R Notebook

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) {
n<-length(x)
k<-floor(n*alpha)
hasil<-0
for(i in 1:n){
  if(i<=k){
    w=k+1
  }
  else if(i>k&&i<=(n-k)){
    w=i
  }
  else{
    w=n-k
  }
  hasil<-hasil+x[w]
}
return(hasil/n)
}
# --- [b] Hitung ordinary mean (alpha=0) dan Winsorized mean 20% (alpha=0.2) ---
winsorized_mean(x,0)

## [1] 81.86667

winsorized_mean(x,0.2)

## [1] 69.73333

alpha_seq <- c(0, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40)
winsor_values <- c()
for(a in alpha_seq){
  hasil <- winsorized_mean(x, a)
  winsor_values <- c(winsor_values, hasil)
} 
df_alpha <- data.frame(
  alpha = alpha_seq,
  winsor_mean = winsor_values
)

library(ggplot2)

ggplot(df_alpha, aes(x = alpha, y = winsor_mean)) +
  geom_line(color = "pink", size = 1) +
  geom_point(color="red",size = 2) +
  labs(title = "Pengaruh Alpha terhadap Winsorized Mean",
       x = "Alpha",
       y = "Winsorized Mean") +
  theme_minimal()

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once per session.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

# --- Baca data CSV ---
df <- read.csv("C:/Users/Nasywa/Documents/SEMESTER 2/Komputasi Stat/Quiz 1 Komstat/data_quiz1.csv")
X <- as.matrix(df[, c("x1", "x2", "x3")])
w <- df$w
# --- [a] Buatlah fungsi weighted_corr(X, w) ---
weighted_corr <- function(X, w) {
  X<-as.matrix(X)
  n<-nrow(X)
  p<-ncol(X)
  W<-diag(w)
  nw<-sum(w)
  xbar<-(t(X)%*%w)/nw
  D <- as.matrix(X) - matrix(1, nrow(X), 1)%*%t(xbar)
  Sw<-(t(D)%*%W%*%D)/nw
  sw<-sqrt(diag(Sw))
  V<-diag(sw)
  Rw<-solve(V)%*%Sw%*%solve(V)
  cor=Rw
 return(list(
  mean = xbar,
  cov = Sw,
  sd = sw,
  cor = Rw
))
}
weighted_corr(X, w)

## $mean
##        [,1]
## x1 73.88530
## x2 65.39059
## x3 17.00938
## 
## $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
## 
## $sd
##       x1       x2       x3 
## 6.177671 6.411527 4.598649 
## 
## $cor
##            [,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(ggplot2)
library(reshape2)

hasil <- weighted_corr(X, w)
Rw <- hasil$cor
df_cor <- as.data.frame(as.table(Rw))

ggplot(df_cor, aes(Var1, Var2, fill = Freq)) +
  geom_tile() + geom_text(aes(label = round(Freq,2))) +
  scale_fill_gradient2(low="#A6CEE3", mid="#F7F7F7", high="#FB9A99") +
  labs(title="Weighted Correlation Matrix") +
  theme_minimal()