# 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 :Hubungan Protein dan Energi
data <- read.csv(file.choose("C:/Users/Asus/Downloads/archive/nilai-gizi.csv"), header = TRUE)
m <- data[c(x="protein_g",y="energy_kcal")]
head(m)
## protein_g energy_kcal
## 1 34.1 199
## 2 3.0 94
## 3 1.0 15
## 4 2.4 38
## 5 16.5 346
## 6 15.0 410
# 2. ANALISIS DESKRIPTIF DAN VISUALISASI
print("Statistik Deskriptif:")
## [1] "Statistik Deskriptif:"
summary(m)
## protein_g energy_kcal
## Min. : 0.000 Min. : 0.0
## 1st Qu.: 1.100 1st Qu.: 70.0
## Median : 3.800 Median : 137.0
## Mean : 7.531 Mean : 196.1
## 3rd Qu.:10.000 3rd Qu.: 295.0
## Max. :79.000 Max. :1710.0
# Scatter plot
ggplot(data, aes(x = protein_g, y = energy_kcal)) +
geom_point(color = "blue", size = 3) +
labs(title = "Hubungan Protein dan Energi",
x = "protein_g", y = "energy_kcal") +
theme_minimal()
# Korelasi
cor_test <- cor.test(data$protein_g, data$energy_kcal)
print(paste("Korelasi Pearson:", round(cor_test$estimate, 4)))
## [1] "Korelasi Pearson: 0.54"
print(paste("p-value korelasi:", round(cor_test$p.value, 4)))
## [1] "p-value korelasi: 0"
# 3. MEMBANGUN MODEL REGRESI
model <- lm(protein_g ~ energy_kcal, data = m)
print("Ringkasan Model Regresi:")
## [1] "Ringkasan Model Regresi:"
summary(model)
##
## Call:
## lm(formula = protein_g ~ energy_kcal, data = m)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.479 -3.806 -1.969 1.601 55.367
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.968872 0.295005 6.674 3.39e-11 ***
## energy_kcal 0.028368 0.001089 26.056 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.273 on 1649 degrees of freedom
## Multiple R-squared: 0.2916, Adjusted R-squared: 0.2912
## F-statistic: 678.9 on 1 and 1649 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$statistic, 4), "\n")
## Statistik W = 0.8238
cat(" p-value =", round(shapiro_test$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 = 288.2846
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$statistic, 4), "\n")
## Statistik DW = 1.781
cat(" p-value =", round(dw_test$p.value, 4), "\n")
## p-value = 0
if(dw_test$p.value > 0.05) {
cat(" Keputusan: Tidak ada autokorelasi\n")
} else {
cat(" Keputusan: Ada autokorelasi\n")
}
## Keputusan: Ada autokorelasi
# 5. INTERPRETASI KOEFISIEN
cat("\n=== INTERPRETASI KOEFISIEN ===\n")
##
## === INTERPRETASI KOEFISIEN ===
intercept <- coef(model)[1]
slope <- coef(model)[2]
cat("Persamaan Regresi: Nilai =", round(intercept, 2), "+", round(slope, 2), "* Jam_Belajar\n")
## Persamaan Regresi: Nilai = 1.97 + 0.03 * Jam_Belajar
cat("\nInterpretasi:\n")
##
## Interpretasi:
cat("1. Intercept (β0 =", round(intercept, 2), "):\n")
## 1. Intercept (β0 = 1.97 ):
cat(" Nilai ujian ketika jam belajar = 0 adalah", round(intercept, 2), "poin\n")
## Nilai ujian ketika jam belajar = 0 adalah 1.97 poin
cat("2. Slope (β1 =", round(slope, 2), "):\n")
## 2. Slope (β1 = 0.03 ):
cat(" Setiap penambahan 1 jam belajar, nilai ujian meningkat", round(slope, 2), "poin\n")
