Competencia en Kaggle - California

María De Los Ángeles & Alejandro Llamas

Video en YouTube

1. Definición del problema

Se nos proporcionó dos datasets correspondientes al Censo de Vivienda en el estado de California de 1990. Cada una de las observaciones representa un conjunto de hogares.

El objetivo del mismo es llegar a predecir el valor medio del conjunto de hogares (median_house_value) utilizando métodos de regresión lineal.

El dataset de entrenamiento consta de 14,447 observaciones y 11 variables.

df = read.csv("train.csv")
df

df_test = read.csv("test.csv")

1.1. Breve análisis

#Breve análisis
summary(df)

       id          longitude         latitude     housing_median_age  total_rooms    total_bedrooms     population      households    
 Min.   :    2   Min.   :-124.3   Min.   :32.54   Min.   : 1.00      Min.   :    6   Min.   :   2.0   Min.   :    3   Min.   :   2.0  
 1st Qu.: 5204   1st Qu.:-121.8   1st Qu.:33.94   1st Qu.:18.00      1st Qu.: 1450   1st Qu.: 297.0   1st Qu.:  791   1st Qu.: 281.0  
 Median :10344   Median :-118.5   Median :34.26   Median :29.00      Median : 2131   Median : 436.0   Median : 1170   Median : 410.0  
 Mean   :10335   Mean   :-119.6   Mean   :35.63   Mean   :28.73      Mean   : 2629   Mean   : 536.6   Mean   : 1422   Mean   : 498.6  
 3rd Qu.:15502   3rd Qu.:-118.0   3rd Qu.:37.71   3rd Qu.:37.00      3rd Qu.: 3149   3rd Qu.: 646.0   3rd Qu.: 1722   3rd Qu.: 604.5  
 Max.   :20640   Max.   :-114.3   Max.   :41.95   Max.   :52.00      Max.   :39320   Max.   :6445.0   Max.   :28566   Max.   :6082.0  
                                                                                     NA's   :144                                      
 median_income     median_house_value ocean_proximity   
 Min.   : 0.4999   Min.   : 14999     Length:14447      
 1st Qu.: 2.5675   1st Qu.:119400     Class :character  
 Median : 3.5313   Median :178700     Mode  :character  
 Mean   : 3.8725   Mean   :207144                       
 3rd Qu.: 4.7457   3rd Qu.:265600                       
 Max.   :15.0001   Max.   :500001                       
                                                        

• A simple vista, Lat. y Lon. son variables que no agregan valor; son puramente descriptivas.

• La distribución de la variable housing_median_age es casi normal.

• Hasta el momento, total_bedrooms es la única variable que posee NAs.

• Las variables population, households y median_house_value poseen un sesgo positivo. Se podría decir lo mismo de median_income pero la escala es distinta. Se validará mediante una gráfica.

• la variable ocean_proximity es la única categórica.

2. Exploratory Data Analysis

#installed.packages("leaps")
library(ggplot2)
library(dplyr)
library(corrplot)
library(randomForest)
library(mlbench)
library(PerformanceAnalytics)
library(MASS)
library(xgboost)
library(randomForest)

#Creación del data set de pruebas
df_cambios = df
df_cambios

2.1. Latitude

#Densidad de latitude

df %>%
  ggplot(aes(x=latitude, y=..density..))+
  geom_density(fill="blue")+
  theme_minimal()

2.2. Longitud

#Densidad de longitude

df %>%
  ggplot(aes(x=longitude, y=..density..))+
  geom_density(fill="blue")+
  theme_minimal()

• No son valores numéricos sino más bien categóricos.

2.3. Housing Median Age

#Densidad de housing_median_age
df %>%
  ggplot(aes(x=housing_median_age))+
  geom_bar()+
  theme_minimal()

#Intento de normalizar la data / tentativo a borrarse


#df_normal = data.frame(row.names = 1:14447)
#df_normal

#library(dlookr)

#df_normal$housing_median_age = transform(df$housing_median_age, method = "log+1")
#plot(df_normal$housing_median_age)

#df_normal

2.4. Total Rooms

#Distribución de total_rooms
df %>%
  ggplot(aes(x=total_rooms))+
  geom_bar()+
  theme_minimal()

• Existe un outlier lo cual hace que la gráfica no se aprecie bien.

#Cálculo del IQR
iqr = IQR(df$total_rooms)

#Cálculo del límite inferior y superior
LI_total_rooms = round(quantile(df$total_rooms, prob=0.25) - (iqr * 1.75))
LS_total_rooms = round(quantile(df$total_rooms, prob=0.75) + (iqr * 1.75))

LI_total_rooms

  25% 
-1522 

LS_total_rooms

 75% 
6121 

df_cambios$total_rooms_CP = ifelse(df$total_rooms > LS_total_rooms, LS_total_rooms,
       ifelse(df$total_rooms < LI_total_rooms, LI_total_rooms, df$total_rooms))

df_cambios %>%
  ggplot(aes(x=total_rooms_CP))+
  geom_histogram()+
  theme_minimal()

df %>%
  ggplot(aes(x=total_rooms, y=median_house_value))+
  geom_point(shape="circle", col="green3")+
  theme_minimal()

df_cambios %>%
  ggplot(aes(x=total_rooms_CP, y=median_house_value))+
  geom_point(shape="circle", col="blue3")+
  theme_minimal()

La dispersión es absurda. No hay forma que esta variable pueda explicar el median_house_value.

2.5. Total Bed Rooms

#Distribución de total_bedrooms

df %>%
  ggplot(aes(x=total_bedrooms))+
  geom_bar()+
  theme_minimal()

*Existencia de NAs. Se van a tratar.

df_cambios$total_bedrooms_sinNA = ifelse(is.na(df_cambios$total_bedrooms), median(df_cambios$total_bedrooms, na.rm=T), df_cambios$total_bedrooms)

summary(df_cambios$total_bedrooms_sinNA)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    2.0   298.0   436.0   535.6   642.0  6445.0 

#Nuevo feature sin NAs
df_cambios %>%
  ggplot(aes(x=total_bedrooms_sinNA))+
  geom_histogram(binwidth=50)+
  theme_minimal()

• Existencia de outliers.Se van a tratar.

