Hands On Mika Mg2 Anreg

library(csv)

## Warning: package 'csv' was built under R version 4.5.2

library(outliers)

## Warning: package 'outliers' was built under R version 4.5.2

df <- read.csv("C:/Analisis Regresi/datania1k.csv")
data <- df[c("Age","Annual_Premium")]
head(data)

##   Age Annual_Premium
## 1  22          36513
## 2  24           2630
## 3  22          35832
## 4  72          36685
## 5  66           2630
## 6  42          31226

tail(data)

##      Age Annual_Premium
## 995   48          47533
## 996   47          29384
## 997   56          47479
## 998   22          29000
## 999   48          45107
## 1000  33          43068

total_missing <- sum(is.na(data))
total_missing

## [1] 0

summary(data)

##       Age        Annual_Premium  
##  Min.   :20.00   Min.   :  2630  
##  1st Qu.:25.00   1st Qu.: 24415  
##  Median :38.00   Median : 31512  
##  Mean   :39.65   Mean   : 30364  
##  3rd Qu.:50.25   3rd Qu.: 39556  
##  Max.   :85.00   Max.   :100278

detect_outliers <- function(data) {
  cat("\n=== DETEKSI OUTLIER ===\n\n")
  
  outlier_report <- list()
  
  for(var in names(data)[sapply(data, is.numeric)]) {
    cat("Analisis outlier untuk variabel:", var, "\n")
    
    # Statistik deskriptif
    stats <- summary(data[[var]])
    iqr_val <- IQR(data[[var]], na.rm = TRUE)
    q1 <- quantile(data[[var]], 0.25, na.rm = TRUE)
    q3 <- quantile(data[[var]], 0.75, na.rm = TRUE)
    lower_bound <- q1 - 1.5 * iqr_val
    upper_bound <- q3 + 1.5 * iqr_val
    
    # Deteksi outlier dengan metode IQR
    outliers_iqr <- data[[var]][data[[var]] < lower_bound | data[[var]] > upper_bound]
    
    # Deteksi outlier dengan metode Z-score
    z_scores <- scale(data[[var]])
    outliers_z <- data[[var]][abs(z_scores) > 3]
    
    # Deteksi outlier dengan metode Grubbs (uji statistik)
    if(length(na.omit(data[[var]])) > 6) {
      tryCatch({
        grubbs_test <- grubbs.test(na.omit(data[[var]]))
        grubbs_outlier <- ifelse(grubbs_test$p.value < 0.05, "Terdeteksi", "Tidak terdeteksi")
      }, error = function(e) {
        grubbs_outlier <- "Tidak dapat dihitung"
      })
    } else {
      grubbs_outlier <- "Data tidak cukup"
    }
    
    # Ringkasan
    outlier_report[[var]] <- list(
      n_outliers_iqr = length(outliers_iqr),
      n_outliers_z = length(outliers_z),
      grubbs_result = grubbs_outlier,
      lower_bound = lower_bound,
      upper_bound = upper_bound,
      outlier_values = unique(round(outliers_iqr, 2))
    )
    
    cat("  - Outlier (IQR method):", length(outliers_iqr), "\n")
    cat("  - Outlier (Z-score > 3):", length(outliers_z), "\n")
    cat("  - Uji Grubbs:", grubbs_outlier, "\n")
    cat("  - Batas bawah:", round(lower_bound, 2), "\n")
    cat("  - Batas atas:", round(upper_bound, 2), "\n")
    
    if(length(outliers_iqr) > 0) {
      cat("  - Nilai outlier:", paste(head(unique(round(outliers_iqr, 2)), 5), collapse = ", "), "\n")
    }
    cat("\n")
  }
  
  return(outlier_report)
}

# Deteksi outlier
outlier_analysis <- detect_outliers(data)

## 
## === DETEKSI OUTLIER ===
## 
## Analisis outlier untuk variabel: Age 
##   - Outlier (IQR method): 0 
##   - Outlier (Z-score > 3): 0 
##   - Uji Grubbs: Tidak terdeteksi 
##   - Batas bawah: -12.88 
##   - Batas atas: 88.12 
## 
## Analisis outlier untuk variabel: Annual_Premium 
##   - Outlier (IQR method): 26 
##   - Outlier (Z-score > 3): 5 
##   - Uji Grubbs: Terdeteksi 
##   - Batas bawah: 1704.5 
##   - Batas atas: 62266.5 
##   - Nilai outlier: 81192, 100278, 63273, 70452, 71918

cor(data)

##                      Age Annual_Premium
## Age            1.0000000      0.1387657
## Annual_Premium 0.1387657      1.0000000

model <- lm(data$Age~data$Annual_Premium,data = data)
cat("\n1. RINGKASAN MODEL:\n")

## 
## 1. RINGKASAN MODEL:

summary_model <- summary(model)
print(summary_model)

## 
## Call:
## lm(formula = data$Age ~ data$Annual_Premium, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -26.016 -14.305  -0.939  10.210  45.079 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         3.559e+01  1.043e+00  34.114  < 2e-16 ***
## data$Annual_Premium 1.339e-04  3.025e-05   4.427 1.06e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.63 on 998 degrees of freedom
## Multiple R-squared:  0.01926,    Adjusted R-squared:  0.01827 
## F-statistic: 19.59 on 1 and 998 DF,  p-value: 1.063e-05

# ===============================
# UJI HIPOTESIS REGRESI (UJI t)
# ===============================

alpha <- 0.05
summary_model <- summary(model)

coef_table <- coef(summary_model)
p_value <- as.numeric(coef_table[2, 4])

cat("\n=== UJI HIPOTESIS (H0) ===\n")

## 
## === UJI HIPOTESIS (H0) ===

cat("H0 : Age tidak berpengaruh signifikan terhadap Annual_Premium\n")

## H0 : Age tidak berpengaruh signifikan terhadap Annual_Premium

cat("H1 : Age berpengaruh signifikan terhadap Annual_Premium\n\n")

## H1 : Age berpengaruh signifikan terhadap Annual_Premium

cat("Nilai p-value:", p_value, "\n")

## Nilai p-value: 1.062773e-05

if(p_value < alpha) {
  cat("Keputusan: Tolak H0\n")
  cat("Kesimpulan: Age berpengaruh signifikan terhadap Annual_Premium\n")
} else {
  cat("Keputusan: Gagal menolak H0\n")
  cat("Kesimpulan: Age tidak berpengaruh signifikan terhadap Annual_Premium\n")
}

## Keputusan: Tolak H0
## Kesimpulan: Age berpengaruh signifikan terhadap Annual_Premium