## Setiap penambahan 1 jam belajar, nilai ujian meningkat 0.03 poin
# 6. ESTIMASI PARAMETER DAN INFERENSI
cat("\n=== ESTIMASI PARAMETER ===\n")
##
## === ESTIMASI PARAMETER ===
conf_int <- confint(model, level = 0.95)
cat("Interval Kepercayaan 95%:\n")
## Interval Kepercayaan 95%:
cat(" Intercept: [", round(conf_int[1,1], 3), ", ", round(conf_int[1,2], 3), "]\n", sep = "")
## Intercept: [1.39, 2.547]
cat(" Slope: [", round(conf_int[2,1], 3), ", ", round(conf_int[2,2], 3), "]\n", sep = "")
## Slope: [0.026, 0.031]
# Uji hipotesis untuk slope
cat("\nUji Hipotesis untuk Slope (β1):\n")
##
## Uji Hipotesis untuk Slope (β1):
cat(" H0: β1 = 0 (tidak ada hubungan linear)\n")
## H0: β1 = 0 (tidak ada hubungan linear)
cat(" H1: β1 ≠ 0 (ada hubungan linear)\n")
## H1: β1 ≠ 0 (ada hubungan linear)
summary_model <- summary(model)
slope_pvalue <- summary_model$coefficients[2, 4]
cat(" p-value =", round(slope_pvalue, 6), "\n")
## p-value = 0
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$r.squared
cat("\nKoefisien Determinasi (R²):\n")
##
## Koefisien Determinasi (R²):
cat(" R² =", round(r_squared, 4), "\n")
## R² = 0.2916
cat(" Artinya:", round(r_squared * 100, 2), "% variasi nilai ujian dapat dijelaskan oleh jam belajar\n")
## Artinya: 29.16 % variasi nilai ujian dapat dijelaskan oleh jam belajar
# 8. VISUALISASI MODEL
ggplot(data, aes(x = protein_g, y = energy_kcal)) +
geom_point(color = "blue", size = 3) +
geom_smooth(method = "lm", se = TRUE, color = "red", fill = "pink") +
labs(title = "Garis Regresi Linear",
subtitle = paste("Y =", round(intercept, 2), "+", round(slope, 2), "X"),
x = "protein_g", y = "energy_kcal") +
theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'
# 9. PREDIKSI
new_data <- data.frame(energy_kcal = c(150, 250))
prediction <- predict(model, newdata = new_data, interval = "confidence")
cat("\n=== PREDIKSI ===\n")
##
## === PREDIKSI ===
cat("Untuk energi 150 kcal, prediksi protein =",
round(prediction[1, "fit"], 2), "gram\n")
## Untuk energi 150 kcal, prediksi protein = 6.22 gram
cat("Untuk energi 250 kcal, prediksi protein =",
round(prediction[2, "fit"], 2), "gram\n")
## Untuk energi 250 kcal, prediksi protein = 9.06 gram
# 10. DIAGNOSTIC PLOTS
par(mfrow = c(2, 2))
plot(model, which = 1:4)
par(mfrow = c(1, 1))
# 11. RINGKASAN LENGKAP
cat("\n=== RINGKASAN ANALISIS ===\n")
##
## === RINGKASAN ANALISIS ===
cat("1. Model: Protein = β0 + β1*Energi + ε\n")
## 1. Model: Protein = β0 + β1*Energi + ε
cat("2. Estimasi: Protein =", round(intercept, 3), "+",
round(slope, 3), "* Energi\n")
## 2. Estimasi: Protein = 1.969 + 0.028 * Energi
cat("3. R² =", round(r_squared, 4), "(", round(r_squared*100, 1), "%)\n")
## 3. R² = 0.2916 ( 29.2 %)
cat("4. Model regresi linear sederhana layak digunakan\n")
## 4. Model regresi linear sederhana layak digunakan
cat("5. Asumsi:\n")
## 5. Asumsi:
cat(" - Normalitas residual: p =", round(shapiro_test$p.value, 4), "\n")
## - Normalitas residual: 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
# 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!"