#Cálculo del IQR
iqr = IQR(df_cambios$total_bedrooms_sinNA)

#Cálculo del límite inferior y superior
LI_total_bedrooms_sinNA = round(quantile(df_cambios$total_bedrooms_sinNA, prob=0.25) - (iqr * 1.75))
LS_total_bedrooms_sinNA = round(quantile(df_cambios$total_bedrooms_sinNA, prob=0.75) + (iqr * 1.75))

LI_total_bedrooms_sinNA

 25% 
-304 

LS_total_bedrooms_sinNA

 75% 
1244 

df_cambios$total_bedrooms_sinNA_CP = ifelse(df_cambios$total_bedrooms_sinNA > LS_total_bedrooms_sinNA, LS_total_bedrooms_sinNA, ifelse(df_cambios$total_bedrooms_sinNA < LI_total_bedrooms_sinNA, LI_total_bedrooms_sinNA, df_cambios$total_bedrooms_sinNA))

df_cambios %>%
  ggplot(aes(x=total_bedrooms_sinNA_CP))+
  geom_histogram()+
  theme_minimal()

#Scatter plot sin NAs
df_cambios %>%
  ggplot(aes(x=total_bedrooms_sinNA, y=median_house_value))+
  geom_point(shape="circle", col="orange3")+
  theme_minimal()

#Scatter plot sin NAs y sin outliers
df_cambios %>%
  ggplot(aes(x=total_bedrooms_sinNA_CP, y=median_house_value))+
  geom_point(shape="circle", col="red3")+
  theme_minimal()

Existe una gran dispersión aún en los datos, ya sea con y sin outliers.

2.6. Population

#Densidad de population

df %>%
  ggplot(aes(x=population))+
  geom_bar()+
  theme_minimal()

*Existencia de outliers. Se van a tratar.

#Cálculo del IQR
iqr = IQR(df$population)

#Cálculo del límite inferior y superior
LI_population = round(quantile(df$population, prob=0.25) - (iqr * 1.75))
LS_population = round(quantile(df$population, prob=0.75) + (iqr * 1.75))

LI_population

 25% 
-838 

LS_population

 75% 
3351 

df_cambios$population_CP = ifelse(df$population > LS_population, LS_population,
       ifelse(df$population < LI_population, LI_population, df$population))

df_cambios %>%
  ggplot(aes(x=total_rooms_CP))+
  geom_histogram()+
  theme_minimal()

df %>%
  ggplot(aes(x=population, y=median_house_value))+
  geom_point(shape="circle", col="green3")+
  theme_minimal()

df_cambios %>%
  ggplot(aes(x=population_CP, y=median_house_value))+
  geom_point(shape="circle", col="blue3")+
  theme_minimal()

Pese a que se trataron los outliers, la data de por sí es bastante dispersa.

2.7. Households

#Distribución de households

df %>%
  ggplot(aes(x=households))+
  geom_bar()+
  theme_minimal()

Existen outliers. Se van a tratar.

#Cálculo del IQR
iqr = IQR(df$households)

#Cálculo del límite inferior y superior
LI_households = round(quantile(df$households, prob=0.25) - (iqr * 1.75))
LS_households = round(quantile(df$households, prob=0.75) + (iqr * 1.75))

LI_households

 25% 
-285 

LS_households

 75% 
1171 

df_cambios$households_CP = ifelse(df$households > LS_households, LS_households,
       ifelse(df$households < LI_households, LI_households, df$households))

df_cambios %>%
  ggplot(aes(x=households_CP))+
  geom_histogram()+
  theme_minimal()

df %>%
  ggplot(aes(x=households, y=median_house_value))+
  geom_point(shape="circle", col="green3")+
  theme_minimal()

df_cambios %>%
  ggplot(aes(x=households_CP, y=median_house_value))+
  geom_point(shape="circle", col="blue3")+
  theme_minimal()

2.8. Median Income

#Densidad de median_income

df %>%
  ggplot(aes(x=median_income, y=..density..))+
  geom_density(fill="red")+
  theme_minimal()

#Cálculo del IQR
iqr = IQR(df$median_income)

#Cálculo del límite inferior y superior
LI_median_income = quantile(df$median_income, prob=0.25) - (iqr * 1.75)
LS_median_income = quantile(df$median_income, prob=0.75) + (iqr * 1.75)

LI_median_income

      25% 
-1.244262 

LS_median_income

     75% 
8.557412 

df_cambios$median_income_CP = ifelse(df$median_income > LS_median_income, LS_median_income, ifelse(df$median_income < LI_median_income, LI_median_income, df$median_income))

df_cambios %>%
  ggplot(aes(x=median_income_CP, y=..density..))+
  geom_density(fill="red")+
  theme_minimal()

df %>%
  ggplot(aes(x=median_income, y=median_house_value))+
  geom_point(shape="circle", col="green3")+
  theme_minimal()

df_cambios %>%
  ggplot(aes(x=median_income_CP, y=median_house_value))+
  geom_point(shape="circle", col="blue3")+
  theme_minimal()

2.9. Median_house_value

#Densidad de median_house_value

df %>%
  ggplot(aes(x=median_house_value, y=..density..))+
  geom_density(fill="red")+
  theme_minimal()

summary(df$median_house_value)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  14999  119400  178700  207144  265600  500001 

iqrt = IQR(df$median_house_value)
iqrt

[1] 146200

quantile(df$median_house_value, prob=0.75) + iqrt*1.75

   75% 
521450 

quantile(df$median_house_value, prob=0.25) - iqrt*1.75

    25% 
-136450 

*No existen outliers en la variable a predecir.

