# 1. MEMUAT PACKAGE DAN DATA
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.5.2
library(lmtest)
## Warning: package 'lmtest' was built under R version 4.5.2
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 4.5.2
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(car)
## Warning: package 'car' was built under R version 4.5.2
## Loading required package: carData
## Warning: package 'carData' was built under R version 4.5.2
# Membaca data dari file CSV
data_raw <- read.csv("C:/Users/user/OneDrive/Documents/BELAJAR!/SMS 4/ANALISIS REGRESI/Heart Attack Data Set.csv")
# Memilih variabel untuk regresi linear sederhana
data <- data.frame(
age = data_raw$age,
chol = data_raw$chol
)
# 2. ANALISIS DESKRIPTIF DAN VISUALISASI
print("Statistik Deskriptif:")
## [1] "Statistik Deskriptif:"
summary(data)
## age chol
## Min. :29.00 Min. :126.0
## 1st Qu.:47.50 1st Qu.:211.0
## Median :55.00 Median :240.0
## Mean :54.37 Mean :246.3
## 3rd Qu.:61.00 3rd Qu.:274.5
## Max. :77.00 Max. :564.0
# Scatter plot
ggplot(data, aes(x = age, y = chol)) +
geom_point(color = "blue", size = 3) +
labs(title = "Hubungan Usia dan Kadar Kolesterol",
x = "Usia", y = "Kadar Kolesterol") +
theme_minimal()
# Korelasi
cor_test <- cor.test(data$age, data$chol)
print(paste("Korelasi Pearson:", round(cor_test$estimate, 4)))
## [1] "Korelasi Pearson: 0.2137"
print(paste("p-value korelasi:", round(cor_test$p.value, 4)))
## [1] "p-value korelasi: 2e-04"
# 3. MEMBANGUN MODEL REGRESI
model <- lm(chol ~ age, data = data)
print("Ringkasan Model Regresi:")
## [1] "Ringkasan Model Regresi:"
summary(model)
##
## Call:
## lm(formula = chol ~ age, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -123.476 -32.560 -5.745 28.024 302.330
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 179.9675 17.7116 10.161 < 2e-16 ***
## age 1.2194 0.3213 3.795 0.000179 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 50.72 on 301 degrees of freedom
## Multiple R-squared: 0.04566, Adjusted R-squared: 0.04249
## F-statistic: 14.4 on 1 and 301 DF, p-value: 0.0001786
# 4. UJI ASUMSI REGRESI LINEAR
cat("\n=== UJI ASUMSI REGRESI LINEAR ===\n")
##
## === UJI ASUMSI REGRESI LINEAR ===
# 4.1 Normalitas Residual
shapiro_test <- shapiro.test(residuals(model))
cat("1. UJI NORMALITAS (Shapiro-Wilk):\n")
## 1. UJI NORMALITAS (Shapiro-Wilk):
cat(" Statistik W =", round(shapiro_test$statistic, 4), "\n")
## Statistik W = 0.9531
cat(" p-value =", round(shapiro_test$p.value, 4), "\n")
## p-value = 0
if(shapiro_test$p.value > 0.05) {
cat(" Keputusan: Residual berdistribusi normal\n")
} else {
cat(" Keputusan: Residual tidak normal\n")
}
## Keputusan: Residual tidak normal
# Q-Q Plot
qqnorm(residuals(model), main = "Q-Q Plot Residual")
qqline(residuals(model), col = "red")
# 4.2 Homoskedastisitas
bp_test <- bptest(model)
cat("\n2. UJI HOMOSKEDASTISITAS (Breusch-Pagan):\n")
##
## 2. UJI HOMOSKEDASTISITAS (Breusch-Pagan):
cat(" Statistik LM =", round(bp_test$statistic, 4), "\n")
## Statistik LM = 4.6622
cat(" p-value =", round(bp_test$p.value, 4), "\n")
## p-value = 0.0308
if(bp_test$p.value > 0.05) {
cat(" Keputusan: Varian residual homogen\n")
} else {
cat(" Keputusan: Ada heteroskedastisitas\n")
}
## Keputusan: Ada heteroskedastisitas
# Plot Residual vs Fitted
plot(fitted(model), residuals(model),
main = "Residual vs Fitted Values",
xlab = "Fitted Values", ylab = "Residuals",
pch = 19, col = "blue")
abline(h = 0, col = "red", lty = 2)
# 4.3 Tidak ada Autokorelasi
dw_test <- dwtest(model)
cat("\n3. UJI AUTOKORELASI (Durbin-Watson):\n")
##
## 3. UJI AUTOKORELASI (Durbin-Watson):
cat(" Statistik DW =", round(dw_test$statistic, 4), "\n")
## Statistik DW = 2.0037
cat(" p-value =", round(dw_test$p.value, 4), "\n")
## p-value = 0.5124
if(dw_test$p.value > 0.05) {
cat(" Keputusan: Tidak ada autokorelasi\n")
