# =========================
# 1. Load Library
# =========================
library(readr)
## Warning: package 'readr' was built under R version 4.5.2
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.5.2
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(stats)
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.5.2
library(corrplot)
## Warning: package 'corrplot' was built under R version 4.5.2
## corrplot 0.95 loaded
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
##
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
##
## recode
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(Metrics)
## Warning: package 'Metrics' was built under R version 4.5.2
library(reshape2)
## Warning: package 'reshape2' was built under R version 4.5.2
# =========================
# 2. Import Data
# =========================
data <- read.csv("C:/Users/Msi user/Downloads/Tugas Anreg Smt 6/StudentsPerformance.csv")
cat("Data Awal:\n")
## Data Awal:
head(data)
## gender race.ethnicity parental.level.of.education lunch
## 1 female group B bachelor's degree standard
## 2 female group C some college standard
## 3 female group B master's degree standard
## 4 male group A associate's degree free/reduced
## 5 male group C some college standard
## 6 female group B associate's degree standard
## test.preparation.course math.score reading.score writing.score
## 1 none 72 72 74
## 2 completed 69 90 88
## 3 none 90 95 93
## 4 none 47 57 44
## 5 none 76 78 75
## 6 none 71 83 78
# =========================
# 3. Pilih Variabel
# =========================
kolom <- c("math_score","reading_score","writing_score","test_preparation_course")
# Cek missing value
colSums(is.na(data))
## gender race.ethnicity
## 0 0
## parental.level.of.education lunch
## 0 0
## test.preparation.course math.score
## 0 0
## reading.score writing.score
## 0 0
# Hapus missing value
data <- na.omit(data)
cat("\nData setelah hapus NA:\n")
##
## Data setelah hapus NA:
colSums(is.na(data))
## gender race.ethnicity
## 0 0
## parental.level.of.education lunch
## 0 0
## test.preparation.course math.score
## 0 0
## reading.score writing.score
## 0 0
# 4. Ubah Variabel Kategori
# =========================
colnames(data) <- c("gender","race","parent_edu","lunch",
"test_preparation_course","math_score",
"reading_score","writing_score")
data$test_preparation_course <- ifelse(data$test_preparation_course == "completed", 1, 0)
# 5. Cek Outlier
# =========================
boxplot(data[kolom],
main = "Boxplot Sebelum Hapus Outlier",
col = "lightblue")
# Menghitung Q1 dan Q3
Q1 <- apply(data[kolom], 2, quantile, probs = 0.25)
Q3 <- apply(data[kolom], 2, quantile, probs = 0.75)
# Menghitung IQR
IQR_val <- Q3 - Q1
# Menentukan batas bawah dan batas atas
lower_bound <- Q1 - 1.5 * IQR_val
upper_bound <- Q3 + 1.5 * IQR_val
# Deteksi outlier
outlier <- sweep(data[kolom], 2, lower_bound, "<") |
sweep(data[kolom], 2, upper_bound, ">")
# Menampilkan jumlah outlier tiap variabel
cat("Jumlah Outlier tiap variabel:\n")
## Jumlah Outlier tiap variabel:
print(colSums(outlier))
## math_score reading_score writing_score
## 8 6 5
## test_preparation_course
## 0
# Menghapus baris yang mengandung outlier
outlier_row <- apply(outlier, 1, any)
data_clean <- data[!outlier_row, ]
# Menampilkan jumlah data sebelum dan sesudah
cat("\nJumlah data sebelum hapus outlier:", nrow(data), "\n")
##
## Jumlah data sebelum hapus outlier: 1000
cat("Jumlah data setelah hapus outlier:", nrow(data_clean), "\n")
## Jumlah data setelah hapus outlier: 988
# Boxplot setelah hapus outlier
boxplot(data_clean[kolom],
main = "Boxplot Setelah Hapus Outlier",
col = "lightgreen")
# Korelasi Pearson
cat("\nKorelasi Pearson\n")
##
## Korelasi Pearson
corr_matrix <- cor(data_clean[kolom], method = "pearson")