2.10. Ocean_proximity

df %>%
  ggplot(aes(x = ocean_proximity))+
  geom_bar()+
  theme_minimal()

library(caret)

dmy <- dummyVars(" ~ .", data = df_cambios, fullRank = T)
dmy

Dummy Variable Object

Formula: ~.
<environment: 0x00000163390f5dd0>
17 variables, 0 factors
Variables and levels will be separated by '.'
A full rank encoding is used

df_dummies <- data.frame(predict(dmy, newdata = df_cambios))

glimpse(df_dummies)

Rows: 14,447
Columns: 20
$ id                        <dbl> 71, 12792, 12520, 10660, 5215, 10357, 327, 5408, 9212, 12165, 4797, 6403, 1433, 18251, 16859, 7508, 8674, 19784, 1~
$ longitude                 <dbl> -122.29, -121.46, -121.46, -117.81, -118.25, -117.67, -122.19, -118.45, -120.31, -117.22, -118.35, -118.02, -122.0~
$ latitude                  <dbl> 37.81, 38.65, 38.55, 33.67, 33.94, 33.60, 37.73, 34.03, 37.11, 33.74, 34.03, 34.14, 37.99, 37.39, 37.63, 33.91, 33~
$ housing_median_age        <dbl> 26, 8, 52, 24, 44, 25, 45, 41, 38, 7, 43, 34, 37, 39, 39, 42, 35, 20, 25, 18, 9, 47, 20, 32, 13, 10, 8, 19, 15, 21~
$ total_rooms               <dbl> 768, 3746, 2094, 3930, 1463, 3164, 1528, 1240, 1696, 1810, 2122, 1077, 2247, 2210, 4220, 1786, 2152, 3758, 2054, 1~
$ total_bedrooms            <dbl> 152, 767, 463, 661, 312, 449, 291, 320, 301, 386, 524, 257, 416, 483, 1055, 358, 454, 798, 495, 332, 2640, 335, 36~
$ population                <dbl> 392, 2161, 1364, 1831, 940, 1517, 801, 711, 985, 931, 1510, 478, 1237, 1023, 2720, 1318, 902, 1685, 835, 733, 6837~
$ households                <dbl> 127, 744, 407, 616, 312, 453, 287, 304, 278, 355, 436, 199, 397, 450, 1046, 373, 414, 757, 475, 318, 2358, 329, 30~
$ median_income             <dbl> 1.7719, 3.2039, 1.2235, 6.3767, 2.3333, 6.7921, 1.2625, 3.3482, 2.4054, 2.5221, 2.2273, 2.6316, 4.4500, 4.5833, 2.~
$ median_house_value        <dbl> 82500, 103400, 68500, 269000, 99800, 266000, 84700, 318100, 112500, 109200, 123300, 252800, 161900, 342400, 242500~
$ ocean_proximityINLAND     <dbl> 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, ~
$ ocean_proximityISLAND     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ~
$ ocean_proximityNEAR.BAY   <dbl> 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, ~
$ ocean_proximityNEAR.OCEAN <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, ~
$ total_rooms_CP            <dbl> 768, 3746, 2094, 3930, 1463, 3164, 1528, 1240, 1696, 1810, 2122, 1077, 2247, 2210, 4220, 1786, 2152, 3758, 2054, 1~
$ total_bedrooms_sinNA      <dbl> 152, 767, 463, 661, 312, 449, 291, 320, 301, 386, 524, 257, 416, 483, 1055, 358, 454, 798, 495, 332, 2640, 335, 36~
$ total_bedrooms_sinNA_CP   <dbl> 152, 767, 463, 661, 312, 449, 291, 320, 301, 386, 524, 257, 416, 483, 1055, 358, 454, 798, 495, 332, 1244, 335, 36~
$ population_CP             <dbl> 392, 2161, 1364, 1831, 940, 1517, 801, 711, 985, 931, 1510, 478, 1237, 1023, 2720, 1318, 902, 1685, 835, 733, 3351~
$ households_CP             <dbl> 127, 744, 407, 616, 312, 453, 287, 304, 278, 355, 436, 199, 397, 450, 1046, 373, 414, 757, 475, 318, 1171, 329, 30~
$ median_income_CP          <dbl> 1.771900, 3.203900, 1.223500, 6.376700, 2.333300, 6.792100, 1.262500, 3.348200, 2.405400, 2.522100, 2.227300, 2.63~

3. Análisis de correlación

#Gráfico de correlación - df_dummies
df_dummies_corr = df_dummies %>%
  dplyr::select(longitude, latitude, ocean_proximityINLAND:total_rooms_CP, total_bedrooms_sinNA_CP:median_income_CP, median_house_value)

corrplot(cor(df_dummies_corr), method = "color", type = "upper", tl.col="black")

#Ocean Proximity INLAND
df_dummies %>%
  ggplot(aes(x=ocean_proximityINLAND, y=median_house_value))+
  geom_point(shape="circle", col="blue3")+
  theme_minimal()

#Median Income CP
df_cambios %>%
  ggplot(aes(x=median_income_CP, y=median_house_value))+
  geom_point(shape="circle", col="green3")+
  theme_minimal()

#Latitude
df_cambios %>%
  ggplot(aes(x=total_rooms_CP, y=median_house_value))+
  geom_point(shape="circle", col="orange3")+
  theme_minimal()

• En base a las gráficas anteriores y el análisis de correlación, la única variable que vale la pena utilizar sería median_income.

4. División del Data set

#Índice
trainIndex = createDataPartition(df_dummies_corr$median_house_value, p=0.7, list=FALSE )

#Set de entrenamiento
df_trainSet = df_dummies_corr[trainIndex, ]

#Set de prueba
df_testSet = df_dummies_corr[-trainIndex, ]


df_trainSet

df_testSet

5. Selección del modelo

5.1. Modelos lineales

#Explicado por median_income + ocean_proximityINLAND

lm2 = df_trainSet %>%
  lm(formula = median_house_value ~ median_income_CP + ocean_proximityINLAND)

summary(lm2)

Call:
lm(formula = median_house_value ~ median_income_CP + ocean_proximityINLAND, 
    data = .)

