KELOMPOK 3 (ANALISIS REGRESI)
NOORHASANAH AFRILIYA ARIYATI
2026-02-04
# Bersihkan environment
rm(list = ls())
# Panggil package
library(dplyr)## Warning: package 'dplyr' was built under R version 4.5.2##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(ggplot2)
library(tidyverse)## Warning: package 'tidyverse' 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 '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 ──
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## ✖ dplyr::filter() masks stats::filter()
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(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.
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## Suggestions and bug-reports can be submitted at: https://github.com/statistikat/VIM/issues
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## Attaching package: 'VIM'
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## The following object is masked from 'package:datasets':
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## sleeplibrary(naniar)## Warning: package 'naniar' was built under R version 4.5.2library(outliers)## Warning: package 'outliers' was built under R version 4.5.2library(ggplot2)
library(mice)## Warning: package 'mice' was built under R version 4.5.2##
## Attaching package: 'mice'
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## cbind, rbind# Import data CSV
data <- read.csv("datania1k.csv")
kolom <- data[, 2]
data_sw<- data[, c("Age", "Annual_Premium")]
head(data_sw)## Age Annual_Premium
## 1 22 36513
## 2 24 2630
## 3 22 35832
## 4 72 36685
## 5 66 2630
## 6 42 31226M I S S I N G V A L U E S
total_missing<- sum (is.na(data_sw))
total_missing## [1] 0O U T L I E R
# O U T L I E R
detect_outliers <- function(data_sw) {
cat("\n=== DETEKSI OUTLIER ===\n\n")
outlier_report <- list()
for(var in names(data_sw)[sapply(data_sw, 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")
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_sw)##
## === 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# 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 <- ggplot(data.frame(value = data[[var]]), aes(x = value)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "lightblue", alpha = 0.7) +
geom_density(color = "darkblue", linewidth = 1) +
geom_vline(xintercept = c(lower_bound, upper_bound),
color = "red", linetype = "dashed", linewidth = 1) +
labs(title = paste("Distribusi dan Outlier:", var),
x = var, y = "Density") +
theme_minimal() +
annotate("text", x = lower_bound, y = 0,
label = "Bawah", vjust = 2, color = "red") +
annotate("text", x = upper_bound, y = 0,
label = "Atas", vjust = 2, color = "red")
print(hist_data)
}
# 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 ===
## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
#S T A T I S T I K D E S K R I F T I F
cat('\n STATISTIKA DESKRIFTIF:\n')##
## STATISTIKA DESKRIFTIF:summary(data_sw)## 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#A N A L I S I S R E G R E S I
# Korelasi
cat("\n2. KORELASI:\n")##
## 2. KORELASI:correlation <- cor(data_sw$Age, data_sw$Annual_Premium)
cat("Koefisien Korelasi (r) =", round(correlation, 4), "\n")## Koefisien Korelasi (r) = 0.1388# Interpretasi korelasi
if (abs(correlation) >= 0.9) {
cat("Interpretasi: Korelasi sangat kuat\n")
} else if (abs(correlation) >= 0.7) {
cat("Interpretasi: Korelasi kuat\n")
} else if (abs(correlation) >= 0.5) {
cat("Interpretasi: Korelasi sedang\n")
} else if (abs(correlation) >= 0.3) {
cat("Interpretasi: Korelasi lemah\n")
} else {
cat("Interpretasi: Korelasi sangat lemah/tidak ada\n")
}## Interpretasi: Korelasi sangat lemah/tidak ada# Model regresi linear sederhana
model <- lm(Annual_Premium ~ Age, data = data_sw)
# Ringkasan model
cat("\n1. RINGKASAN MODEL:\n")##
## 1. RINGKASAN MODEL:summary_model <- summary(model)
print(summary_model)##
## Call:
## lm(formula = Annual_Premium ~ Age, data = data_sw)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32960 -5971 1517 9265 72308
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24662.40 1386.17 17.792 < 2e-16 ***
## Age 143.79 32.48 4.427 1.06e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16200 on 998 degrees of freedom
## Multiple R-squared: 0.01926, Adjusted R-squared: 0.01827
## F-statistic: 19.59 on 1 and 998 DF, p-value: 1.063e-05cat("\n\n=== PENGUJIAN HIPOTESIS ===\n")##
##
## === PENGUJIAN HIPOTESIS ===# 6.1 Hipotesis untuk Koefisien Regresi (Slope)
cat("\n1. UJI HIPOTESIS UNTUK SLOPE (β1):\n")##
## 1. UJI HIPOTESIS UNTUK SLOPE (β1):cat(" Hipotesis Nol (H0): β1 = 0 (Tidak ada hubungan linear)\n")## Hipotesis Nol (H0): β1 = 0 (Tidak ada hubungan linear)cat(" Hipotesis Alternatif (H1): β1 ≠ 0 (Ada hubungan linear)\n")## Hipotesis Alternatif (H1): β1 ≠ 0 (Ada hubungan linear)# Dari output summary model
coef_table <- summary_model$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) = 0.05if (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