print(corr_matrix)
## math_score reading_score writing_score
## math_score 1.0000000 0.8014054 0.7833488
## reading_score 0.8014054 1.0000000 0.9506286
## writing_score 0.7833488 0.9506286 1.0000000
## test_preparation_course 0.1671689 0.2328474 0.3087789
## test_preparation_course
## math_score 0.1671689
## reading_score 0.2328474
## writing_score 0.3087789
## test_preparation_course 1.0000000
# Heatmap korelasi
library(ggplot2)
library(reshape2)
corr_melt <- melt(corr_matrix)
ggplot(corr_melt, aes(Var1, Var2, fill = value)) +
geom_tile() +
geom_text(aes(label = round(value,2))) +
scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0) +
labs(title = "Heatmap Korelasi Pearson",
x = "",
y = "") +
theme_minimal()
# Korelasi dengan math_score
variabel <- c("reading_score","writing_score","test_preparation_course")
for (var in variabel) {
test <- cor.test(data_clean$math_score, data_clean[[var]])
cat(var, "r =", round(test$estimate,3),
"p =", round(test$p.value,4), "\n")
}
## reading_score r = 0.801 p = 0
## writing_score r = 0.783 p = 0
## test_preparation_course r = 0.167 p = 0
# =========================
# Mendefinisikan variabel dependen (Y)
# =========================
Y <- data_clean$math_score
# =========================
# Mendefinisikan variabel independen (X)
# =========================
X <- data_clean[, c("reading_score","writing_score","test_preparation_course")]
# Menambahkan konstanta (intercept)
X <- cbind(constant = 1, X)
# =========================
# Model Regresi Linear
# =========================
model <- lm(math_score ~ reading_score + writing_score + test_preparation_course,
data = data_clean)
# Ringkasan model
summary(model)
##
## Call:
## lm(formula = math_score ~ reading_score + writing_score + test_preparation_course,
## data = data_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23.3142 -6.0720 0.2119 6.0936 24.3132
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.99903 1.38461 6.499 1.28e-10 ***
## reading_score 0.57645 0.06395 9.014 < 2e-16 ***
## writing_score 0.26207 0.06310 4.153 3.56e-05 ***
## test_preparation_course -1.34823 0.60848 -2.216 0.0269 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.552 on 984 degrees of freedom
## Multiple R-squared: 0.6488, Adjusted R-squared: 0.6477
## F-statistic: 606 on 3 and 984 DF, p-value: < 2.2e-16
# =========================
# Mengambil koefisien model
# =========================
coef_model <- coef(model)
b0 <- coef_model["(Intercept)"]
b1 <- coef_model["reading_score"]
b2 <- coef_model["writing_score"]
b3 <- coef_model["test_preparation_course"]
cat("\nPersamaan Model:\n")
##
## Persamaan Model:
cat(sprintf("Y = %.3f + (%.3f)X1 + (%.3f)X2 + (%.3f)X3\n",
b0, b1, b2, b3))
## Y = 8.999 + (0.576)X1 + (0.262)X2 + (-1.348)X3
# =========================
# R-square
# =========================
r2 <- summary(model)$r.squared
adj_r2 <- summary(model)$adj.r.squared
cat(sprintf("\nR-square = %.3f\n", r2))
##
## R-square = 0.649
cat(sprintf("Adjusted R-square = %.3f\n", adj_r2))
## Adjusted R-square = 0.648
# =========================
# Interpretasi R-square
# =========================
cat("\nInterpretasi R-square:\n")
##
## Interpretasi R-square:
cat(sprintf("Nilai R-square sebesar %.3f menunjukkan bahwa %.2f%% variasi nilai matematika siswa ",
r2, r2*100))
## Nilai R-square sebesar 0.649 menunjukkan bahwa 64.88% variasi nilai matematika siswa
cat("dapat dijelaskan oleh variabel reading_score, writing_score, dan test_preparation_course secara bersama-sama, ")
## dapat dijelaskan oleh variabel reading_score, writing_score, dan test_preparation_course secara bersama-sama,
cat(sprintf("sedangkan sisanya sebesar %.2f%% dijelaskan oleh faktor lain di luar model.\n",
(1-r2)*100))