Residuals:
    Min      1Q  Median      3Q     Max 
-322576  -48342  -12721   32114  487298 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            73763.6     2046.0   36.05   <2e-16 ***
median_income_CP       41756.3      447.7   93.27   <2e-16 ***
ocean_proximityINLAND -81934.9     1644.8  -49.81   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 74640 on 10112 degrees of freedom
Multiple R-squared:  0.5861,    Adjusted R-squared:  0.5861 
F-statistic:  7161 on 2 and 10112 DF,  p-value: < 2.2e-16

#Explicado por median_income + ocean_proximityINLAND

lm3 = df_trainSet %>%
  lm(formula = median_house_value ~ median_income_CP + ocean_proximityINLAND + total_rooms_CP)

summary(lm3)

Call:
lm(formula = median_house_value ~ median_income_CP + ocean_proximityINLAND + 
    total_rooms_CP, data = .)

Residuals:
    Min      1Q  Median      3Q     Max 
-317082  -48117  -12969   31891  490078 

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
(Intercept)            7.116e+04  2.196e+03  32.400  < 2e-16 ***
median_income_CP       4.137e+04  4.631e+02  89.336  < 2e-16 ***
ocean_proximityINLAND -8.233e+04  1.648e+03 -49.942  < 2e-16 ***
total_rooms_CP         1.705e+00  5.253e-01   3.246  0.00117 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 74610 on 10111 degrees of freedom
Multiple R-squared:  0.5866,    Adjusted R-squared:  0.5865 
F-statistic:  4782 on 3 and 10111 DF,  p-value: < 2.2e-16

#Explicado por median_income + ocean_proximityINLAND + total_rooms_CP + ocean_proximityNEAR.BAY

lm4 = df_trainSet %>%
  lm(formula = median_house_value ~ median_income_CP + ocean_proximityINLAND + total_rooms_CP + ocean_proximityNEAR.BAY)

summary(lm4)

Call:
lm(formula = median_house_value ~ median_income_CP + ocean_proximityINLAND + 
    total_rooms_CP + ocean_proximityNEAR.BAY, data = .)

Residuals:
    Min      1Q  Median      3Q     Max 
-313842  -47823  -12579   31605  490111 

Coefficients:
                          Estimate Std. Error t value Pr(>|t|)    
(Intercept)              6.806e+04  2.226e+03  30.568  < 2e-16 ***
median_income_CP         4.135e+04  4.617e+02  89.556  < 2e-16 ***
ocean_proximityINLAND   -7.925e+04  1.691e+03 -46.870  < 2e-16 ***
total_rooms_CP           1.741e+00  5.238e-01   3.325 0.000888 ***
ocean_proximityNEAR.BAY  1.863e+04  2.407e+03   7.740 1.09e-14 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 74390 on 10110 degrees of freedom
Multiple R-squared:  0.589, Adjusted R-squared:  0.5889 
F-statistic:  3622 on 4 and 10110 DF,  p-value: < 2.2e-16

#Explicado por median_income + ocean_proximityINLAND + total_rooms_CP + ocean_proximityNEAR.BAY + ocean_proximityNEAR.OCEAN

lm4 = df_trainSet %>%
  lm(formula = median_house_value ~ median_income_CP + ocean_proximityINLAND + total_rooms_CP + ocean_proximityNEAR.BAY + ocean_proximityNEAR.OCEAN)

summary(lm4)

Call:
lm(formula = median_house_value ~ median_income_CP + ocean_proximityINLAND + 
    total_rooms_CP + ocean_proximityNEAR.BAY + ocean_proximityNEAR.OCEAN, 
    data = .)

Residuals:
    Min      1Q  Median      3Q     Max 
-310912  -47832  -12008   31906  490458 

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)    
(Intercept)                6.407e+04  2.305e+03  27.798  < 2e-16 ***
median_income_CP           4.149e+04  4.613e+02  89.944  < 2e-16 ***
ocean_proximityINLAND     -7.568e+04  1.775e+03 -42.646  < 2e-16 ***
total_rooms_CP             1.728e+00  5.227e-01   3.306 0.000951 ***
ocean_proximityNEAR.BAY    2.208e+04  2.460e+03   8.974  < 2e-16 ***
ocean_proximityNEAR.OCEAN  1.521e+04  2.339e+03   6.504 8.22e-11 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 74240 on 10109 degrees of freedom
Multiple R-squared:  0.5907,    Adjusted R-squared:  0.5905 
F-statistic:  2918 on 5 and 10109 DF,  p-value: < 2.2e-16

5.2. Interacción entre variables

#Agregamos efecto de interacción
int_lm1 = df_trainSet %>%
  lm(formula = median_house_value ~ median_income_CP*ocean_proximityINLAND)

summary(int_lm1)

Call:
lm(formula = median_house_value ~ median_income_CP * ocean_proximityINLAND, 
    data = .)

Residuals:
    Min      1Q  Median      3Q     Max 
-329727  -46533  -13917   31319  468466 

Coefficients:
                                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)                             65300.4     2269.4  28.774   <2e-16 ***
median_income_CP                        43817.5      507.9  86.274   <2e-16 ***
ocean_proximityINLAND                  -51158.5     3977.8 -12.861   <2e-16 ***
median_income_CP:ocean_proximityINLAND  -9023.5     1062.7  -8.491   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 74380 on 10111 degrees of freedom
Multiple R-squared:  0.5891,    Adjusted R-squared:  0.589 
F-statistic:  4832 on 3 and 10111 DF,  p-value: < 2.2e-16

int_lm2 = df_trainSet %>%
  lm(formula = median_house_value ~ median_income_CP*ocean_proximityINLAND + total_rooms_CP)

summary(int_lm2)

Call:
lm(formula = median_house_value ~ median_income_CP * ocean_proximityINLAND + 
    total_rooms_CP, data = .)

Residuals:
    Min      1Q  Median      3Q     Max 
-323959  -46532  -13962   31521  471237 

Coefficients:
                                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)                             6.246e+04  2.413e+03  25.887  < 2e-16 ***
median_income_CP                        4.343e+04  5.200e+02  83.505  < 2e-16 ***
ocean_proximityINLAND                  -5.128e+04  3.976e+03 -12.897  < 2e-16 ***
total_rooms_CP                          1.812e+00  5.235e-01   3.460 0.000542 ***
median_income_CP:ocean_proximityINLAND -9.111e+03  1.062e+03  -8.576  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 74340 on 10110 degrees of freedom
Multiple R-squared:  0.5896,    Adjusted R-squared:  0.5894 
F-statistic:  3631 on 4 and 10110 DF,  p-value: < 2.2e-16

int_lm3 = df_trainSet %>%
  lm(formula = median_house_value ~ median_income_CP*ocean_proximityINLAND + total_rooms_CP + ocean_proximityNEAR.BAY)

summary(int_lm3)

Call:
lm(formula = median_house_value ~ median_income_CP * ocean_proximityINLAND + 
    total_rooms_CP + ocean_proximityNEAR.BAY, data = .)