} else {
cat(" Keputusan: Ada autokorelasi\n")
}
## Keputusan: Tidak ada autokorelasi
# 5. INTERPRETASI KOEFISIEN
cat("\n=== INTERPRETASI KOEFISIEN ===\n")
##
## === INTERPRETASI KOEFISIEN ===
intercept <- coef(model)[1]
slope <- coef(model)[2]
cat("Persamaan Regresi: Chol =", round(intercept, 2), "+", round(slope, 2), "* Age\n")
## Persamaan Regresi: Chol = 179.97 + 1.22 * Age
cat("\nInterpretasi:\n")
##
## Interpretasi:
cat("1. Intercept (β0 =", round(intercept, 2), "):\n")
## 1. Intercept (β0 = 179.97 ):
cat(" Kadar kolesterol ketika usia = 0 adalah", round(intercept, 2), "\n")
## Kadar kolesterol ketika usia = 0 adalah 179.97
cat("2. Slope (β1 =", round(slope, 2), "):\n")
## 2. Slope (β1 = 1.22 ):
cat(" Setiap penambahan 1 tahun usia, kadar kolesterol berubah sebesar", round(slope, 2), "\n")
## Setiap penambahan 1 tahun usia, kadar kolesterol berubah sebesar 1.22
# 6. ESTIMASI PARAMETER DAN INFERENSI
cat("\n=== ESTIMASI PARAMETER ===\n")
##
## === ESTIMASI PARAMETER ===
conf_int <- confint(model, level = 0.95)
cat("Interval Kepercayaan 95%:\n")
## Interval Kepercayaan 95%:
cat(" Intercept: [", round(conf_int[1,1], 3), ", ", round(conf_int[1,2], 3), "]\n", sep = "")
## Intercept: [145.113, 214.822]
cat(" Slope: [", round(conf_int[2,1], 3), ", ", round(conf_int[2,2], 3), "]\n", sep = "")
## Slope: [0.587, 1.852]
# Uji hipotesis untuk slope
cat("\nUji Hipotesis untuk Slope (β1):\n")
##
## Uji Hipotesis untuk Slope (β1):
cat(" H0: β1 = 0 (tidak ada hubungan linear)\n")
## H0: β1 = 0 (tidak ada hubungan linear)
cat(" H1: β1 ≠0 (ada hubungan linear)\n")
## H1: β1 ≠0 (ada hubungan linear)
summary_model <- summary(model)
slope_pvalue <- summary_model$coefficients[2, 4]
cat(" p-value =", round(slope_pvalue, 6), "\n")
## p-value = 0.000179
if(slope_pvalue < 0.05) {
cat(" Keputusan: Tolak H0, ada hubungan linear signifikan\n")
} else {
cat(" Keputusan: Gagal tolak H0, tidak ada hubungan linear signifikan\n")
}
## Keputusan: Tolak H0, ada hubungan linear signifikan
# 7. KOEFISIEN DETERMINASI
r_squared <- summary_model$r.squared
cat("\nKoefisien Determinasi (R²):\n")
##
## Koefisien Determinasi (R²):
cat(" R² =", round(r_squared, 4), "\n")
## R² = 0.0457
cat(" Artinya:", round(r_squared * 100, 2), "% variasi kadar kolesterol dapat dijelaskan oleh usia\n")
## Artinya: 4.57 % variasi kadar kolesterol dapat dijelaskan oleh usia
# 8. VISUALISASI MODEL
ggplot(data, aes(x = age, y = chol)) +
geom_point(color = "blue", size = 3) +
geom_smooth(method = "lm", se = TRUE, color = "red", fill = "pink") +
labs(title = "Garis Regresi Linear",
subtitle = paste("Y =", round(intercept, 2), "+", round(slope, 2), "X"),
x = "Usia", y = "Kadar Kolesterol") +
theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'
# 9. PREDIKSI
new_data <- data.frame(age = c(40, 60))
prediction <- predict(model, newdata = new_data, interval = "confidence")
cat("\n=== PREDIKSI ===\n")
##
## === PREDIKSI ===
cat("Untuk usia 40 tahun, prediksi kolesterol =", round(prediction[1, "fit"], 2), "\n")
## Untuk usia 40 tahun, prediksi kolesterol = 228.75
cat("Untuk usia 60 tahun, prediksi kolesterol =", round(prediction[2, "fit"], 2), "\n")
## Untuk usia 60 tahun, prediksi kolesterol = 253.13
# 10. DIAGNOSTIC PLOTS
par(mfrow = c(2, 2))
plot(model, which = 1:4)
par(mfrow = c(1, 1))
# 11. RINGKASAN LENGKAP
cat("\n=== RINGKASAN ANALISIS ===\n")
##
## === RINGKASAN ANALISIS ===
cat("Model regresi linear sederhana telah dibangun untuk melihat pengaruh usia terhadap kadar kolesterol.\n")
## Model regresi linear sederhana telah dibangun untuk melihat pengaruh usia terhadap kadar kolesterol.
cat("Interpretasi dilakukan berdasarkan uji asumsi, uji hipotesis, dan koefisien determinasi.\n")
## Interpretasi dilakukan berdasarkan uji asumsi, uji hipotesis, dan koefisien determinasi.