## sedangkan sisanya sebesar 35.12% dijelaskan oleh faktor lain di luar model.
# =========================
# Uji Asumsi Klasik
# =========================
# 1. Normalitas (Shapiro-Wilk)
residual <- resid(model)
# Ambil maksimal 1000 sampel (biar tidak error kalau data kecil)
set.seed(123)
res_sample <- sample(residual, min(length(residual), 1000))
shapiro_test <- shapiro.test(res_sample)
print(shapiro_test)
##
## Shapiro-Wilk normality test
##
## data: res_sample
## W = 0.99626, p-value = 0.01796
if (shapiro_test$p.value > 0.05){
cat("Residual berdistribusi normal sehingga asumsi normalitas terpenuhi.\n")
} else {
cat("Residual tidak berdistribusi normal sehingga asumsi normalitas tidak terpenuhi.\n")
}
## Residual tidak berdistribusi normal sehingga asumsi normalitas tidak terpenuhi.
# =========================
# 2. Multikolinearitas (VIF)
# =========================
library(car)
vif_values <- vif(model)
cat("\nUji Multikolinearitas (VIF):\n")
##
## Uji Multikolinearitas (VIF):
print(vif_values)
## reading_score writing_score test_preparation_course
## 10.841969 11.334855 1.154183
if (all(vif_values < 10)) {
cat("Interpretasi: Tidak terdapat multikolinearitas antar variabel bebas (reading, writing, test preparation).\n")
} else {
cat("Interpretasi: Terdapat multikolinearitas pada beberapa variabel bebas.\n")
}
## Interpretasi: Terdapat multikolinearitas pada beberapa variabel bebas.
# =========================
# 3. Heteroskedastisitas (Breusch-Pagan)
# =========================
library(lmtest)
bp_test <- bptest(model)
cat("\nUji Heteroskedastisitas (Breusch-Pagan):\n")
##
## Uji Heteroskedastisitas (Breusch-Pagan):
print(bp_test)
##
## studentized Breusch-Pagan test
##
## data: model
## BP = 4.5466, df = 3, p-value = 0.2082
if (bp_test$p.value > 0.05) {
cat("Interpretasi: Tidak terjadi heteroskedastisitas (model bersifat homoskedastis).\n")
} else {
cat("Interpretasi: Terjadi heteroskedastisitas pada model regresi.\n")
}
## Interpretasi: Tidak terjadi heteroskedastisitas (model bersifat homoskedastis).
# =========================
# 4. Autokorelasi (Durbin-Watson)
# =========================
dw_test <- dwtest(model)
cat("\nUji Autokorelasi (Durbin-Watson):\n")
##
## Uji Autokorelasi (Durbin-Watson):
print(dw_test)
##
## Durbin-Watson test
##
## data: model
## DW = 2.0453, p-value = 0.7617
## alternative hypothesis: true autocorrelation is greater than 0
dw_value <- dw_test$statistic
cat("Nilai DW =", dw_value, "\n")
## Nilai DW = 2.045269
if (dw_value > 1.5 & dw_value < 2.5) {
cat("Interpretasi: Tidak terdapat autokorelasi pada residual.\n")
} else if (dw_value <= 1.5) {
cat("Interpretasi: Terdapat autokorelasi positif.\n")
} else {
cat("Interpretasi: Terdapat autokorelasi negatif.\n")
}
## Interpretasi: Tidak terdapat autokorelasi pada residual.
#Prediksi
data_clean$prediksi_math_score <- predict(model)
# =========================
# Evaluasi Model
# =========================
# Nilai aktual
Y <- data_clean$math_score
# Nilai prediksi
pred <- data_clean$prediksi_math_score
# RMSE
rmse <- sqrt(mean((Y - pred)^2))
# MAE
mae <- mean(abs(Y - pred))
# MAPE
mape <- mean(abs((Y - pred) / Y)) * 100
cat("RMSE =", rmse, "\n")
## RMSE = 8.534905
cat("MAE =", mae, "\n")
## MAE = 6.98042
cat("MAPE =", mape, "%\n")
## MAPE = 11.26838 %
cat("\nInterpretasi Evaluasi Model:\n")
##
## Interpretasi Evaluasi Model:
cat(sprintf("RMSE sebesar %.3f menunjukkan rata-rata besar kesalahan prediksi dalam satuan yang sama dengan nilai matematika siswa (math_score).\n", rmse))
## RMSE sebesar 8.535 menunjukkan rata-rata besar kesalahan prediksi dalam satuan yang sama dengan nilai matematika siswa (math_score).