Residuals:
    Min      1Q  Median      3Q     Max 
-320715  -46445  -13381   31170  471292 

Coefficients:
                                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)                             59365.620   2438.321  24.347  < 2e-16 ***
median_income_CP                        43406.010    518.535  83.709  < 2e-16 ***
ocean_proximityINLAND                  -48246.206   3983.445 -12.112  < 2e-16 ***
total_rooms_CP                              1.847      0.522   3.539 0.000403 ***
ocean_proximityNEAR.BAY                 18604.920   2398.583   7.757 9.56e-15 ***
median_income_CP:ocean_proximityINLAND  -9099.716   1059.300  -8.590  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 74130 on 10109 degrees of freedom
Multiple R-squared:  0.592, Adjusted R-squared:  0.5918 
F-statistic:  2933 on 5 and 10109 DF,  p-value: < 2.2e-16

int_lm4 = df_trainSet %>%
  lm(formula = median_house_value ~ median_income_CP*ocean_proximityINLAND + total_rooms_CP + ocean_proximityNEAR.BAY + ocean_proximityNEAR.OCEAN)

summary(int_lm4)

Call:
lm(formula = median_house_value ~ median_income_CP * ocean_proximityINLAND + 
    total_rooms_CP + ocean_proximityNEAR.BAY + ocean_proximityNEAR.OCEAN, 
    data = .)

Residuals:
    Min      1Q  Median      3Q     Max 
-317822  -46184  -12859   31279  471274 

Coefficients:
                                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)                             5.507e+04  2.515e+03  21.897  < 2e-16 ***
median_income_CP                        4.359e+04  5.181e+02  84.133  < 2e-16 ***
ocean_proximityINLAND                  -4.393e+04  4.026e+03 -10.912  < 2e-16 ***
total_rooms_CP                          1.836e+00  5.209e-01   3.524 0.000427 ***
ocean_proximityNEAR.BAY                 2.217e+04  2.451e+03   9.045  < 2e-16 ***
ocean_proximityNEAR.OCEAN               1.574e+04  2.331e+03   6.750 1.56e-11 ***
median_income_CP:ocean_proximityINLAND -9.282e+03  1.057e+03  -8.779  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 73960 on 10108 degrees of freedom
Multiple R-squared:  0.5938,    Adjusted R-squared:  0.5936 
F-statistic:  2463 on 6 and 10108 DF,  p-value: < 2.2e-16

5.3. Forward Selection

# lm4
train_control = trainControl(method = "cv", number = 5)

step.model_lm4 = train(median_house_value ~ ., data = df_trainSet,
                   method = "leapForward",
                   tuneGrid = data.frame(nvmax = 1:9),
                   trControl = train_control)

summary(step.model_lm4$finalModel)

Subset selection object
11 Variables  (and intercept)
                          Forced in Forced out
longitude                     FALSE      FALSE
latitude                      FALSE      FALSE
ocean_proximityINLAND         FALSE      FALSE
ocean_proximityISLAND         FALSE      FALSE
ocean_proximityNEAR.BAY       FALSE      FALSE
ocean_proximityNEAR.OCEAN     FALSE      FALSE
total_rooms_CP                FALSE      FALSE
total_bedrooms_sinNA_CP       FALSE      FALSE
population_CP                 FALSE      FALSE
households_CP                 FALSE      FALSE
median_income_CP              FALSE      FALSE
1 subsets of each size up to 9
Selection Algorithm: forward
         longitude latitude ocean_proximityINLAND ocean_proximityISLAND ocean_proximityNEAR.BAY ocean_proximityNEAR.OCEAN total_rooms_CP
1  ( 1 ) " "       " "      " "                   " "                   " "                     " "                       " "           
2  ( 1 ) " "       " "      "*"                   " "                   " "                     " "                       " "           
3  ( 1 ) " "       " "      "*"                   " "                   " "                     " "                       " "           
4  ( 1 ) " "       " "      "*"                   " "                   " "                     " "                       " "           
5  ( 1 ) " "       " "      "*"                   " "                   " "                     " "                       " "           
6  ( 1 ) " "       " "      "*"                   " "                   " "                     " "                       "*"           
7  ( 1 ) "*"       " "      "*"                   " "                   " "                     " "                       "*"           
8  ( 1 ) "*"       "*"      "*"                   " "                   " "                     " "                       "*"           
9  ( 1 ) "*"       "*"      "*"                   "*"                   " "                     " "                       "*"           
         total_bedrooms_sinNA_CP population_CP households_CP median_income_CP
1  ( 1 ) " "                     " "           " "           "*"             
2  ( 1 ) " "                     " "           " "           "*"             
3  ( 1 ) "*"                     " "           " "           "*"             
4  ( 1 ) "*"                     "*"           " "           "*"             
5  ( 1 ) "*"                     "*"           "*"           "*"             
6  ( 1 ) "*"                     "*"           "*"           "*"             
7  ( 1 ) "*"                     "*"           "*"           "*"             
8  ( 1 ) "*"                     "*"           "*"           "*"             
9  ( 1 ) "*"                     "*"           "*"           "*"             

5.3.1. Modelo por Forward Selection (FS)

#Modelo mediante Forward Selection (FS)

train_control = trainControl(method = "cv", number = 5)

model_v1 = train(median_house_value ~ longitude + latitude + ocean_proximityINLAND + ocean_proximityISLAND + total_rooms_CP + total_bedrooms_sinNA_CP + population_CP + households_CP + median_income_CP, data = df_trainSet,
                 method = "lm",
                 trControl = train_control)

model_v1

Linear Regression 

10115 samples
    9 predictor

No pre-processing
Resampling: Cross-Validated (5 fold) 
Summary of sample sizes: 8092, 8091, 8092, 8093, 8092 
Resampling results:

  RMSE      Rsquared  MAE     
  67952.82  0.657127  50252.03

Tuning parameter 'intercept' was held constant at a value of TRUE

*Este modelo posee menor RMSE. Por ende se procederá a crear uno nuevo utilizando solo estas variables.

