Análisis Interactivo de la base de datos mtcars

1. Análisis de normalidad

Probamos la normalidad en la variable mpg, como ejemplo de variable dependiente.

# Histograma y prueba de normalidad
p_hist <- ggplot(mtcars, aes(x = mpg)) +
  geom_histogram(bins = 10, fill = "lightblue", color = "black") +
  ggtitle("Histograma de mpg")
ggplotly(p_hist)

qqnorm(mtcars$mpg)
qqline(mtcars$mpg, col = "red")

# Prueba de Shapiro-Wilk
shapiro.test(mtcars$mpg)

## 
##  Shapiro-Wilk normality test
## 
## data:  mtcars$mpg
## W = 0.94756, p-value = 0.1229

2. Análisis descriptivo

summary(mtcars)

##       mpg             cyl             disp             hp       
##  Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0  
##  1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5  
##  Median :19.20   Median :6.000   Median :196.3   Median :123.0  
##  Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7  
##  3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0  
##  Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0  
##       drat             wt             qsec             vs        
##  Min.   :2.760   Min.   :1.513   Min.   :14.50   Min.   :0.0000  
##  1st Qu.:3.080   1st Qu.:2.581   1st Qu.:16.89   1st Qu.:0.0000  
##  Median :3.695   Median :3.325   Median :17.71   Median :0.0000  
##  Mean   :3.597   Mean   :3.217   Mean   :17.85   Mean   :0.4375  
##  3rd Qu.:3.920   3rd Qu.:3.610   3rd Qu.:18.90   3rd Qu.:1.0000  
##  Max.   :4.930   Max.   :5.424   Max.   :22.90   Max.   :1.0000  
##        am              gear            carb      
##  Min.   :0.0000   Min.   :3.000   Min.   :1.000  
##  1st Qu.:0.0000   1st Qu.:3.000   1st Qu.:2.000  
##  Median :0.0000   Median :4.000   Median :2.000  
##  Mean   :0.4062   Mean   :3.688   Mean   :2.812  
##  3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:4.000  
##  Max.   :1.0000   Max.   :5.000   Max.   :8.000

Gráficos exploratorios

# Boxplots interactivos
p1 <- ggplot(mtcars, aes(x = "", y = mpg)) + geom_boxplot() + ggtitle("mpg")
p2 <- ggplot(mtcars, aes(x = "", y = hp)) + geom_boxplot() + ggtitle("hp")
p3 <- ggplot(mtcars, aes(x = "", y = wt)) + geom_boxplot() + ggtitle("wt")

subplot(ggplotly(p1), ggplotly(p2), ggplotly(p3), nrows = 1, margin = 0.05)

3. Modelación con LOESS

3.1 Modelo con una variable explicativa (wt)

loess_model1 <- loess(mpg ~ wt, data = mtcars)
mtcars$pred_loess1 <- predict(loess_model1)

p_loess1 <- ggplot(mtcars, aes(x = wt, y = mpg)) +
  geom_point() +
  geom_line(aes(y = pred_loess1), color = "blue", size = 1.2) +
  ggtitle("LOESS: mpg ~ wt")

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

ggplotly(p_loess1)

3.2 Modelo con múltiples variables (wt y hp)

loess_model2 <- loess(mpg ~ wt + hp, data = mtcars)
mtcars$loess_pred <- predict(loess_model2)

p_loess2 <- ggplot(mtcars, aes(x = mpg, y = loess_pred)) +
  geom_point() +
  geom_abline(slope = 1, intercept = 0, color = "red") +
  ggtitle("Predicción LOESS vs Real")
ggplotly(p_loess2)

3.3 Pronóstico LOESS

# Nuevo ejemplo de predicción
nuevo <- data.frame(wt = 3, hp = 110)
predict(loess_model2, newdata = nuevo)

##        1 
## 20.46099

4. Modelación con Random Forest

4.1 Modelo con una variable (wt)

set.seed(123)
rf1 <- randomForest(mpg ~ wt, data = mtcars, importance = TRUE)
print(rf1)

## 
## Call:
##  randomForest(formula = mpg ~ wt, data = mtcars, importance = TRUE) 
##                Type of random forest: regression
##                      Number of trees: 500
## No. of variables tried at each split: 1
## 
##           Mean of squared residuals: 10.0435
##                     % Var explained: 71.46

4.2 Modelo con múltiples variables (wt y hp)

rf2 <- randomForest(mpg ~ wt + hp, data = mtcars, importance = TRUE)
print(rf2)

## 
## Call:
##  randomForest(formula = mpg ~ wt + hp, data = mtcars, importance = TRUE) 
##                Type of random forest: regression
##                      Number of trees: 500
## No. of variables tried at each split: 1
## 
##           Mean of squared residuals: 5.932878
##                     % Var explained: 83.14

varImpPlot(rf2)

