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## SOAL NOMOR 1 ##
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_w <- x_sorted
if(k > 0){
x_w[1:k] <- x_sorted[k+1]
x_w[(n-k+1):n] <- x_sorted[n-k]
}
return(mean(x_w))
}
mean_biasa <- mean(x)
mean_winsor <- winsorized_mean(x, 0.2)
mean_biasa## [1] 81.86667mean_winsor## [1] 69.73333#=========================
# VISUALISASI DATA
#=========================
winsorize_data <- function(x, alpha) {
n <- length(x)
k <- floor(n * alpha)
x_sorted <- sort(x)
if (k > 0) {
x_sorted[1:k] <- x_sorted[k+1]
x_sorted[(n-k+1):n] <- x_sorted[n-k]
}
return(x_sorted)
}
plot_winsorized <- function(x, alpha) {
x_w <- winsorize_data(x, alpha)
par(mfrow = c(1, 2))
plot(1:length(x), x,
pch = 19, col = "blue",
main = "Sebelum Winsorizing",
xlab = "Index", ylab = "Nilai")
abline(lm(x ~ I(1:length(x))), col = "red", lwd = 2)
plot(1:length(x_w), x_w,
pch = 19, col = "darkgreen",
main = "Setelah Winsorizing",
xlab = "Index", ylab = "Nilai")
abline(lm(x_w ~ I(1:length(x_w))), col = "red", lwd = 2)
par(mfrow = c(1,1))
}
plot_winsorized(x, 0.2)
#========================
# INTERPRETASI DATA
#========================
# Sebelum winsorizing, terdapat nilai ekstrem yang membuat pola data kurang stabil dan garis regresi menjadi bias. Setelah winsorizing, nilai ekstrem tersebut dikurangi pengaruhnya sehingga data menjadi lebih merata dan garis regresi lebih merepresentasikan tren sebenarnya. Dengan demikian, winsorizing membantu mengurangi efek outlier pada data.
## SOAL NOMOR 2##
data <- read.csv("C:/Users/AISYAH/OneDrive/Documents/data_quiz1.csv", header = TRUE)
dataw <- as.numeric(data$w)
X <- as.matrix(data[, c("x1","x2","x3")])
weighted_corr <- function(X, w){
n <- nrow(X)
p <- ncol(X)
nw <- sum(w)
W <- diag(w)
one <- matrix(1, n, 1)
x_bar <- (t(X) %*% W %*% one) / nw
D <- X - one %*% t(x_bar)
S_w <- (t(D) %*% W %*% D) / nw
s_w <- sqrt(diag(S_w))
V <- diag(s_w)
R_w <- solve(V) %*% S_w %*% solve(V)
cat("=== Matriks Bobot (W) ===\n")
print(round(W, 4))
cat("\n=== Mean Tertimbang ===\n")
print(round(x_bar, 4))
cat("\n=== Matriks Kovarians (S_w) ===\n")
print(round(S_w, 4))
cat("\n=== Standar Deviasi (s_w) ===\n")
print(round(s_w, 4))
cat("\n=== Matriks Korelasi (R_w) ===\n")
print(round(R_w, 4))
}
weighted_corr(X, w)## === Matriks Bobot (W) ===
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 14.34 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [2,] 0.00 14.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [3,] 0.00 0.00 12.49 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [4,] 0.00 0.00 0.00 11.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [5,] 0.00 0.00 0.00 0.00 17.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [6,] 0.00 0.00 0.00 0.00 0.00 15.24 0.00 0.00 0.00 0.00 0.00 0.00
## [7,] 0.00 0.00 0.00 0.00 0.00 0.00 34.73 0.00 0.00 0.00 0.00 0.00
## [8,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 17.97 0.00 0.00 0.00 0.00
## [9,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 33.13 0.00 0.00 0.00
## [10,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 35.93 0.00 0.00
## [11,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15.55 0.00
## [12,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 16.54
## [13,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [14,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [15,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [16,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [17,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [18,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [19,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [20,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [21,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [22,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [23,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [24,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [25,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [26,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [27,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [28,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [29,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [30,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [31,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [32,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [33,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [34,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [35,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [36,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [37,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [38,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [2,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [3,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [4,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [5,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [6,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [7,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [8,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [9,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [10,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [11,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [12,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [13,] 17.25 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [14,] 0.00 14.93 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [15,] 0.00 0.00 7.24 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [16,] 0.00 0.00 0.00 9.85 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [17,] 0.00 0.00 0.00 0.00 11.1 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [18,] 0.00 0.00 0.00 0.00 0.0 12.89 0.00 0.00 0.00 0.00 0.00 0.00
## [19,] 0.00 0.00 0.00 0.00 0.0 0.00 11.14 0.00 0.00 0.00 0.00 0.00