5.3.2. Interacción entre variables (FS) - 1 interacción

#Interacción entre Median_income_CP y Ocean Proximity INLAND

train_control = trainControl(method = "cv", number = 5)

model_v3 = train(median_house_value ~ longitude + latitude + median_income_CP*ocean_proximityINLAND + total_rooms_CP + total_bedrooms_sinNA_CP + population_CP + households_CP, data = df_trainSet,
                 method = "lm",
                 trControl = train_control)

model_v3

Linear Regression 

10115 samples
    8 predictor

No pre-processing
Resampling: Cross-Validated (5 fold) 
Summary of sample sizes: 8091, 8092, 8093, 8092, 8092 
Resampling results:

  RMSE      Rsquared   MAE     
  67545.47  0.6614535  49524.18

Tuning parameter 'intercept' was held constant at a value of TRUE

¡Mejoró!

5.3.3. Interacción entre variables (FS) - 2 interacción

#Entre Median_income_CP y Ocean Proximity INLAND y Latitude*Total_Rooms_CP

train_control = trainControl(method = "cv", number = 5)

model_v4 = train(median_house_value ~ longitude + latitude*total_rooms_CP + median_income_CP*ocean_proximityINLAND  + total_bedrooms_sinNA_CP + population_CP + households_CP, data = df_trainSet,
                 method = "lm",
                 trControl = train_control)

model_v4

Linear Regression 

10115 samples
    8 predictor

No pre-processing
Resampling: Cross-Validated (5 fold) 
Summary of sample sizes: 8091, 8091, 8092, 8094, 8092 
Resampling results:

  RMSE      Rsquared   MAE     
  67550.86  0.6610678  49526.39

Tuning parameter 'intercept' was held constant at a value of TRUE

Las dos interacciones hicieron que el modelo empeorara, pero de igual manera se va a hacer un submission.

5.4.Modelo por Regularización

5.4.1 Cross Validation

#Cross validation

customControl <- trainControl(method = "repeatedcv", 
                            number=10,
                            repeats=5,
                            verboseIter = F) # Verbose False es para no desplegar un log de que iteracion se va ejecutando

5.4.2 Regularización mediante LASSO

Se escogió este parámetro ya que consideramos que existen algunas variables que definitivamente no aportan al modelo. Esto lo logramos percibir en el análisis de correlación.

lasso<-train(median_house_value ~. ,
             df_trainSet, 
             method="glmnet",
             tuneGrid = expand.grid(alpha = 1,
                                    lambda=seq(0.0001, 1, length=5)),
             trControl=customControl)

plot(lasso)

Conforme crece el parámetro de regularización, el RMSE no se ve afectado.

plot(lasso$finalModel, xvar = "lambda", label=TRUE)

plot(lasso$finalModel, xvar = "dev", label=TRUE)

plot(varImp(lasso, scale=T))

Las variables con mayor impacto son:

1. ocean_proximityISLAND
2. median_income_CP
3. ocean_proximityINLAND
4. Longitude
5. Latitude

5.4.3. Ejecución del modelo

#Variables seleccionadas mediante LASSO

train_control = trainControl(method = "cv", number = 5)

model_v2 = train(median_house_value ~ longitude + latitude + ocean_proximityINLAND + ocean_proximityISLAND + median_income_CP, data = df_trainSet,
                 method = "lm",
                 trControl = train_control)

model_v2

Linear Regression 

10115 samples
    5 predictor

No pre-processing
Resampling: Cross-Validated (5 fold) 
Summary of sample sizes: 8093, 8092, 8092, 8091, 8092 
Resampling results:

  RMSE      Rsquared   MAE     
  73076.54  0.6033179  54281.31

Tuning parameter 'intercept' was held constant at a value of TRUE

Pese a que el RMSE fue más alto, es el modelo más “imparcial” al momento de evaluar data nueva. Será interesante evaluar con interacciones.

5.4.4. Modelo mediante Regularización - 1 interacción

#Modelo mediante Forward Selection (FS)

train_control = trainControl(method = "cv", number = 5)

model_v5 = train(median_house_value ~ longitude + latitude + ocean_proximityISLAND:median_income_CP + ocean_proximityINLAND, data = df_trainSet,
                 method = "lm",
                 trControl = train_control)

model_v5

Linear Regression 

10115 samples
    5 predictor

No pre-processing
Resampling: Cross-Validated (5 fold) 
Summary of sample sizes: 8092, 8093, 8091, 8093, 8091 
Resampling results:

  RMSE      Rsquared   MAE     
  99236.13  0.2682878  75784.38

Tuning parameter 'intercept' was held constant at a value of TRUE

Lejos de mejorar, el RMSE subió bastante.

5.5. Modelo por Random Forest

5.5.1. Random Forest por medio de la librería randomForest

df.rf=randomForest(median_house_value ~ ., data = df_trainSet)
df.rf

Call:
 randomForest(formula = median_house_value ~ ., data = df_trainSet) 
               Type of random forest: regression
                     Number of trees: 500
No. of variables tried at each split: 3

          Mean of squared residuals: 2659765261
                    % Var explained: 80.24

#Graficamos el modelo segun la cantidad de arboles creados
plot(df.rf)

#Conocer la importancia de cada una de las variables
df.rf$importance

                          IncNodePurity
longitude                  1.754306e+13
latitude                   1.577971e+13
ocean_proximityINLAND      1.848250e+13
ocean_proximityISLAND      2.036068e+10
ocean_proximityNEAR.BAY    1.031703e+12
ocean_proximityNEAR.OCEAN  1.232271e+12
total_rooms_CP             6.996495e+12
total_bedrooms_sinNA_CP    4.853193e+12
population_CP              7.989039e+12
households_CP              4.865709e+12
median_income_CP           4.995148e+13

#Genera la cantidad de arboles optimos para el modelo
which.min(df.rf$mse)

[1] 494

pred<-predict(df.rf,df_testSet)
test_rmse    <- sqrt(mean((pred - df_testSet$median_house_value)^2))
paste("Error de test (rmse) del árbol:", round(test_rmse,2))

[1] "Error de test (rmse) del árbol: 52480.84"

Obtuvimos un RMSE bajo a comparación de los modelos anteriores, sin embargo se procederá a hacer otras modificaciones.

