Análisis Exploratorio de Datos: Boston

1. Cargar y explorar el dataset

data("Boston")

skim(Boston)
Data summary
Name Boston
Number of rows 506
Number of columns 14
_______________________
Column type frequency:
numeric 14
________________________
Group variables None

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
crim 0 1 3.61 8.60 0.01 0.08 0.26 3.68 88.98 ▇▁▁▁▁
zn 0 1 11.36 23.32 0.00 0.00 0.00 12.50 100.00 ▇▁▁▁▁
indus 0 1 11.14 6.86 0.46 5.19 9.69 18.10 27.74 ▇▆▁▇▁
chas 0 1 0.07 0.25 0.00 0.00 0.00 0.00 1.00 ▇▁▁▁▁
nox 0 1 0.55 0.12 0.38 0.45 0.54 0.62 0.87 ▇▇▆▅▁
rm 0 1 6.28 0.70 3.56 5.89 6.21 6.62 8.78 ▁▂▇▂▁
age 0 1 68.57 28.15 2.90 45.02 77.50 94.07 100.00 ▂▂▂▃▇
dis 0 1 3.80 2.11 1.13 2.10 3.21 5.19 12.13 ▇▅▂▁▁
rad 0 1 9.55 8.71 1.00 4.00 5.00 24.00 24.00 ▇▂▁▁▃
tax 0 1 408.24 168.54 187.00 279.00 330.00 666.00 711.00 ▇▇▃▁▇
ptratio 0 1 18.46 2.16 12.60 17.40 19.05 20.20 22.00 ▁▃▅▅▇
black 0 1 356.67 91.29 0.32 375.38 391.44 396.22 396.90 ▁▁▁▁▇
lstat 0 1 12.65 7.14 1.73 6.95 11.36 16.96 37.97 ▇▇▅▂▁
medv 0 1 22.53 9.20 5.00 17.02 21.20 25.00 50.00 ▂▇▅▁▁ 
head(Boston)
##      crim zn indus chas   nox    rm  age    dis rad tax ptratio  black lstat
## 1 0.00632 18  2.31    0 0.538 6.575 65.2 4.0900   1 296    15.3 396.90  4.98
## 2 0.02731  0  7.07    0 0.469 6.421 78.9 4.9671   2 242    17.8 396.90  9.14
## 3 0.02729  0  7.07    0 0.469 7.185 61.1 4.9671   2 242    17.8 392.83  4.03
## 4 0.03237  0  2.18    0 0.458 6.998 45.8 6.0622   3 222    18.7 394.63  2.94
## 5 0.06905  0  2.18    0 0.458 7.147 54.2 6.0622   3 222    18.7 396.90  5.33
## 6 0.02985  0  2.18    0 0.458 6.430 58.7 6.0622   3 222    18.7 394.12  5.21
##   medv
## 1 24.0
## 2 21.6
## 3 34.7
## 4 33.4
## 5 36.2
## 6 28.7
dim(Boston)
## [1] 506  14
str(Boston)
## 'data.frame':    506 obs. of  14 variables:
##  $ crim   : num  0.00632 0.02731 0.02729 0.03237 0.06905 ...
##  $ zn     : num  18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
##  $ indus  : num  2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
##  $ chas   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ nox    : num  0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
##  $ rm     : num  6.58 6.42 7.18 7 7.15 ...
##  $ age    : num  65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
##  $ dis    : num  4.09 4.97 4.97 6.06 6.06 ...
##  $ rad    : int  1 2 2 3 3 3 5 5 5 5 ...
##  $ tax    : num  296 242 242 222 222 222 311 311 311 311 ...
##  $ ptratio: num  15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
##  $ black  : num  397 397 393 395 397 ...
##  $ lstat  : num  4.98 9.14 4.03 2.94 5.33 ...
##  $ medv   : num  24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
summary(Boston)
##       crim                zn             indus            chas        
##  Min.   : 0.00632   Min.   :  0.00   Min.   : 0.46   Min.   :0.00000  
##  1st Qu.: 0.08205   1st Qu.:  0.00   1st Qu.: 5.19   1st Qu.:0.00000  
##  Median : 0.25651   Median :  0.00   Median : 9.69   Median :0.00000  
##  Mean   : 3.61352   Mean   : 11.36   Mean   :11.14   Mean   :0.06917  
##  3rd Qu.: 3.67708   3rd Qu.: 12.50   3rd Qu.:18.10   3rd Qu.:0.00000  
##  Max.   :88.97620   Max.   :100.00   Max.   :27.74   Max.   :1.00000  
##       nox               rm             age              dis        
##  Min.   :0.3850   Min.   :3.561   Min.   :  2.90   Min.   : 1.130  
##  1st Qu.:0.4490   1st Qu.:5.886   1st Qu.: 45.02   1st Qu.: 2.100  
##  Median :0.5380   Median :6.208   Median : 77.50   Median : 3.207  
##  Mean   :0.5547   Mean   :6.285   Mean   : 68.57   Mean   : 3.795  
##  3rd Qu.:0.6240   3rd Qu.:6.623   3rd Qu.: 94.08   3rd Qu.: 5.188  
##  Max.   :0.8710   Max.   :8.780   Max.   :100.00   Max.   :12.127  
##       rad              tax           ptratio          black       
##  Min.   : 1.000   Min.   :187.0   Min.   :12.60   Min.   :  0.32  
##  1st Qu.: 4.000   1st Qu.:279.0   1st Qu.:17.40   1st Qu.:375.38  
##  Median : 5.000   Median :330.0   Median :19.05   Median :391.44  
##  Mean   : 9.549   Mean   :408.2   Mean   :18.46   Mean   :356.67  
##  3rd Qu.:24.000   3rd Qu.:666.0   3rd Qu.:20.20   3rd Qu.:396.23  
##  Max.   :24.000   Max.   :711.0   Max.   :22.00   Max.   :396.90  
##      lstat            medv      
##  Min.   : 1.73   Min.   : 5.00  
##  1st Qu.: 6.95   1st Qu.:17.02  
##  Median :11.36   Median :21.20  
##  Mean   :12.65   Mean   :22.53  
##  3rd Qu.:16.95   3rd Qu.:25.00  
##  Max.   :37.97   Max.   :50.00

