# 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)
## Loading required package: carData
## Warning: package 'carData' was built under R version 4.5.2
#data
data<- read.csv("C:/Users/ASUS/OneDrive/Semester 4/Analisis Regresi/student-mat.csv")
df<- data[,c("absences","G3")]
print('Stats')
## [1] "Stats"
summary(df)
## absences G3
## Min. : 0.000 Min. : 0.00
## 1st Qu.: 0.000 1st Qu.: 8.00
## Median : 4.000 Median :11.00
## Mean : 5.709 Mean :10.42
## 3rd Qu.: 8.000 3rd Qu.:14.00
## Max. :75.000 Max. :20.00
# Scatter plot
ggplot(data, aes(x = df$absences, y = df$G3)) +
geom_point(color = "blue", size = 3) +
labs(title = "Hubungan Absences dan Nilai akhir siswa",
x = "Absensi", y = "Nilai akhir") +
theme_minimal()
# Korelasi
cor_test <- cor.test(df$absences, df$G3)
print(paste("Korelasi Pearson:", round(cor_test$estimate, 4)))
## [1] "Korelasi Pearson: 0.0342"
print(paste("p-value korelasi:", round(cor_test$p.value, 4)))
## [1] "p-value korelasi: 0.4973"
# 3. MEMBANGUN MODEL REGRESI
model <- lm(df$G3 ~ df$absences, df = df)
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'df' will be disregarded
print("Ringkasan Model Regresi:")
## [1] "Ringkasan Model Regresi:"
summary(model)
##
## Call:
## lm(formula = df$G3 ~ df$absences, df = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.3033 -2.3033 0.5007 3.4811 9.6183
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.30327 0.28347 36.347 <2e-16 ***
## df$absences 0.01961 0.02886 0.679 0.497
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.585 on 393 degrees of freedom
## Multiple R-squared: 0.001173, Adjusted R-squared: -0.001369
## F-statistic: 0.4615 on 1 and 393 DF, p-value: 0.4973
# 4. UJI ASUMSI REGRESI LINEAR
cat("\n=== UJI ASUMSI REGRESI LINEAR ===\n")
##
## === UJI ASUMSI REGRESI LINEAR ===
# 4.1 Normalitas Residual
shapiro_test <- shapiro.test(residuals(model))
cat("1. UJI NORMALITAS (Shapiro-Wilk):\n")
## 1. UJI NORMALITAS (Shapiro-Wilk):
cat(" Statistik W =", round(shapiro_test$statistic, 4), "\n")
## Statistik W = 0.9351
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$statistic, 4), "\n")
## Statistik LM = 21.0522
cat(" p-value =", round(bp_test$p.value, 4), "\n")
## p-value = 0
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 = 1.9877
cat(" p-value =", round(dw_test$p.value, 4), "\n")
## p-value = 0.4497
if(dw_test$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: Nilai Akhir =", round(intercept, 2), "+", round(slope, 2), "* Absences\n")
## Persamaan Regresi: Nilai Akhir = 10.3 + 0.02 * Absences
cat("\nInterpretasi:\n")
##
## Interpretasi:
cat("1. Intercept (β0 =", round(intercept, 2), "):\n")
## 1. Intercept (β0 = 10.3 ):
cat(" Nilai akhir ketika absensi = 0 adalah", round(intercept, 2), "poin\n")
## Nilai akhir ketika absensi = 0 adalah 10.3 poin
cat("2. Slope (β1 =", round(slope, 2), "):\n")
## 2. Slope (β1 = 0.02 ):
cat(" Setiap penambahan 1 absensi, nilai akhir", round(slope, 2), "poin\n")
## Setiap penambahan 1 absensi, nilai akhir 0.02 poin
# 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: [9.746, 10.861]
cat(" Slope: [", round(conf_int[2,1], 3), ", ", round(conf_int[2,2], 3), "]\n", sep = "")
## Slope: [-0.037, 0.076]
# 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$coefficients[2, 4]
cat(" p-value =", round(slope_pvalue, 6), "\n")
## p-value = 0.497332
if(slope_pvalue < 0.05) {
cat(" Keputusan: Tolak H0, ada hubungan linear signifikan\n")
} else {
cat(" Keputusan: Gagal tolak H0, tidak ada hubungan linear signifikan\n")
}
## Keputusan: Gagal tolak H0, tidak ada hubungan linear signifikan
# 7. KOEFISIEN DETERMINASI
r_squared <- summary_model$r.squared
cat("\nKoefisien Determinasi (R²):\n")
##
## Koefisien Determinasi (R²):
cat(" R² =", round(r_squared, 4), "\n")
## R² = 0.0012
cat(" Artinya:", round(r_squared * 100, 2), "% variasi nilai akhir dapat dijelaskan oleh absensi\n")
## Artinya: 0.12 % variasi nilai akhir dapat dijelaskan oleh absensi
# 8. VISUALISASI MODEL
ggplot(data, aes(x = df$absences, y = df$G3)) +
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 = "Absences", y = "Nilai akhir") +
theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'
# 9. PREDIKSI
new_data <- data.frame(absences = c(12, 15))
prediction <- predict(model, newdata = new_data, interval = "confidence")
## Warning: 'newdata' had 2 rows but variables found have 395 rows
cat("\n=== PREDIKSI ===\n")
##
## === PREDIKSI ===
cat("Untuk 12 Absences, prediksi nilai =", round(prediction[1, "fit"], 2), "\n")
## Untuk 12 Absences, prediksi nilai = 10.42
cat("Untuk 15 Absences, prediksi nilai =", round(prediction[2, "fit"], 2), "\n")
## Untuk 15 Absences, prediksi nilai = 10.38
# 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: Nilai_Akhir = β0 + β1*Absences + ε\n")
## 1. Model: Nilai_Akhir = β0 + β1*Absences + ε
cat("2. Estimasi: Y =", round(intercept, 3), "+", round(slope, 3), "* X\n")
## 2. Estimasi: Y = 10.303 + 0.02 * X
cat("3. R² =", round(r_squared, 4), "(", round(r_squared*100, 1), "%)\n")
## 3. R² = 0.0012 ( 0.1 %)
cat("4. Uji F (model): p-value =",
round(summary_model$fstatistic[1], 4), "\n")
## 4. Uji F (model): p-value = 0.4615
cat("5. Asumsi:\n")
## 5. Asumsi:
cat(" - Normalitas: p =", round(shapiro_test$p.value, 4), "\n")
## - Normalitas: p = 0
cat(" - Homoskedastisitas: p =", round(bp_test$p.value, 4), "\n")
## - Homoskedastisitas: p = 0
cat(" - Autokorelasi: p =", round(dw_test$p.value, 4), "\n")
## - Autokorelasi: p = 0.4497
# Simpan hasil
hasil <- list(
model = model,
coefficients = coef(model),
r_squared = r_squared,
assumptions = list(
normality = shapiro_test$p.value,
homoscedasticity = bp_test$p.value,
autocorrelation = dw_test$p.value
),
confidence_intervals = conf_int
)
print("Analisis regresi linear sederhana selesai!")
## [1] "Analisis regresi linear sederhana selesai!"