6.92e-08 ***
Airco            3.799e+02  6.736e+01   5.640 2.20e-08 ***
Powered_Windows  2.436e+02  6.389e+01   3.813 0.000145 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 867.5 on 1031 degrees of freedom
Multiple R-squared:  0.747, Adjusted R-squared:  0.7455 
F-statistic: 507.4 on 6 and 1031 DF,  p-value: < 2.2e-16

A partir de este modelo de regresión lineal, observo lo siguiente:

• El precio base de un vehiculo es de 3.231e+03.
  
• El modelo tiene un accuracy de 0.747, que es un valor notablemente menor al primer modelo. Sin embargo, tras las selecciones de variables, es posible que no sufra problemas de colinealidad.

Plot Residuos

par(mfrow=c(2,2))
plot(linearMod_2)

A partir de este modelo de regresión lineal, observo lo siguiente:

• En el grafico Residuals vs Fitted se observa una curva, casi recta, que tiende a cero, que es lo deseable.
  
• En el grafico Normal Q-Q se observa que la mayoria de los puntos se adecuan a la recta, posiblemente sea necesario retrabajo del dataSet.
  
• En el grafico Scale-Location se observa una curva, casi recta, que tiende a cero, que es lo deseable. Posiblemente sea necesario retrabajo del dataSet.
  
• En el grafico Residuals vs Leverage se observa que todos los valores se encuentran dentro de la distancia de Cook, lo cual es lo deseable. Sin embargo posiblemente haya que realizar observaciones sobre los puntos 690 y 1035. Lo cual quizas tenga que implicar un retrabajo.

Plot Residuos: Histograma

residuos = resid(linearMod_2)
hist(residuos, col = "blue", freq = F)
lines(density(residuos), col = "red", lwd=2)

rug(residuos)

El Histograma de los residuos muestra una distribución muy similar a la distribucion normal, lo cual es deseable.