# 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
# Import dataset
df <- read.csv("C:/Users/LENOVO/Downloads/archive (2)/post_covid_health_effects_dataset.csv")
data <- df[, c("Age", "Days_to_Recovery")]
# 2. ANALISIS DESKRIPTIF DAN VISUALISASI
print("Statistik Deskriptif:")
## [1] "Statistik Deskriptif:"
summary(data)
## Age Days_to_Recovery
## Min. :18.00 Min. : 7.00
## 1st Qu.:32.00 1st Qu.: 52.75
## Median :45.00 Median :103.00
## Mean :44.22 Mean : 96.86
## 3rd Qu.:57.00 3rd Qu.:141.25
## Max. :69.00 Max. :179.00
# Scatter plot
ggplot(data, aes(x = Age, y = Days_to_Recovery)) +
geom_point(color = "blue", size = 3) +
labs(title = "Hubungan Umur dan Lama Pemulihan COVID",
x = "Umur (Age)", y = "Lama Pemulihan (Hari)") +
theme_minimal()
# Korelasi
cor_test <- cor.test(data$Age, data$Days_to_Recovery)
print(paste("Korelasi Pearson:", round(cor_test$estimate, 4)))
## [1] "Korelasi Pearson: -0.0366"
print(paste("p-value korelasi:", round(cor_test$p.value, 4)))
## [1] "p-value korelasi: 0.4136"
# 3. MEMBANGUN MODEL REGRESI
model <- lm(Days_to_Recovery ~ Age, data = data)
print("Ringkasan Model Regresi:")
## [1] "Ringkasan Model Regresi:"
summary(model)
##
## Call:
## lm(formula = Days_to_Recovery ~ Age, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -91.369 -44.086 6.376 43.494 84.102
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 102.3496 7.0879 14.440 <2e-16 ***
## Age -0.1242 0.1518 -0.818 0.414
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 50.98 on 498 degrees of freedom
## Multiple R-squared: 0.001343, Adjusted R-squared: -0.0006626
## F-statistic: 0.6696 on 1 and 498 DF, p-value: 0.4136
# 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$statistic, 4), "\n")
## Statistik W = 0.9472
cat(" p-value =", round(shapiro_test$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 = 0.18
cat(" p-value =", round(bp_test$p.value, 4), "\n")
## p-value = 0.6713
if(bp_test$p.value > 0.05) {
cat(" Keputusan: Varian residual homogen\n")
} else {
cat(" Keputusan: Ada heteroskedastisitas\n")
}
## Keputusan: Varian residual homogen
# 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 Uji Autokorelasi
dw_test <- dwtest(model)
cat("\n3. UJI AUTOKORELASI (Durbin-Watson):\n")
##
## 3. UJI AUTOKORELASI (Durbin-Watson):
cat(" Statistik DW =", round(dw_test$statistic, 4), "\n")
## Statistik DW = 2.034
cat(" p-value =", round(dw_test$p.value, 4), "\n")
## p-value = 0.6483
if(dw_test$p.value > 0.05) {
cat(" Keputusan: Tidak ada autokorelasi\n")
} else {
cat(" Keputusan: Ada autokorelasi\n")
}
## Keputusan: Tidak ada autokorelasi
# 5. INTERPRETASI KOEFISIEN
cat("\n=== INTERPRETASI KOEFISIEN ===\n")
##
## === INTERPRETASI KOEFISIEN ===
intercept <- coef(model)[1]
slope <- coef(model)[2]
cat("Persamaan Regresi: Days_to_Recovery =",
round(intercept, 2), "+", round(slope, 2), "* Age\n")
## Persamaan Regresi: Days_to_Recovery = 102.35 + -0.12 * Age
cat("\nInterpretasi:\n")
##
## Interpretasi:
cat("1. Intercept (β0 =", round(intercept, 2), "):\n")
## 1. Intercept (β0 = 102.35 ):
cat(" Lama pemulihan ketika umur = 0 adalah",
round(intercept, 2), "hari\n")
## Lama pemulihan ketika umur = 0 adalah 102.35 hari
cat("2. Slope (β1 =", round(slope, 2), "):\n")
