Tugas Mandiri hands-on minggu 3
Widya Anjelina Putri
2026-02-11
# 1. MEMUAT PACKAGE DAN DATA
library(ggplot2)
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(car)## Loading required package: carData# Memuat data BankNote Authentication
data_asli <- read.csv("C:/Users/LENOVO/Downloads/BankNoteAuthentication.csv")
# Menentukan variabel X dan Y
data <- data.frame(
variance = data_asli$variance,
class = data_asli$class
)
# 2. ANALISIS DESKRIPTIF DAN VISUALISASI
print("Statistik Deskriptif:")## [1] "Statistik Deskriptif:"summary(data)## variance class
## Min. :-7.0421 Min. :0.0000
## 1st Qu.:-1.7730 1st Qu.:0.0000
## Median : 0.4962 Median :0.0000
## Mean : 0.4337 Mean :0.4446
## 3rd Qu.: 2.8215 3rd Qu.:1.0000
## Max. : 6.8248 Max. :1.0000# Scatter plot
ggplot(data, aes(x = variance, y = class)) +
geom_point(color = "blue", size = 3) +
labs(title = "Hubungan Variance dan Class",
x = "Variance", y = "Class") +
theme_minimal()
# Korelasi
cor_test <- cor.test(data$variance, data$class)
print(paste("Korelasi Pearson:", round(cor_test$estimate, 4)))## [1] "Korelasi Pearson: -0.7248"print(paste("p-value korelasi:", round(cor_test$p.value, 4)))## [1] "p-value korelasi: 0"# 3. MEMBANGUN MODEL REGRESI
model <- lm(class ~ variance, data = data)
print("Ringkasan Model Regresi:")## [1] "Ringkasan Model Regresi:"summary(model)##
## Call:
## lm(formula = class ~ variance, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.04282 -0.23618 0.00702 0.24282 0.80357
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.499583 0.009356 53.40 <2e-16 ***
## variance -0.126751 0.003255 -38.94 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3426 on 1370 degrees of freedom
## Multiple R-squared: 0.5254, Adjusted R-squared: 0.5251
## F-statistic: 1517 on 1 and 1370 DF, p-value: < 2.2e-16# 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$statistic, 4), "\n")## Statistik W = 0.9931cat(" p-value =", round(shapiro_test$p.value, 4), "\n")## p-value = 0if(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 = 53.2321cat(" p-value =", round(bp_test$p.value, 4), "\n")## p-value = 0if(bp_test$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$statistic, 4), "\n")## Statistik DW = 0.8856cat(" p-value =", round(dw_test$p.value, 4), "\n")## p-value = 0if(dw_test$p.value > 0.05) {
cat(" Keputusan: Tidak ada autokorelasi\n")
} else {
cat(" Keputusan: Ada autokorelasi\n")
}## Keputusan: Ada autokorelasi# 5. INTERPRETASI KOEFISIEN
cat("\n=== INTERPRETASI KOEFISIEN ===\n")##
## === INTERPRETASI KOEFISIEN ===intercept <- coef(model)[1]
slope <- coef(model)[2]
cat("Persamaan Regresi: Class =", round(intercept, 3), "+",
round(slope, 3), "* Variance\n")## Persamaan Regresi: Class = 0.5 + -0.127 * Variancecat("\nInterpretasi:\n")##
## Interpretasi:cat("1. Intercept (β0 =", round(intercept, 3), "):\n")## 1. Intercept (β0 = 0.5 ):cat(" Nilai class ketika variance = 0 adalah",
round(intercept, 3), "\n")## Nilai class ketika variance = 0 adalah 0.5cat("2. Slope (β1 =", round(slope, 3), "):\n")## 2. Slope (β1 = -0.127 ):cat(" Setiap kenaikan 1 satuan variance, nilai class berubah sebesar",
