Tugas

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

winsorized_mean <- function(x, alpha){
  
  n <- length(x)
  k <- floor(n * alpha)
  
  x_sorted <- sort(x)
  
  x_sorted[1:k] <- x_sorted[k+1]
  x_sorted[(n-k+1):n] <- x_sorted[n-k]
  
  return(mean(x_sorted))
}


mean_x <- mean(x)
winsor_mean <- winsorized_mean(x, 0.2)

mean_x

## [1] 81.86667

winsor_mean

## [1] 69.73333

winsorized_data <- function(x, alpha){
  
  n <- length(x)
  k <- floor(n * alpha)
  
  x_sorted <- sort(x)
  
  x_sorted[1:k] <- x_sorted[k+1]
  x_sorted[(n-k+1):n] <- x_sorted[n-k]
  
  return(x_sorted)
}

x_win <- winsorized_data(x, 0.2)



hist(x,
     col="skyblue",
     main="Histogram Output Produksi Mesin",
     xlab="Output Produksi",
     ylab="Frekuensi")

boxplot(x,
        col="orange",
        main="Boxplot Output Produksi Mesin")

boxplot(x, x_win,
        col=c("orange","lightgreen"),
        names=c("Asli","Winsorized"),
        main="Perbandingan Data Asli vs Winsorized")

data <- read.csv("C:/Users/Vicky/OneDrive/Dokumen/data_quiz1.csv")

head(data)

##               kota x1 x2   x3     w
## 1     Kab. Pacitan 86 55 10.2 14.34
## 2    Kab. Ponorogo 78 64 15.8 14.19
## 3  Kab. Trenggalek 83 58 11.5 12.49
## 4 Kab. Tulungagung 75 68 17.3 11.45
## 5      Kab. Blitar 80 60 13.6 17.45
## 6      Kab. Kediri 74 66 16.8 15.24

X <- data[, c("x1","x2","x3")]
w <- data$w


weighted_corr <- function(X, w){
  
  X <- as.matrix(X)
  n <- nrow(X)
  
  W <- diag(w)
  nw <- sum(w)
  
  one <- matrix(1, n, 1)
  
  
  mean_w <- (1/nw) * t(X) %*% W %*% one
  
  
  D <- X - matrix(one %*% t(mean_w), n, ncol(X))
  
  
  Sw <- (1/nw) * t(D) %*% W %*% D
  
 
  sw <- sqrt(diag(Sw))
  
  V <- diag(sw)
  
 
  Rw <- solve(V) %*% Sw %*% solve(V)
  
  return(list(
    mean_w = mean_w,
    Sw = Sw,
    sw = sw,
    Rw = Rw
  ))
}


hasil <- weighted_corr(X, w)


hasil$mean_w

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

hasil$Sw

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

hasil$sw

##       x1       x2       x3 
## 6.177671 6.411527 4.598649

hasil$Rw

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