Anreg Minggu 2
Herlinasari
2026-02-04
#Install dan load packages yang diperlukan
if (!require("tidyverse")) install.packages("tidyverse")## Loading required package: tidyverse## Warning: package 'tidyverse' was built under R version 4.5.2## Warning: package 'ggplot2' was built under R version 4.5.2## Warning: package 'tibble' was built under R version 4.5.2## Warning: package 'tidyr' was built under R version 4.5.2## Warning: package 'readr' was built under R version 4.5.2## Warning: package 'purrr' was built under R version 4.5.2## Warning: package 'dplyr' was built under R version 4.5.2## Warning: package 'stringr' was built under R version 4.5.2## Warning: package 'forcats' was built under R version 4.5.2## Warning: package 'lubridate' was built under R version 4.5.2## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.6
## ✔ forcats 1.0.1 ✔ stringr 1.6.0
## ✔ ggplot2 4.0.1 ✔ tibble 3.3.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.2
## ✔ purrr 1.2.1## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsif (!require("VIM")) install.packages("VIM")## Loading required package: VIM## Warning: package 'VIM' was built under R version 4.5.2## Loading required package: colorspace## Warning: package 'colorspace' was built under R version 4.5.2## Loading required package: grid
## VIM is ready to use.
##
## Suggestions and bug-reports can be submitted at: https://github.com/statistikat/VIM/issues
##
## Attaching package: 'VIM'
##
## The following object is masked from 'package:datasets':
##
## sleepif (!require("naniar")) install.packages("naniar")## Loading required package: naniar## Warning: package 'naniar' was built under R version 4.5.2if (!require("outliers")) install.packages("outliers")## Loading required package: outliers## Warning: package 'outliers' was built under R version 4.5.2if (!require("ggplot2")) install.packages("ggplot2")
library(tidyverse)
library(VIM)
library(naniar)
library(outliers)
library(ggplot2)
library(mice)## Warning: package 'mice' was built under R version 4.5.2##
## Attaching package: 'mice'
##
## The following object is masked from 'package:stats':
##
## filter
##
## The following objects are masked from 'package:base':
##
## cbind, rbindlibrary(dplyr)
library(csv)## Warning: package 'csv' was built under R version 4.5.2df <- read.csv("C:/Users/LENOVO/Downloads/datania1k.csv")
data <- df[c("Age","Annual_Premium")]
head(data)## Age Annual_Premium
## 1 22 36513
## 2 24 2630
## 3 22 35832
## 4 72 36685
## 5 66 2630
## 6 42 31226tail(data)## Age Annual_Premium
## 995 48 47533
## 996 47 29384
## 997 56 47479
## 998 22 29000
## 999 48 45107
## 1000 33 43068DATA HILANG
cat("\n=== CEK MISSING VALUE ===\n\n")##
## === CEK MISSING VALUE ===total_missing <- sum(is.na(data))
total_missing## [1] 0OUTLIER
# 3. Deteksi outlier
detect_outliers <- function(data) {
cat("\n=== DETEKSI OUTLIER ===\n\n")
outlier_report <- list()
for(var in names(data)[sapply(data, is.numeric)]) {
cat("Analisis outlier untuk variabel:", var, "\n")
# Statistik deskriptif
stats <- summary(data[[var]])
iqr_val <- IQR(data[[var]], na.rm = TRUE)
q1 <- quantile(data[[var]], 0.25, na.rm = TRUE)
q3 <- quantile(data[[var]], 0.75, na.rm = TRUE)
lower_bound <- q1 - 1.5 * iqr_val
upper_bound <- q3 + 1.5 * iqr_val
# Deteksi outlier dengan metode IQR
outliers_iqr <- data[[var]][data[[var]] < lower_bound | data[[var]] > upper_bound]
# Deteksi outlier dengan metode Z-score
z_scores <- scale(data[[var]])
outliers_z <- data[[var]][abs(z_scores) > 3]