2. Medidas descriptivas

Variables continuas clave

variables_g1 <- c("medv","rm","lstat","crim","tax")

boston_g1 <- Boston %>%
  select(all_of(variables_g1))

Media y desviación estándar

mean(boston_g1$medv)
## [1] 22.53281
sapply(Boston[variables_g1], mean)
##       medv         rm      lstat       crim        tax 
##  22.532806   6.284634  12.653063   3.613524 408.237154
sapply(Boston[variables_g1], sd)
##        medv          rm       lstat        crim         tax 
##   9.1971041   0.7026171   7.1410615   8.6015451 168.5371161

3. Histogramas

Boston %>%
  select(medv, rm, lstat) %>%
  pivot_longer(cols = everything(),
               names_to = "variable",
               values_to = "valor") %>%
  ggplot(aes(x = valor, fill = variable)) +
  geom_histogram(color = "white", bins = 15) +
  facet_wrap(~variable, scales = "free_x") +
  scale_fill_brewer(palette = "Set2") +
  labs(title = "Histogramas de medv, rm y lstat") +
  theme_minimal()

4. Histogramas individuales

ggplot(Boston, aes(x = medv)) +
  geom_histogram(fill = "skyblue", color = "white", bins = 23) +
  ggtitle("Histograma de medv") +
  theme_minimal()

ggplot(Boston, aes(x = rm)) +
  geom_histogram(fill = "salmon", color = "white", bins = 23) +
  ggtitle("Histograma de rm") +
  theme_minimal()

ggplot(Boston, aes(x = lstat)) +
  geom_histogram(fill = "lightgreen", color = "white", bins = 23) +
  ggtitle("Histograma de lstat") +
  theme_minimal()

Se utilizan 23 bins porque es aproximadamente la raíz cuadrada del número de observaciones.

5. Boxplots

Boston %>%
  select(medv, lstat) %>%
  pivot_longer(cols = everything(),
               names_to = "variable",
               values_to = "valor") %>%
  ggplot(aes(x = variable, y = valor, fill = variable)) +
  geom_boxplot() +
  scale_fill_brewer(palette = "Set2") +
  ggtitle("Boxplot de medv y lstat") +
  theme_minimal()

6. Gráficos de dispersión

Boston %>%
  select(medv, rm, lstat, crim, tax) %>%
  pivot_longer(cols = -medv,
               names_to = "variable",
               values_to = "valor") %>%
  ggplot(aes(x = valor, y = medv, color = variable)) +
  geom_point() +
  facet_wrap(~variable, scales = "free_x") +
  scale_color_brewer(palette = "Set1") +
  ggtitle("Relación de medv", subtitle = "Gráficos por faceta") +
  theme_minimal()

7. Gráficos de dispersión individuales

ggplot(Boston, aes(x = lstat, y = medv)) +
  geom_point(color = "pink") +
  scale_x_log10() +
  ggtitle("medv vs lstat") +
  theme_minimal()

ggplot(Boston, aes(x = crim, y = medv)) +
  geom_point(color = "purple") +
  scale_x_log10() +
  ggtitle("medv vs crim (escala log)") +
  theme_minimal()

ggplot(Boston, aes(x = tax, y = medv)) +
  geom_point(color = "orange") +
  scale_x_log10() +
  ggtitle("medv vs tax") +
  theme_minimal()

8. Matriz de correlación visual

ggpairs(Boston[,c("medv","rm","lstat")])

Conclusión

El análisis exploratorio de la base Boston permite observar la distribución de las variables, identificar valores atípicos y analizar las relaciones entre variables clave. En particular, se observa que variables como rm y lstat tienen una relación importante con medv, que representa el valor mediano de las viviendas.