Лабораторная работа 6

Установка и загрузка необходимых библиотек

# Проверяем и устанавливаем необходимые пакеты
if (!require(ggplot2)) {
  install.packages("ggplot2")
  library(ggplot2)
}

if (!require(GGally)) {
  install.packages("GGally")
  library(GGally)
}

if (!require(reshape2)) {
  install.packages("reshape2")
  library(reshape2)
}

Парные графики для набора данных Iris

ggpairs(iris, aes(color = Species, alpha = 0.4)) + 
  ggtitle("Pairplot of Iris Dataset")

Боксплоты по видам

ggplot(melt(iris, id.vars = "Species"), aes(x=variable, y=value, fill=Species)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  ggtitle("Boxplots of Iris Features by Species")

Бутстрап-анализ

Функция бутстрепа

bootstrap <- function(data, n_bootstraps = 1000, statistic = mean, ci = 95) {
  boot_samples <- replicate(n_bootstraps, {
    sample_data <- sample(data, size = length(data), replace = TRUE)
    statistic(sample_data)
  })
  
  lower <- quantile(boot_samples, (100 - ci)/200)
  upper <- quantile(boot_samples, 1 - (100 - ci)/200)
  mean_val <- mean(boot_samples)
  
  list(samples = boot_samples, mean = mean_val, ci = c(lower, upper))
}

Применение к длине лепестков Versicolor

# Выделяем данные для вида versicolor
versicolor <- iris[iris$Species == "versicolor", "Petal.Length"]
result <- bootstrap(versicolor)

# Визуализация результатов
hist(result$samples, breaks = 30, 
     main = "Bootstrap Distribution of Mean Petal Length for Versicolor",
     xlab = "Mean Petal Length", col = "lightblue", border = "black")
abline(v = result$mean, col = "red", lty = 2, lwd = 2)
abline(v = result$ci[1], col = "green", lty = 2, lwd = 2)
abline(v = result$ci[2], col = "green", lty = 2, lwd = 2)
legend("topright", 
       legend = c(paste("Bootstrap Mean:", round(result$mean, 2)),
                  paste("95% CI: (", round(result$ci[1], 2), ",", 
                        round(result$ci[2], 2), ")")),
       col = c("red", "green"), lty = 2, lwd = 2)

Сравнение результатов

cat("Original mean:", mean(versicolor), "\n")

## Original mean: 4.26

cat("Bootstrap mean:", result$mean, "\n")

## Bootstrap mean: 4.262146

cat("95% CI:", result$ci, "\n")

## 95% CI: 4.134 4.388