Quiz_Nadhif Muhammad Firaas_5003251160

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# ==============================================================================
# TEMPLATE JAWABAN KUIS
# Komputasi Statistika, Kelas D
# Prodi S1 Statistika FSAD ITS - Semester Genap 2025/2026
# Kamis, 12 Maret 2026
# ==============================================================================
# Nama  : Nadhif Muhammad Firaas
# NRP   : 5003251160
# Kelas : D
# ==============================================================================


# ==============================================================================
# Soal 1 [TOTAL 50 poin] - Winsorized Mean
# ==============================================================================

# Data
x <- c(12, 45, 52, 58, 61, 63, 67, 70, 72, 75, 78, 82, 88, 95, 310)

# --- [a] Buatlah fungsi winsorized_mean(x, alpha) ---

winsorized_mean <- function(x, alpha) {
  x <- sort(x)
  hasil <- 0
  n <- length(x)
  k <- floor(n * alpha)
  y <- x
  
  for(i in 1:n){
    if(i <= k){
      y[i] <- x[k+1]
    }else if(i > k && i <= (n-k)){
      y[i] <- x[i]
    }else if(i > (n-k)){
      y[i] <- x[n-k]
    }
  }
  for(i in 1:n){
    hasil <- hasil + y[i]
  }
  
  return(hasil/n)
}

# --- [b] Hitung ordinary mean (alpha=0) dan Winsorized mean 20% (alpha=0.2) ---

# Ordinary mean
ordinary_mean = winsorized_mean(x, 0)
print("Ordinary Mean = ")

## [1] "Ordinary Mean = "

ordinary_mean

## [1] 81.86667

# Winsorized mean 20%
winsorized_mean = winsorized_mean(x, 0.2)
print("Winsorized Mean = ")

## [1] "Winsorized Mean = "

winsorized_mean

## [1] 69.73333

#histogram
library(ggplot2)
ggplot(data.frame(x), aes(x)) +
  geom_histogram(bins = 10) +
  labs(title = "Histogram Data Original") +
  theme_minimal()

#hasil analisis berdasarkan visualisasi data
print("histogram menunjukkan sebagian besar data ada di kisaran 50-100, tapi ada satu outlier besar (310) yang membuat distribusi miring ke kanan. Akibatnya, mean biasa jadi kurang representatif, sehingga winsorized mean lebih cocok karena mengurangi pengaruh nilai ekstem.")

## [1] "histogram menunjukkan sebagian besar data ada di kisaran 50-100, tapi ada satu outlier besar (310) yang membuat distribusi miring ke kanan. Akibatnya, mean biasa jadi kurang representatif, sehingga winsorized mean lebih cocok karena mengurangi pengaruh nilai ekstem."

# ==============================================================================
# Soal 2 [TOTAL 60 poin] - Weighted Multivariate Descriptive Statistics
# ==============================================================================

# --- Baca data CSV ---
df <- read.csv("C:/Users/Hp/Downloads/RSTUDIO/Quiz 1 Komstat/data_quiz1.csv", header = T, sep = ",")
X <- as.matrix(df[, c("x1", "x2", "x3")])
w <- df$w
df

# --- [a] Buatlah fungsi weighted_corr(X, w) ---

weighted_corr <- function(X, w) {
  X <- as.matrix(X)
  w <- as.numeric(w)
  
  n <- nrow(X)
  p <- ncol(X)
  
  W <- diag(w)
  one <- matrix(1, n, 1)
  n_w <- as.numeric(t(one) %*% matrix(w, n, 1))
  x_bar_w <- (t(X) %*% W %*% one) / n_w
  D <- X - one %*% t(x_bar_w)
  S_w <- (t(D) %*% W %*% D) / n_w
  s_w <- sqrt(diag(S_w))
  V <- diag(as.vector(s_w))
  R_w <- solve(V) %*% S_w %*% solve(V)
  
  return(list(
    W = W,
    x_bar_w = x_bar_w,
    S_w = S_w,
    s_w = s_w,
    R_w = R_w
  ))
}

# --- [b] Aplikasikan fungsi pada data ---

# Panggil fungsi
hasil <- weighted_corr(X,w)

# Tampilkan vektor mean tertimbang
hasil$x_bar_w

##        [,1]
## x1 73.88530
## x2 65.39059
## x3 17.00938

# Tampilkan matriks varians-kovarians tertimbang
hasil$S_w

##           x1        x2        x3
## x1  38.16362 -37.75105 -27.15386
## x2 -37.75105  41.10767  29.16587
## x3 -27.15386  29.16587  21.14757

# Tampilkan vektor standar deviasi tertimbang
hasil$s_w

##       x1       x2       x3 
## 6.177671 6.411527 4.598649

# Tampilkan matriks korelasi tertimbang
hasil$R_w

##            [,1]       [,2]       [,3]
## [1,]  1.0000000 -0.9531095 -0.9558207
## [2,] -0.9531095  1.0000000  0.9891979
## [3,] -0.9558207  0.9891979  1.0000000

#correlation heatmap
library(corrplot)

## corrplot 0.95 loaded

corrplot(hasil$R_w,
  method  = "color",
  type    = "upper",
  addCoef.col = "white")

#hasil analisis berdasarkan visualisasi data
print("Pada heatmap, terlihat x2 dan x3 mempunyai hubungan yang sangat kuat dan searah (jika satu naik, maka yang lain juga ikut naik). Sedangkan nilai x1 berlawanan arah dengan keduanya. Ini menunjukkan adanya hubungan yang sangat kuat antar variabel, bahkan bisa jadi beberapa variabel membawa informasi yang hampir sama.")

## [1] "Pada heatmap, terlihat x2 dan x3 mempunyai hubungan yang sangat kuat dan searah (jika satu naik, maka yang lain juga ikut naik). Sedangkan nilai x1 berlawanan arah dengan keduanya. Ini menunjukkan adanya hubungan yang sangat kuat antar variabel, bahkan bisa jadi beberapa variabel membawa informasi yang hampir sama."

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Quiz_Nadhif Muhammad Firaas_5003251160_D