cat(sprintf("MAE sebesar %.3f menunjukkan rata-rata kesalahan absolut antara nilai matematika aktual dengan nilai hasil prediksi model.\n", mae))
## MAE sebesar 6.980 menunjukkan rata-rata kesalahan absolut antara nilai matematika aktual dengan nilai hasil prediksi model.
if (mape < 10) {
cat(sprintf("MAPE sebesar %.2f%% menunjukkan model memiliki akurasi sangat baik.\n", mape))
} else if (mape < 20) {
cat(sprintf("MAPE sebesar %.2f%% menunjukkan model memiliki akurasi baik.\n", mape))
} else if (mape < 50) {
cat(sprintf("MAPE sebesar %.2f%% menunjukkan model memiliki akurasi cukup.\n", mape))
} else {
cat(sprintf("MAPE sebesar %.2f%% menunjukkan model memiliki akurasi rendah.\n", mape))
}
## MAPE sebesar 11.27% menunjukkan model memiliki akurasi baik.
# =========================
# Menampilkan hasil prediksi
# =========================
hasil <- data_clean[, c("math_score","prediksi_math_score")]
cat("\nTabel Hasil Prediksi:\n")
##
## Tabel Hasil Prediksi:
print(hasil)
## math_score prediksi_math_score
## 1 72 69.89657
## 2 69 82.59341
## 3 90 88.13424
## 4 47 53.38774
## 5 76 73.61734
## 6 71 77.28580
## 7 88 86.52394
## 8 40 44.00709
## 9 64 62.10225
## 10 38 56.68951
## 11 58 53.75494
## 12 40 50.24342
## 13 65 74.82256
## 14 78 67.50006
## 15 50 54.75091
## 16 69 72.67420
## 17 88 82.84106
## 19 46 43.91689
## 20 54 58.41937
## 21 66 65.28446
## 22 65 69.22942
## 23 44 54.01701
## 24 69 70.21095
## 25 74 69.54430
## 26 73 70.52533
## 27 69 54.54115
## 28 67 68.42929
## 29 70 66.38505
## 30 62 69.00574
## 31 69 71.04947
## 32 63 62.45452
## 33 56 67.53795
## 34 40 43.16857
## 35 97 80.63988
## 36 81 75.04674
## 37 74 77.44324
## 38 50 61.35393
## 39 75 82.59341
## 40 57 56.21819
## 41 55 58.31424
## 42 58 68.90061
## 43 53 59.46764
## 44 59 62.41663
## 45 50 55.43198
## 46 65 55.06529
## 47 55 61.36836
## 48 66 69.84426
## 49 57 70.22538
## 50 82 77.56230
## 51 53 53.28312
## 52 77 65.24657
## 53 53 45.36975
## 54 88 73.61734
## 55 71 78.87264
## 56 33 43.90247
## 57 82 79.18702
## 58 52 53.54519
## 59 58 56.86138
## 61 79 69.17710
## 62 39 40.39094
## 63 62 58.57630
## 64 69 73.72197
## 65 59 57.89523
## 66 67 61.87807
## 67 45 40.02425
## 68 60 69.89657
## 69 61 57.10902
## 70 39 60.82979
## 71 58 63.09821
## 72 63 55.86592
## 73 41 50.97732
## 74 61 56.53257
## 75 49 47.98993
## 76 44 42.59212
## 78 80 73.84152
## 79 61 69.17710
## 80 62 66.01835
## 81 47 50.34855
## 82 49 46.73241
## 83 50 48.89570
## 84 72 62.40221
## 85 42 40.39094
## 86 73 76.60472
## 87 76 79.90649
## 88 71 69.32012
## 89 58 66.90919
## 90 73 80.06343
## 91 65 69.89657
## 