round(slope, 3), "\n")## Setiap kenaikan 1 satuan variance, nilai class berubah sebesar -0.127# 6. ESTIMASI PARAMETER DAN INFERENSI
cat("\n=== ESTIMASI PARAMETER ===\n")##
## === ESTIMASI PARAMETER ===conf_int <- confint(model, level = 0.95)
cat("Interval Kepercayaan 95%:\n")## Interval Kepercayaan 95%:cat(" Intercept: [", round(conf_int[1,1], 3), ", ",
round(conf_int[1,2], 3), "]\n", sep = "")## Intercept: [0.481, 0.518]cat(" Slope: [", round(conf_int[2,1], 3), ", ",
round(conf_int[2,2], 3), "]\n", sep = "")## Slope: [-0.133, -0.12]# Uji hipotesis untuk slope
cat("\nUji Hipotesis untuk Slope (β1):\n")##
## Uji Hipotesis untuk Slope (β1):cat(" H0: β1 = 0 (tidak ada hubungan linear)\n")## H0: β1 = 0 (tidak ada hubungan linear)cat(" H1: β1 ≠ 0 (ada hubungan linear)\n")## H1: β1 ≠ 0 (ada hubungan linear)summary_model <- summary(model)
slope_pvalue <- summary_model$coefficients[2, 4]
cat(" p-value =", round(slope_pvalue, 6), "\n")## p-value = 0if(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$r.squared
cat("\nKoefisien Determinasi (R²):\n")##
## Koefisien Determinasi (R²):cat(" R² =", round(r_squared, 4), "\n")## R² = 0.5254cat(" Artinya:", round(r_squared * 100, 2),
"% variasi class dapat dijelaskan oleh variance\n")## Artinya: 52.54 % variasi class dapat dijelaskan oleh variance# 8. VISUALISASI MODEL
ggplot(data, aes(x = variance, y = class)) +
geom_point(color = "blue", size = 3) +
geom_smooth(method = "lm", se = TRUE, color = "red", fill = "pink") +
labs(title = "Garis Regresi Linear",
subtitle = paste("Y =", round(intercept, 2), "+",
round(slope, 2), "X"),
x = "Variance", y = "Class") +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
# 9. PREDIKSI
new_data <- data.frame(variance = c(-2, 0, 2))
prediction <- predict(model, newdata = new_data, interval = "confidence")
cat("\n=== PREDIKSI ===\n")##
## === PREDIKSI ===cat("Untuk variance = -2, prediksi class =",
round(prediction[1, "fit"], 3), "\n")## Untuk variance = -2, prediksi class = 0.753cat("Untuk variance = 0, prediksi class =",
round(prediction[2, "fit"], 3), "\n")## Untuk variance = 0, prediksi class = 0.5cat("Untuk variance = 2, prediksi class =",
round(prediction[3, "fit"], 3), "\n")## Untuk variance = 2, prediksi class = 0.246# 10. DIAGNOSTIC PLOTS
par(mfrow = c(2, 2))
plot(model, which = 1:4)
par(mfrow = c(1, 1))
# 11. RINGKASAN LENGKAP
cat("\n=== RINGKASAN ANALISIS ===\n")##
## === RINGKASAN ANALISIS ===cat("1. Model: Class = β0 + β1*Variance + ε\n")## 1. Model: Class = β0 + β1*Variance + εcat("2. Estimasi: Y =", round(intercept, 3),
"+", round(slope, 3), "* X\n")## 2. Estimasi: Y = 0.5 + -0.127 * Xcat("3. R² =", round(r_squared, 4),
"(", round(r_squared*100, 1), "%)\n")## 3. R² = 0.5254 ( 52.5 %)cat("4. Asumsi:\n")## 4. Asumsi:cat(" - Normalitas: p =", round(shapiro_test$p.value, 4), "\n")## - Normalitas: p = 0cat(" - Homoskedastisitas: p =", round(bp_test$p.value, 4), "\n")## - Homoskedastisitas: p = 0cat(" - Autokorelasi: p =", round(dw_test$p.value, 4), "\n")## - Autokorelasi: p = 0print("Analisis regresi linear sederhana selesai!")## [1] "Analisis regresi linear sederhana selesai!"```