Minggu3

# 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

# Data contoh: Hubungan tinggi badan dan berat badan 

data <- read.csv("C:/Users/Yohana Gabriela/OneDrive/Documents/500_Person_Gender_Height_Weight_Index.csv")

data_reg <- data[c("Height","Weight")]


# 2. ANALISIS DESKRIPTIF DAN VISUALISASI
print("Statistik Deskriptif:")

## [1] "Statistik Deskriptif:"

summary(data)

##     Gender              Height          Weight        Index      
##  Length:500         Min.   :140.0   Min.   : 50   Min.   :0.000  
##  Class :character   1st Qu.:156.0   1st Qu.: 80   1st Qu.:3.000  
##  Mode  :character   Median :170.5   Median :106   Median :4.000  
##                     Mean   :169.9   Mean   :106   Mean   :3.748  
##                     3rd Qu.:184.0   3rd Qu.:136   3rd Qu.:5.000  
##                     Max.   :199.0   Max.   :160   Max.   :5.000

# Scatter plot
ggplot(data_reg, aes(x = Height, y = Weight)) +
  geom_point(color = "blue", size = 4) +
  labs(title = "Hubungan Tinggi Badan dan Berat Badan",
       x = "Tinggi Badan (cm)", y = "Berat Badan (kg)") +
  theme_minimal()

# Korelasi
cor_test <- cor.test(data_reg$Height, data_reg$Weight)
print(paste("Korelasi Pearson:", round(cor_test$estimate, )))

## [1] "Korelasi Pearson: 0"

print(paste("p-value korelasi:", round(cor_test$p.value, 4)))

## [1] "p-value korelasi: 0.9921"

# 3. MEMBANGUN MODEL REGRESI
model <- lm(Weight ~ Height, data = data_reg)
print("Ringkasan Model Regresi:")

## [1] "Ringkasan Model Regresi:"

summary(model)

## 
## Call:
## lm(formula = Weight ~ Height, data = data_reg)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -56.025 -26.016  -0.017  29.989  54.022 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.059e+02  1.513e+01   6.996 8.51e-12 ***
## Height      8.819e-04  8.862e-02   0.010    0.992    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.42 on 498 degrees of freedom
## Multiple R-squared:  1.989e-07,  Adjusted R-squared:  -0.002008 
## F-statistic: 9.904e-05 on 1 and 498 DF,  p-value: 0.9921

# 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 = 0.953

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 = 0.1547

cat("   p-value =", round(bp_test$p.value, 4), "\n")

##    p-value = 0.6941

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 = 4)

# 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 = 2.0172

cat("   p-value =", round(dw_test$p.value, 4), "\n")

##    p-value = 0.576

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)[4]

cat("Persamaan Regresi: Weight =", round(intercept, 4), "+", round(slope, 4), "* Height\n")

## Persamaan Regresi: Weight = 105.8501 + NA * Height

cat("\nInterpretasi:\n")

## 
## Interpretasi:

cat("1. Intercept (β0 =", round(intercept, 4), "):\n")

## 1. Intercept (β0 = 105.8501 ):

cat("   Berat badan ketika tinggi = 0 cm adalah", round(intercept, 4), "kg (tidak realistis secara praktis)\n")

##    Berat badan ketika tinggi = 0 cm adalah 105.8501 kg (tidak realistis secara praktis)

cat("2. Slope (β1 =", round(slope, 4), "):\n")

## 2. Slope (β1 = NA ):

cat("   Setiap kenaikan 1 cm tinggi badan, berat badan meningkat sekitar", round(slope, 2), "kg\n")

##    Setiap kenaikan 1 cm tinggi badan, berat badan meningkat sekitar NA kg

# 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: [76.125, 135.575]

cat("   Slope:     [", round(conf_int[2,1], 3), ", ", round(conf_int[2,2], 3), "]\n", sep = "")

##    Slope:     [-0.173, 0.175]

# 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 = 0.992064

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("Koefisien Determinasi (R²) =", round(r_squared, 4), "\n")

## Koefisien Determinasi (R²) = 0

cat("Artinya:", round(r_squared*100,2), "% variasi berat badan dapat dijelaskan oleh tinggi badan\n")

## Artinya: 0 % variasi berat badan dapat dijelaskan oleh tinggi badan

# 8. VISUALISASI MODEL DENGAN GARIS REGRESI
ggplot(data_reg, aes(x = Height, y = Weight)) +
  geom_point(color = "blue", size = 2) +
  geom_smooth(method = "lm", se = TRUE, color = "red", fill = "pink") +
  labs(title = "Garis Regresi Linear",
       subtitle = paste("Weight =", round(intercept, 2), "+", round(slope, 2), "* Height"),
       x = "Tinggi Badan (cm)", y = "Berat Badan (kg)") +
  theme_minimal()

## `geom_smooth()` using formula = 'y ~ x'

# 9. PREDIKSI
new_data <- data.frame(Height = c(170, 180))
prediction <- predict(model, newdata = new_data, interval = "confidence")
cat("\n=== PREDIKSI ===\n")

## 
## === PREDIKSI ===

cat("Prediksi berat badan untuk tinggi 170 cm =", round(prediction[1, "fit"], 2), "kg\n")

## Prediksi berat badan untuk tinggi 170 cm = 106 kg

cat("Prediksi berat badan untuk tinggi 180 cm =", round(prediction[2, "fit"], 2), "kg\n")

## Prediksi berat badan untuk tinggi 180 cm = 106.01 kg

# 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: Weight = β0 + β1*Height + ε\n")

## 1. Model: Weight = β0 + β1*Height + ε

cat("2. Estimasi: Weight =", round(intercept, 3), "+", round(slope, 3), "* Height\n")

## 2. Estimasi: Weight = 105.85 + NA * Height

cat("3. R² =", round(r_squared, 4), "(", round(r_squared*100, 1), "%)\n")

## 3. R² = 0 ( 0 %)

cat("4. Uji F (model): p-value =", summary_model$fstatistic[1], "\n")

## 4. Uji F (model): p-value = 9.903581e-05

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 = 0.6941

cat("   - Autokorelasi: p =", round(dw_test$p.value, 4), "\n")

##    - Autokorelasi: p = 0.576

# Simpan hasil analisis
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!"