## [20,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 7.06 0.00 0.00 0.00 0.00
## [21,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 13.96 0.00 0.00 0.00
## [22,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 23.13 0.00 0.00
## [23,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 19.74 0.00
## [24,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 17.53
## [25,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [26,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [27,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [28,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [29,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [30,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [31,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [32,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [33,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [34,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [35,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [36,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [37,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [38,] 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36]
## [1,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [2,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [3,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [4,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [5,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [6,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [7,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [8,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [9,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [10,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [11,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [12,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [13,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [14,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [15,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [16,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [17,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [18,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [19,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [20,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [21,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [22,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [23,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [24,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [25,] 12.56 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [26,] 0.00 13.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [27,] 0.00 0.00 12.28 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [28,] 0.00 0.00 0.00 7.95 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [29,] 0.00 0.00 0.00 0.00 20.84 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [30,] 0.00 0.00 0.00 0.00 0.00 0.67 0.00 0.00 0.00 0.00 0.0 0.00
## [31,] 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.00 0.00 0.00 0.0 0.00
## [32,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.11 0.00 0.00 0.0 0.00
## [33,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.55 0.00 0.0 0.00
## [34,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.39 0.0 0.00
## [35,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.2 0.00
## [36,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.36
## [37,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [38,] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.00
## [,37] [,38]
## [1,] 0.00 0.00
## [2,] 0.00 0.00
## [3,] 0.00 0.00
## [4,] 0.00 0.00
## [5,] 0.00 0.00
## [6,] 0.00 0.00
## [7,] 0.00 0.00
## [8,] 0.00 0.00
## [9,] 0.00 0.00
## [10,] 0.00 0.00
## [11,] 0.00 0.00
## [12,] 0.00 0.00
## [13,] 0.00 0.00
## [14,] 0.00 0.00
## [15,] 0.00 0.00
## [16,] 0.00 0.00
## [17,] 0.00 0.00
## [18,] 0.00 0.00
## [19,] 0.00 0.00
## [20,] 0.00 0.00
## [21,] 0.00 0.00
## [22,] 0.00 0.00
## [23,] 0.00 0.00
## [24,] 0.00 0.00
## [25,] 0.00 0.00
## [26,] 0.00 0.00
## [27,] 0.00 0.00
## [28,] 0.00 0.00
## [29,] 0.00 0.00
## [30,] 0.00 0.00
## [31,] 0.00 0.00
## [32,] 0.00 0.00
## [33,] 0.00 0.00
## [34,] 0.00 0.00
## [35,] 0.00 0.00
## [36,] 0.00 0.00
## [37,] 3.36 0.00
## [38,] 0.00 1.94
##
## === Mean Tertimbang ===
## [,1]
## x1 73.8853
## x2 65.3906
## x3 17.0094
##
## === Matriks Kovarians (S_w) ===
## x1 x2 x3
## x1 38.1636 -37.7510 -27.1539
## x2 -37.7510 41.1077 29.1659
## x3 -27.1539 29.1659 21.1476
##
## === Standar Deviasi (s_w) ===
## x1 x2 x3
## 6.1777 6.4115 4.5986
##
## === Matriks Korelasi (R_w) ===
## [,1] [,2] [,3]
## [1,] 1.0000 -0.9531 -0.9558
## [2,] -0.9531 1.0000 0.9892
## [3,] -0.9558 0.9892 1.0000# =========================
# VISUALISASI DATA
# =========================
data <- read.csv("C:/Users/AISYAH/OneDrive/Documents/data_quiz1.csv", header = TRUE)
datax1 <- data$x1
x2 <- data$x2
x3 <- data$x3
w <- data$w
plot_scatter <- function(x, y, judul, xlab, ylab) {
plot(x, y,
main = judul,
xlab = xlab,
ylab = ylab,
pch = 16)
model <- lm(y ~ x)
abline(model, col = "red", lwd = 2)
}
par(mfrow = c(1,3), oma = c(0,0,3,0))
plot_scatter(x1, x2, "Plot 1", "x1", "x2")
plot_scatter(x1, x3, "Plot 2", "x1", "x3")
plot_scatter(x2, x3, "Plot 3", "x2", "x3")
mtext("Visualisasi Data", outer = TRUE, cex = 1.5, font = 2)
#======================
# INTERPRETASI DATA
#======================
# Dari ketiga plot, hubungan antar variabel terlihat cukup jelas. Pada plot x1 dengan x2 dan x1 dengan x3, terlihat kecenderungan hubungan negatif, artinya semakin besar nilai x1 maka nilai x2 dan x3 cenderung menurun. Sebaliknya, pada plot x2 dengan x3, terlihat hubungan positif, di mana kenaikan x2 diikuti dengan kenaikan x3.Add a new chunk by clicking the Insert Chunk button on the toolbar or by pressing Ctrl+Alt+I.
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