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#nomor 1
winsorized_mean <- function(x, alpha){

  x <- sort(x)
  n <- length(x)
  k <- floor(n * alpha)

  y <- x

  if(k > 0){
    y[1:k] <- x[k+1]
    y[(n-k+1):n] <- x[n-k]
  }

  return(list(
    data_winsor = y,
    mean = mean(y)
  ))
}

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

mean(x)                

## [1] 81.86667

boxplot(x, main="Sebelum Winsorizing")

result <- winsorized_mean(x,0.2)
boxplot(result$data_winsor, main="Setelah Winsorizing")

#nomor 2

library(readxl)
data <- read.csv("~/Documents/komstat/data_quiz1.csv")
head(data)

X <- as.matrix(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)    
  
  xw <- (1/nw) * t(X) %*% W %*% one
  
  D <- X - one %*% t(xw)
  
  Sw <- (1/nw) * t(D) %*% W %*% D
  
  sw <- sqrt(diag(Sw))
  
  V <- diag(sw)
  

  Rw <- solve(V) %*% Sw %*% solve(V)
  
  return(list(
    W = W,
    mean = xw,
    cov = Sw,
    sd = sw,
    corr = Rw
  ))
}
hasil <- weighted_corr(X,w)

hasil$mean

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

hasil$cov

##           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$sd

##       x1       x2       x3 
## 6.177671 6.411527 4.598649

hasil$corr

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

library(corrplot)

## corrplot 0.95 loaded

corrplot(hasil$corr, method="circle")

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##interpretasi no 1 Mean biasa (81.87) lebih besar dari winsorized mean (69.73) karena adanya nilai ekstrem yaitu 310. Setelah winsorizing, nilai ekstrem diganti sehingga rata-rata menjadi lebih stabil. ##interpretasi no 2 jika kualitas air meningkat, ruang hijau juga meningkat, tetapi kualitas udara cenderung berlawanan dengan keduanya, karena Kualitas udara (x1) memiliki hubungan negatif yang kuat dengan kualitas air (x2) dan ruang hijau (x3)dan Sedangkan kualitas air (x2) dan ruang hijau (x3) memiliki hubungan positif yang sangat kuat