4.3 Pronóstico Random Forest

predict(rf2, newdata = data.frame(wt = 3, hp = 110))

##        1 
## 21.15276

5. Additional Interactive Visualizations

5.1 Mapa de calor de la matriz de correlación

Para explorar las relaciones entre las variables del conjunto de datos, creamos un mapa de calor interactivo de la matriz de correlación.

cor_matrix <- cor(mtcars)
p_corr <- plot_ly(
  x = colnames(cor_matrix), 
  y = colnames(cor_matrix), 
  z = cor_matrix, 
  type = "heatmap", 
  colorscale = "RdBu",
  zmin = -1, zmax = 1
) %>% 
  layout(
    title = "Correlation Matrix of mtcars Variables",
    xaxis = list(title = ""),
    yaxis = list(title = "")
  )
p_corr

5.2 Matriz de diagrama de dispersión interactivo

Una matriz de diagrama de dispersión ayuda a visualizar las relaciones por pares entre mpg, wt y hp.

p_scatter <- plot_ly(mtcars) %>%
  add_trace(
    x = ~wt, y = ~mpg, type = "scatter", mode = "markers", 
    name = "wt vs mpg", marker = list(color = "blue")
  ) %>%
  add_trace(
    x = ~hp, y = ~mpg, type = "scatter", mode = "markers", 
    name = "hp vs mpg", marker = list(color = "red")
  ) %>%
  add_trace(
    x = ~wt, y = ~hp, type = "scatter", mode = "markers", 
    name = "wt vs hp", marker = list(color = "green")
  ) %>%
  layout(
    title = "Scatter Plot Matrix: mpg, wt, hp",
    xaxis = list(title = "wt / hp"),
    yaxis = list(title = "mpg / hp")
  )
p_scatter

##5.3 Gráficos de residuos para la evaluación de modelos

Gráficos de residuos para modelos LOESS y de Bosque Aleatorio para evaluar errores de predicción.

# Calculate residuals
mtcars$loess_resid <- mtcars$mpg - mtcars$loess_pred
mtcars$rf_pred <- predict(rf2)
mtcars$rf_resid <- mtcars$mpg - mtcars$rf_pred

# LOESS Residual Plot
p_resid_loess <- ggplot(mtcars, aes(x = loess_pred, y = loess_resid)) +
  geom_point() +
  geom_hline(yintercept = 0, color = "red") +
  ggtitle("LOESS Residuals") +
  xlab("Predicted mpg") + ylab("Residuals")
p_resid_loess <- ggplotly(p_resid_loess)

# Random Forest Residual Plot
p_resid_rf <- ggplot(mtcars, aes(x = rf_pred, y = rf_resid)) +
  geom_point() +
  geom_hline(yintercept = 0, color = "red") +
  ggtitle("Random Forest Residuals") +
  xlab("Predicted mpg") + ylab("Residuals")
p_resid_rf <- ggplotly(p_resid_rf)

subplot(p_resid_loess, p_resid_rf, nrows = 1, margin = 0.05, titleX = TRUE, titleY = TRUE)

##5.4 Gráfico interactivo de importancia de variables para el modelo de Bosque aleatorio

Versión interactiva del gráfico de importancia de variables para el modelo de Bosque aleatorio.

imp <- as.data.frame(importance(rf2))
imp$Variable <- rownames(imp)
p_varimp <- plot_ly(
  data = imp, 
  x = ~`%IncMSE`, y = ~Variable, type = "bar",
  marker = list(color = "lightgreen")
) %>%
  layout(
    title = "Random Forest Variable Importance",
    xaxis = list(title = "% Increase in MSE"),
    yaxis = list(title = "Variable")
  )
p_varimp

5.5 Diagrama de dispersión 3D para el modelo LOESS

Un diagrama de dispersión 3D para visualizar la relación entre mpg, wt y hp con la superficie de predicción LOESS.

p_3d <- plot_ly(mtcars) %>%
  add_markers(
    x = ~wt, y = ~hp, z = ~mpg, 
    marker = list(size = 5, color = ~mpg, colorscale = "Viridis"),
    name = "Actual"
  ) %>%
  add_markers(
    x = ~wt, y = ~hp, z = ~loess_pred, 
    marker = list(size = 5, color = "red", opacity = 0.5),
    name = "Predicted"
  ) %>%
  layout(
    title = "3D Scatter: mpg vs wt and hp (LOESS Predictions)",
    scene = list(
      xaxis = list(title = "wt"),
      yaxis = list(title = "hp"),
      zaxis = list(title = "mpg")
    )
  )
p_3d