# Deteksi outlier dengan metode Grubbs (uji statistik)
if(length(na.omit(data[[var]])) > 6) {
tryCatch({
grubbs_test <- grubbs.test(na.omit(data[[var]]))
grubbs_outlier <- ifelse(grubbs_test$p.value < 0.05, "Terdeteksi", "Tidak terdeteksi")
}, error = function(e) {
grubbs_outlier <- "Tidak dapat dihitung"
})
} else {
grubbs_outlier <- "Data tidak cukup"
}
# Ringkasan
outlier_report[[var]] <- list(
n_outliers_iqr = length(outliers_iqr),
n_outliers_z = length(outliers_z),
grubbs_result = grubbs_outlier,
lower_bound = lower_bound,
upper_bound = upper_bound,
outlier_values = unique(round(outliers_iqr, 2))
)
cat(" - Outlier (IQR method):", length(outliers_iqr), "\n")
cat(" - Outlier (Z-score > 3):", length(outliers_z), "\n")
cat(" - Uji Grubbs:", grubbs_outlier, "\n")
cat(" - Batas bawah:", round(lower_bound, 2), "\n")
cat(" - Batas atas:", round(upper_bound, 2), "\n")
grubbs_outlier <- NA
if(length(outliers_iqr) > 0) {
cat(" - Nilai outlier:", paste(head(unique(round(outliers_iqr, 2)), 5), collapse = ", "), "\n")
}
cat("\n")
}
return(outlier_report)
}
# Deteksi outlier
outlier_analysis <- detect_outliers(data)##
## === DETEKSI OUTLIER ===
##
## Analisis outlier untuk variabel: Age
## - Outlier (IQR method): 0
## - Outlier (Z-score > 3): 0
## - Uji Grubbs: Tidak terdeteksi
## - Batas bawah: -12.88
## - Batas atas: 88.12
##
## Analisis outlier untuk variabel: Annual_Premium
## - Outlier (IQR method): 26
## - Outlier (Z-score > 3): 5
## - Uji Grubbs: Terdeteksi
## - Batas bawah: 1704.5
## - Batas atas: 62266.5
## - Nilai outlier: 81192, 100278, 63273, 70452, 71918# 4. Visualisasi outlier
visualize_outliers <- function(data) {
cat("\n=== VISUALISASI OUTLIER ===\n")
numeric_vars <- names(data)[sapply(data, is.numeric)]
# Boxplot untuk setiap variabel numerik
par(mfrow = c(2, 3))
for(var in numeric_vars[1:min(6, length(numeric_vars))]) {
boxplot(data[[var]], main = var, col = "lightblue",
ylab = "Nilai", outline = TRUE)
grid()
}
par(mfrow = c(1, 1))
# Histogram dengan overlay outlier
for(var in numeric_vars[1:min(3, length(numeric_vars))]) {
# Hitung batas outlier
q1 <- quantile(data[[var]], 0.25, na.rm = TRUE)
q3 <- quantile(data[[var]], 0.75, na.rm = TRUE)
iqr_val <- IQR(data[[var]], na.rm = TRUE)
lower_bound <- q1 - 1.5 * iqr_val
upper_bound <- q3 + 1.5 * iqr_val
# Identifikasi outlier
is_outlier <- data[[var]] < lower_bound | data[[var]] > upper_bound
# Plot histogram
hist(data[[var]],
breaks = 30,
col = "lightblue",
main = paste("Distribusi dan Outlier:", var),
xlab = var)
abline(v = c(lower_bound, upper_bound),
col = "red", lty = 2, lwd = 2)
}
# Scatter plot matrix untuk melihat outlier multivariat
if(length(numeric_vars) >= 3) {
pairs(data[, numeric_vars[1:min(4, length(numeric_vars))]],
main = "Scatter Plot Matrix untuk Deteksi Outlier",
pch = 19, col = alpha("blue", 0.6))
}
}
# Jalankan visualisasi
visualize_outliers(data)##
## === VISUALISASI OUTLIER ===
#Statistika Deskriptif
cat("\n=====STATISTIK DESKRIPPTIIF======")##
## =====STATISTIK DESKRIPPTIIF======summary(data)## Age Annual_Premium
## Min. :20.00 Min. : 2630
## 1st Qu.:25.00 1st Qu.: 24415
## Median :38.00 Median : 31512
## Mean :39.65 Mean : 30364
## 3rd Qu.:50.25 3rd Qu.: 39556
## Max. :85.00 Max. :100278#Analisis Regresi
cat("\n=== ANALISIS REGRESI ===\n\n")##
## === ANALISIS REGRESI ===# Korelasi
cat("\n2. KORELASI:\n")##
## 2. KORELASI:correlation <- cor(data$Age, data$Annual_Premium)
cat("Koefisien Korelasi (r) =", round(correlation, 4), "\n")## Koefisien Korelasi (r) = 0.1388#Regresi Linear Sederhana
model <- lm(Annual_Premium~Age, data = data)