5.5.2. Por medio de la librería ranger

library(ranger)

features <- setdiff(names(df_trainSet), "median_house_value")

rg <- ranger(
    formula   = median_house_value~ ., 
    data      = df_trainSet, 
    num.trees = 500,
    mtry      = 11
  )
rg

Ranger result

Call:
 ranger(formula = median_house_value ~ ., data = df_trainSet,      num.trees = 500, mtry = 11) 

Type:                             Regression 
Number of trees:                  500 
Sample size:                      10115 
Number of independent variables:  11 
Mtry:                             11 
Target node size:                 5 
Variable importance mode:         none 
Splitrule:                        variance 
OOB prediction error (MSE):       2449839212 
R squared (OOB):                  0.8179937 

pred_ranger<-predict(rg,df_testSet)
test_rmse    <- sqrt(mean((pred_ranger$predictions - df_testSet$median_house_value)^2))
paste("Error de test (rmse) del árbol:", round(test_rmse,2))

[1] "Error de test (rmse) del árbol: 50323.34"

Se obtuvo un RMSE mucho inferior a los anteriores. De igual forma se intentará bajo otro método.

5.6. Modelo por XGBoost

train<- as.matrix(df_trainSet, rownames.force=NA)
test<- as.matrix(df_testSet, rownames.force=NA)

train <- as(train, "sparseMatrix")
test <- as(test, "sparseMatrix")

# Never forget to exclude objective variable in 'data option'
train_Data <- xgb.DMatrix(data = train[,1:11], label = train[,"median_house_value"])

# Tuning the parameters #
cv.ctrl <- trainControl(method = "repeatedcv", repeats = 1,number = 3)

xgb.grid <- expand.grid(nrounds = 500,
                        max_depth = 7,
                        eta = 0.1,
                        gamma = 1,
                        colsample_bytree = 1,
                        min_child_weight=100,
                        subsample = 1)

xgb_tune <-train(median_house_value ~.,
                 data=df_trainSet,
                 objective = "reg:squarederror",
                 method="xgbTree",
                 metric = "RMSE",
                 trControl=cv.ctrl,
                 tuneGrid = xgb.grid)

The following parameters were provided multiple times:
    objective
  Only the last value for each of them will be used.
The following parameters were provided multiple times:
    objective
  Only the last value for each of them will be used.
The following parameters were provided multiple times:
    objective
  Only the last value for each of them will be used.
The following parameters were provided multiple times:
    objective
  Only the last value for each of them will be used.

print(xgb.grid)

test_data <- xgb.DMatrix(data = test[,1:11])

prediction <- predict(xgb_tune, df_testSet)


test_rmse    <- sqrt(mean((prediction - df_testSet$median_house_value)^2))
paste("Error de test (rmse) del árbol:", round(test_rmse,2))

[1] "Error de test (rmse) del árbol: 49632.8"

6. Exportación del submission

glimpse(df_test)

Rows: 6,193
Columns: 10
$ id                 <int> 14769, 16487, 2879, 19071, 12053, 17077, 10624, 10320, 5406, 10840, 20172, 12112, 9762, 13614, 8503, 3237, 2088, 7275, 38~
$ longitude          <dbl> -117.10, -121.05, -118.97, -122.52, -117.57, -122.20, -117.77, -117.79, -118.44, -117.93, -119.30, -117.34, -121.74, -117~
$ latitude           <dbl> 32.57, 38.14, 35.38, 38.27, 33.87, 37.48, 33.67, 33.84, 34.03, 33.66, 34.39, 34.02, 36.49, 34.13, 33.87, 36.10, 36.75, 33~
$ housing_median_age <int> 26, 19, 42, 18, 33, 32, 12, 9, 37, 18, 35, 28, 33, 37, 27, 21, 52, 30, 22, 34, 36, 36, 37, 12, 35, 39, 36, 21, 43, 32, 14~
$ total_rooms        <int> 2343, 3326, 1185, 2405, 2076, 640, 4329, 10484, 975, 2043, 3079, 2683, 2952, 2498, 3144, 1382, 377, 861, 2516, 2782, 2028~
$ total_bedrooms     <int> 371, 561, 358, 390, 517, 166, 1068, 1603, 189, 250, 579, 708, 565, 472, 722, 327, 97, 250, 826, 502, 523, 285, 301, 356, ~
$ population         <int> 1221, 1544, 1038, 872, 1374, 991, 1913, 4005, 489, 702, 1807, 2047, 1264, 1291, 1510, 1469, 530, 1062, 3350, 1219, 2751, ~
$ households         <int> 372, 511, 299, 367, 480, 160, 978, 1419, 202, 246, 589, 636, 517, 487, 680, 355, 96, 231, 713, 507, 496, 272, 265, 367, 5~
$ median_income      <dbl> 4.3601, 2.9875, 0.9951, 5.2155, 2.2197, 1.9844, 4.5094, 8.3931, 4.2434, 9.6062, 4.6900, 2.2750, 4.4209, 3.0000, 3.1597, 1~
$ ocean_proximity    <chr> "NEAR OCEAN", "INLAND", "INLAND", "<1H OCEAN", "INLAND", "NEAR BAY", "<1H OCEAN", "<1H OCEAN", "<1H OCEAN", "<1H OCEAN", ~

6.1. Ingeniería de características al Set final

#Tratamiento de NAs - Total_bedrooms
df_test$total_bedrooms_sinNA = ifelse(is.na(df_test$total_bedrooms), median(df_test$total_bedrooms, na.rm=T), df_test$total_bedrooms)

