library(dplyr)
library(knitr)
library(kableExtra)

data <- tibble::tribble(
  ~"CC.AA.", ~"Automovil", ~"TV-Color", ~"Video", ~"Microondas", ~"Lavajillas", ~"Telefono",
  "Espana", 69.0, 97.6, 62.4, 32.3, 17.0, 85.2,
  "Andalucia", 66.7, 98.0, 82.7, 24.1, 12.7, 74.7,
  "Aragon", 67.2, 97.5, 56.8, 43.4, 20.6, 88.4,
  "Asturias", 63.7, 95.2, 52.1, 24.4, 13.3, 88.1,
  "Balerares", 71.9, 98.8, 62.4, 29.8, 10.1, 87.9,
  "Canarias", 72.7, 96.8, 68.4, 27.9, 5.8, 75.4,
  "Cantabria", 63.4, 94.9, 48.9, 36.5, 11.2, 80.5,
  "Castilla y Leon", 65.8, 97.1, 47.7, 28.1, 14.0, 85.0,
  "Cast.-La Mancha", 61.5, 97.3, 53.6, 21.7, 7.1, 72.9,
  "Cataluna", 70.4, 98.1, 71.1, 36.8, 19.8, 92.2,
  "Com.-Valenciana", 72.7, 98.4, 68.2, 26.6, 12.1, 84.4,
  "Extremadura", 60.5, 97.7, 43.7, 20.7, 11.7, 67.1,
  "Galicia", 65.5, 91.3, 42.7, 13.5, 14.6, 85.9,
  "Madrid", 74.0, 99.4, 76.3, 53.9, 32.3, 95.7,
  "Murcia", 69.0, 98.7, 59.3, 19.5, 12.1, 81.4,
  "Navarra", 76.4, 99.3, 60.6, 44.0, 20.6, 87.4,
  "Pais Vasco", 71.3, 98.3, 61.6, 45.7, 23.7, 94.3,
  "La Rioja", 64.9, 98.6, 54.4, 44.4, 17.6, 83.4
)

data %>% kbl(caption = "Tabla de datos", format = "html")  %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))

library(MASS)
library(ggplot2)

data_numeric <- data %>% select_if(is.numeric)
# Distancia de Mahalanobis
mahalanobis_dist <- mahalanobis(
  x = data_numeric,
  center = colMeans(data_numeric, na.rm = TRUE),
  cov = cov(data_numeric, use = "pairwise.complete.obs")
)
p_value <- 0.001
threshold <- qchisq(1 - p_value, df = ncol(data_numeric))

# Los outliers
data <- data %>% mutate(Mahalanobis = mahalanobis_dist,
                        Outlier = ifelse(Mahalanobis > threshold, "Si", "No"))

# Visualización de la distancia de Mahalanobis
ggplot(data, aes(x = seq_along(Mahalanobis), y = Mahalanobis, color = Outlier)) +
  geom_point(size = 3) +
  geom_hline(yintercept = threshold, linetype = "dashed", color = "blue") +
  labs(
    title = "Deteccion de Outliers mediante la Distancia de Mahalanobis",
    x = "Observaciones",
    y = "Distancia de Mahalanobis"
  ) +
  theme_minimal()

library(factoextra)
dist_matrix <- dist(scale(data_numeric))

# Método Ward
hc_ward <- hclust(dist_matrix, method = "ward.D2")
fviz_dend(hc_ward, main = "Metodo Ward", cex = 0.8)

# Método Complete
hc_complete <- hclust(dist_matrix, method = "complete")
fviz_dend(hc_complete, main = "Metodo Complete", cex = 0.8)

# Método Average
hc_average <- hclust(dist_matrix, method = "average")
fviz_dend(hc_average, main = "Metodo Average", cex = 0.8)

library(NbClust)
Datos.NbClust <- data[,c("Automovil", "TV-Color", "Video", "Microondas", "Lavajillas", "Telefono")]
res.wardD2 <- NbClust(Datos.NbClust, distance = "euclidean", min.nc=2, max.nc=15, method = "ward.D2", index = "alllong")

library(cluster)
hc_ward <- hclust(dist_matrix, method = "ward.D2")
grupo.ward <- cutree(hc_ward, k = 2, h = NULL)
datos.caso3.grupos <- cbind(Datos.NbClust, grupo.ward)
datos.caso3.grupos$id <- NULL

round(aggregate(datos.caso3.grupos, list(grupo.ward), mean ), 2)

datos.caso3.grupos.kmeans <- data_numeric
c1 <- c(66.87, 96.82, 56.01, 25.43, 11.81, 80.71)
c2 <- c(70.70, 98.53, 63.47, 44.70, 22.43, 90.23)
solucion <- kmeans(datos.caso3.grupos.kmeans, rbind(c1, c2))
# Centroides finales
centroides_fin <- solucion$centers
# Visualización de los resultados
kable(centroides_fin, caption = "Centroides Finales de los Clusters")

# Método Ward
hc_ward_2 <- hclust(dist_matrix, method = "ward.D2")
fviz_dend(hc_ward_2, k = 2, cex = 0.7, 
          main = "Dendrograma - Método Ward", 
          rect = TRUE, rect_fill = FALSE, 
          rect_border = "red")

# Método averege
hc_average_2 <- hclust(dist_matrix, method = "average")
fviz_dend(hc_average_2, k = 2, cex = 0.7, 
          main = "Dendrograma - Método Average", 
          rect = TRUE, rect_fill = FALSE, 
          rect_border = "red")

# Método complete
hc_complete_2 <- hclust(dist_matrix, method = "complete")
fviz_dend(hc_complete_2, k = 2, cex = 0.7, 
          main = "Dendrograma - Método Complete", 
          rect = TRUE, rect_fill = FALSE, 
          rect_border = "red")

data_cluster <- as.factor(solucion$cluster)

resultados_t <- data.frame(
  Variable = character(),
  Grupo_1 = numeric(),
  Grupo_2 = numeric(),
  Prueba_t = numeric(),
  stringsAsFactors = FALSE
)

for (variable in colnames(datos.caso3.grupos.kmeans)) {
  grupo1 <- datos.caso3.grupos.kmeans[data_cluster == 1, variable, drop = TRUE]
  grupo2 <- datos.caso3.grupos.kmeans[data_cluster == 2, variable, drop = TRUE]
  prueba_t <- t.test(grupo1, grupo2)
  
  resultados_t <- rbind(resultados_t, data.frame(
    Variable = variable,
    Grupo_1_Media = mean(grupo1, na.rm = TRUE),
    Grupo_2_Media = mean(grupo2, na.rm = TRUE),
    Prueba_t = prueba_t$p.value
  ))
}

kable(resultados_t, caption = "Resultados de la Prueba t para Cada Variable")