summary(model)##
## Call:
## lm(formula = Annual_Premium ~ Age, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32960 -5971 1517 9265 72308
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24662.40 1386.17 17.792 < 2e-16 ***
## Age 143.79 32.48 4.427 1.06e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16200 on 998 degrees of freedom
## Multiple R-squared: 0.01926, Adjusted R-squared: 0.01827
## F-statistic: 19.59 on 1 and 998 DF, p-value: 1.063e-05#Ringkasan model
cat("\n1. RINGKASAN MODEL:\n")##
## 1. RINGKASAN MODEL:summary_model <- summary(model)
print(summary_model)##
## Call:
## lm(formula = Annual_Premium ~ Age, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32960 -5971 1517 9265 72308
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24662.40 1386.17 17.792 < 2e-16 ***
## Age 143.79 32.48 4.427 1.06e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16200 on 998 degrees of freedom
## Multiple R-squared: 0.01926, Adjusted R-squared: 0.01827
## F-statistic: 19.59 on 1 and 998 DF, p-value: 1.063e-05#PENGUJIAN HIPOTESIS
# ----------------------
cat("\n\n=== PENGUJIAN HIPOTESIS ===\n")##
##
## === PENGUJIAN HIPOTESIS ===# 6.1 Hipotesis untuk Koefisien Regresi (Slope)
cat("\n1. UJI HIPOTESIS UNTUK SLOPE (β1):\n")##
## 1. UJI HIPOTESIS UNTUK SLOPE (β1):cat(" Hipotesis Nol (H0): β1 = 0 (Tidak ada hubungan linear)\n")## Hipotesis Nol (H0): β1 = 0 (Tidak ada hubungan linear)cat(" Hipotesis Alternatif (H1): β1 ≠ 0 (Ada hubungan linear)\n")## Hipotesis Alternatif (H1): β1 ≠ 0 (Ada hubungan linear)# Dari output summary model
coef_table <- summary_model$coefficients
slope_p_value <- coef_table[2, 4]
cat("\n Hasil Uji:\n")##
## Hasil Uji:cat(" t-statistik =", round(coef_table[2, 3], 4), "\n")## t-statistik = 4.4266cat(" p-value =", round(slope_p_value, 6), "\n")## p-value = 1.1e-05alpha <- 0.05
cat("Tingkat signifikansi (α) =", alpha, "\n")## Tingkat signifikansi (α) = 0.05# Dari output summary model
coef_table <- summary_model$coefficients
slope_p_value <- coef_table[2, 4]
cat("\n Hasil Uji:\n")##
## Hasil Uji:cat(" t-statistik =", round(coef_table[2, 3], 4), "\n")## t-statistik = 4.4266cat(" p-value =", round(slope_p_value, 6), "\n")## p-value = 1.1e-05alpha <- 0.05
cat(" Tingkat signifikansi (α) =", alpha, "\n")## Tingkat signifikansi (α) = 0.05if (slope_p_value < alpha) {
cat("\n KEPUTUSAN: Tolak H0\n")
cat(" KESIMPULAN: Ada bukti statistik yang cukup untuk menyatakan bahwa\n")
cat(" terdapat hubungan linear yang signifikan antara Age dan Annual Premium\n")
} else {
cat("\n KEPUTUSAN: Gagal tolak H0\n")
cat(" KESIMPULAN: Tidak ada bukti statistik yang cukup untuk menyatakan bahwa\n")
cat(" terdapat hubungan linear yang signifikan antara Age dan Annual Premium\n")
}##
## KEPUTUSAN: Tolak H0
## KESIMPULAN: Ada bukti statistik yang cukup untuk menyatakan bahwa
## terdapat hubungan linear yang signifikan antara Age dan Annual Premium# Plot
x <- data$Age
y <- data$Annual_Premium
x_Age <- "Age"
y_AnnualPremium <- "Annual Premium"
par(mfrow = c(2, 2))
plot(x, y, main = paste("Scatter Plot:", x_Age, "vs", y_AnnualPremium),
xlab = x_Age, ylab = y_AnnualPremium, pch = 19, col = "blue")
abline(model, col = "red", lwd = 2)
qqnorm(resid(model), main = "Q-Q Plot Residual")
qqline(resid(model), col = "red")
plot(fitted(model), resid(model),
main = "Residual vs Fitted",
xlab = "Fitted Values", ylab = "Residuals",
pch = 19, col = "blue")
abline(h = 0, col = "red", lty = 2)
hist(resid(model), main = "Histogram Residual",
xlab = "Residuals", col = "lightblue")
par(mfrow = c(1, 1))