## 2. Slope (β1 = -0.12 ):
cat(" Setiap kenaikan 1 tahun umur, lama pemulihan berubah",
round(slope, 2), "hari\n")
## Setiap kenaikan 1 tahun umur, lama pemulihan berubah -0.12 hari
# 6. ESTIMASI PARAMETER DAN INFERENSI
cat("\n=== ESTIMASI PARAMETER ===\n")
##
## === ESTIMASI PARAMETER ===
conf_int <- confint(model, level = 0.95)
cat("Interval Kepercayaan 95%:\n")
## Interval Kepercayaan 95%:
cat(" Intercept: [", round(conf_int[1,1], 3), ", ",
round(conf_int[1,2], 3), "]\n", sep = "")
## Intercept: [88.424, 116.275]
cat(" Slope: [", round(conf_int[2,1], 3), ", ",
round(conf_int[2,2], 3), "]\n", sep = "")
## Slope: [-0.422, 0.174]
# Uji hipotesis slope
cat("\nUji Hipotesis untuk Slope (β1):\n")
##
## Uji Hipotesis untuk Slope (β1):
cat(" H0: β1 = 0 (tidak ada hubungan linear)\n")
## H0: β1 = 0 (tidak ada hubungan linear)
cat(" H1: β1 ≠ 0 (ada hubungan linear)\n")
## H1: β1 ≠ 0 (ada hubungan linear)
summary_model <- summary(model)
slope_pvalue <- summary_model$coefficients[2, 4]
cat(" p-value =", round(slope_pvalue, 6), "\n")
## p-value = 0.413595
if(slope_pvalue < 0.05) {
cat(" Keputusan: Tolak H0, ada hubungan linear signifikan\n")
} else {
cat(" Keputusan: Gagal tolak H0\n")
}
## Keputusan: Gagal tolak H0
# 7. KOEFISIEN DETERMINASI
r_squared <- summary_model$r.squared
cat("\nKoefisien Determinasi (R²):\n")
##
## Koefisien Determinasi (R²):
cat(" R² =", round(r_squared, 4), "\n")
## R² = 0.0013
cat(" Artinya:", round(r_squared * 100, 2),
"% variasi lama pemulihan dijelaskan oleh umur\n")
## Artinya: 0.13 % variasi lama pemulihan dijelaskan oleh umur
# 8. VISUALISASI MODEL
ggplot(data, aes(x = Age, y = Days_to_Recovery)) +
geom_point(color = "blue", size = 3) +
geom_smooth(method = "lm", se = TRUE,
color = "red", fill = "pink") +
labs(title = "Garis Regresi Linear",
subtitle = paste("Y =", round(intercept, 2), "+",
round(slope, 2), "X"),
x = "Age", y = "Days to Recovery") +
theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'
# 9. PREDIKSI
new_data <- data.frame(Age = c(25, 60))
prediction <- predict(model, newdata = new_data,
interval = "confidence")
cat("\n=== PREDIKSI ===\n")
##
## === PREDIKSI ===
cat("Untuk umur 25 tahun, prediksi lama pemulihan =",
round(prediction[1, "fit"], 2), "hari\n")
## Untuk umur 25 tahun, prediksi lama pemulihan = 99.24 hari
cat("Untuk umur 60 tahun, prediksi lama pemulihan =",
round(prediction[2, "fit"], 2), "hari\n")
## Untuk umur 60 tahun, prediksi lama pemulihan = 94.9 hari
# 10. DIAGNOSTIC PLOTS
par(mfrow = c(2, 2))
plot(model, which = 1:4)
par(mfrow = c(1, 1))
# 11. RINGKASAN LENGKAP
cat("\n=== RINGKASAN ANALISIS ===\n")
##
## === RINGKASAN ANALISIS ===
cat("1. Model: Days_to_Recovery = β0 + β1*Age + ε\n")
## 1. Model: Days_to_Recovery = β0 + β1*Age + ε
cat("2. Estimasi: Y =", round(intercept, 3), "+",
round(slope, 3), "* X\n")
## 2. Estimasi: Y = 102.35 + -0.124 * X
cat("3. R² =", round(r_squared, 4),
"(", round(r_squared*100, 1), "%)\n")
## 3. R² = 0.0013 ( 0.1 %)
hasil <- list(
model = model,
coefficients = coef(model),
r_squared = r_squared,
assumptions = list(
normality = shapiro_test$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!"