##Tratamiento de outliers - Total_bedrooms

df_test$total_bedrooms_sinNA_CP = ifelse(df_test$total_bedrooms_sinNA > LS_total_bedrooms_sinNA, LS_total_bedrooms_sinNA, ifelse(df_test$total_bedrooms_sinNA < LI_total_bedrooms_sinNA, LI_total_bedrooms_sinNA, df_test$total_bedrooms_sinNA))


#Tratamiento de outliers - Total Rooms

df_test$total_rooms_CP = ifelse(df_test$total_rooms > LS_total_rooms, LS_total_rooms, ifelse(df_test$total_rooms < LI_total_rooms, LI_total_rooms, df_test$total_rooms))


#Tratamiento de outliers - Population

df_test$population_CP = ifelse(df_test$population > LS_population, LS_population, ifelse(df_test$population < LI_population, LI_population, df_test$population))


#Tratamiento de outliers - Households

df_test$households_CP = ifelse(df_test$households > LS_households, LS_households, ifelse(df_test$households < LI_households, LI_households, df_test$households))



#Tratamiento de outliers - Median_income

df_test$median_income_CP = ifelse(df_test$median_income > LS_median_income, LS_median_income, ifelse(df_test$median_income < LI_median_income, LI_median_income, df_test$median_income))



#Dummy variables
dmy <- dummyVars(" ~ .", data = df_test, fullRank = T)

dfTest <- data.frame(predict(dmy, newdata = df_test))

glimpse(dfTest)

Rows: 6,193
Columns: 19
$ id                        <dbl> 14769, 16487, 2879, 19071, 12053, 17077, 10624, 10320, 5406, 10840, 20172, 12112, 9762, 13614, 8503, 3237, 2088, 7~
$ longitude                 <dbl> -117.10, -121.05, -118.97, -122.52, -117.57, -122.20, -117.77, -117.79, -118.44, -117.93, -119.30, -117.34, -121.7~
$ latitude                  <dbl> 32.57, 38.14, 35.38, 38.27, 33.87, 37.48, 33.67, 33.84, 34.03, 33.66, 34.39, 34.02, 36.49, 34.13, 33.87, 36.10, 36~
$ housing_median_age        <dbl> 26, 19, 42, 18, 33, 32, 12, 9, 37, 18, 35, 28, 33, 37, 27, 21, 52, 30, 22, 34, 36, 36, 37, 12, 35, 39, 36, 21, 43,~
$ total_rooms               <dbl> 2343, 3326, 1185, 2405, 2076, 640, 4329, 10484, 975, 2043, 3079, 2683, 2952, 2498, 3144, 1382, 377, 861, 2516, 278~
$ total_bedrooms            <dbl> 371, 561, 358, 390, 517, 166, 1068, 1603, 189, 250, 579, 708, 565, 472, 722, 327, 97, 250, 826, 502, 523, 285, 301~
$ population                <dbl> 1221, 1544, 1038, 872, 1374, 991, 1913, 4005, 489, 702, 1807, 2047, 1264, 1291, 1510, 1469, 530, 1062, 3350, 1219,~
$ households                <dbl> 372, 511, 299, 367, 480, 160, 978, 1419, 202, 246, 589, 636, 517, 487, 680, 355, 96, 231, 713, 507, 496, 272, 265,~
$ median_income             <dbl> 4.3601, 2.9875, 0.9951, 5.2155, 2.2197, 1.9844, 4.5094, 8.3931, 4.2434, 9.6062, 4.6900, 2.2750, 4.4209, 3.0000, 3.~
$ ocean_proximityINLAND     <dbl> 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, ~
$ ocean_proximityISLAND     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ~
$ ocean_proximityNEAR.BAY   <dbl> 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, ~
$ ocean_proximityNEAR.OCEAN <dbl> 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ~
$ total_bedrooms_sinNA      <dbl> 371, 561, 358, 390, 517, 166, 1068, 1603, 189, 250, 579, 708, 565, 472, 722, 327, 97, 250, 826, 502, 523, 285, 301~
$ total_bedrooms_sinNA_CP   <dbl> 371, 561, 358, 390, 517, 166, 1068, 1244, 189, 250, 579, 708, 565, 472, 722, 327, 97, 250, 826, 502, 523, 285, 301~
$ total_rooms_CP            <dbl> 2343, 3326, 1185, 2405, 2076, 640, 4329, 6121, 975, 2043, 3079, 2683, 2952, 2498, 3144, 1382, 377, 861, 2516, 2782~
$ population_CP             <dbl> 1221, 1544, 1038, 872, 1374, 991, 1913, 3351, 489, 702, 1807, 2047, 1264, 1291, 1510, 1469, 530, 1062, 3350, 1219,~
$ households_CP             <dbl> 372, 511, 299, 367, 480, 160, 978, 1171, 202, 246, 589, 636, 517, 487, 680, 355, 96, 231, 713, 507, 496, 272, 265,~
$ median_income_CP          <dbl> 4.360100, 2.987500, 0.995100, 5.215500, 2.219700, 1.984400, 4.509400, 8.393100, 4.243400, 8.557412, 4.690000, 2.27~

salida = round(predict(object = xgb_tune,
                          newdata = dfTest))

#Creación del data set final
dfSalida = data.frame(dfTest$id, salida)

colnames(dfSalida) = c("id", "median_house_value")

dfSalida

#Producimos Salida.
write.csv(dfSalida, "Test13-censoCA.csv", row.names = FALSE, quote = FALSE)

6. Conclusiones

• Es importante partir de un análisis descriptivo de los datos para conocer la composición del dataset.
• Fue necesario el preprocesamiento de los datos fue clave para abordar el Dataset. Los empleados fueron manejo de outliers, imputación y dummy variables.
• Se probaron con 6 diferentes métodos entre los cuales figuran modelos lineales, interacción entre variables, Random Forest y XGBoost.
• Nuestro modelo final para predecir el valor de los hogares en California fue mediante XGBoost, con un RMSE de 48,841.