92 27 38.03283
## 93 71 73.14552
## 94 43 46.69452
## 95 79 82.68412
## 96 78 75.83295
## 97 65 61.94481
## 98 63 67.50006
## 99 58 63.86949
## 100 65 63.86949
## 101 79 65.17983
## 102 68 69.70124
## 103 85 84.78016
## 104 60 45.33186
## 105 98 80.81175
## 106 58 66.49018
## 107 87 92.85098
## 108 66 60.73959
## 109 52 71.15410
## 110 70 64.76083
## 111 77 84.63765
## 112 62 53.54519
## 113 54 51.86815
## 114 51 56.58488
## 115 99 91.50275
## 116 84 72.77882
## 117 75 79.48698
## 118 78 76.97142
## 119 51 61.30162
## 120 55 65.80860
## 121 79 84.00838
## 122 91 83.06524
## 123 88 85.63311
## 124 63 56.53257
## 125 83 74.24611
## 126 87 86.29976
## 127 72 65.75628
## 128 65 71.43059
## 129 82 75.66108
## 130 51 50.61062
## 131 89 78.91053
## 132 53 39.46223
## 133 87 68.65296
## 134 75 76.35708
## 135 74 72.84556
## 136 58 53.28312
## 137 51 49.52396
## 138 70 55.37967
## 139 59 64.60338
## 140 71 60.89704
## 141 76 69.11036
## 142 59 61.51137
## 143 42 53.50730
## 144 57 46.10364
## 145 88 71.52129
## 147 88 77.07605
## 148 73 65.49422
## 149 68 72.11217
## 150 100 89.66826
## 151 62 64.35574
## 152 77 65.44190
## 153 59 65.29889
## 154 54 49.56235
## 155 62 63.60742
## 156 70 82.01696
## 157 66 70.74952
## 158 60 59.31020
## 159 61 80.02554
## 160 66 61.51137
## 161 82 72.00704
## 162 75 80.65431
## 163 49 53.17849
## 164 52 52.39229
## 165 81 85.88075
## 166 96 91.50275
## 167 53 50.41529
## 168 58 71.90242
## 169 68 75.93757
## 170 67 69.22942
## 171 72 69.12479
## 172 94 80.16805
## 173 79 79.80136
## 174 63 65.96604
## 175 43 51.20150
## 176 81 82.90780
## 177 46 53.97913
## 178 71 72.21680
## 179 52 64.25061
## 180 97 91.50275
## 181 62 66.50460
## 182 46 63.18841
## 183 50 50.13880
## 184 65 67.11894
## 185 45 50.46761
## 186 65 63.30747
## 187 80 69.84375
## 188 62 63.51722
## 189 48 50.76756
## 190 77 82.52667
## 191 66 64.55107
## 192 76 76.19964
## 193 62 63.18841
## 194 77 59.63901
## 195 69 78.34850
## 196 61 54.33139
## 197 59 64.46037
## 198 55 54.64578
## 199 45 53.96470
## 200 78 74.45586
## 201 67 78.61057
## 202 65 75.87083
## 203 69 71.46848
## 204 57 66.59480
## 205 59 43.64040
## 206 74 69.02016
## 207 82 60.98724
## 208 81 73.68408
## 209 74 75.60876
## 210 58 61.45906
## 211 80 73.89384
## 213 42 60.46310
## 214 60 51.72564
## 215 87 81.33538
## 216 84 75.15136
## 217 83 80.28761
## 218 34 43.43064
## 219 66 71.73055
## 220 61 54.60789
## 221 56 66.24254
## 222 87 77.12836
## 223 55 62.71659
## 224 86 74.77024
## 225 52 64.82757
## 226 45 55.43198
## 227 72 69.11036
## 228 57 51.97328
## 229 68 67.27588
## 230 88 87.04808
## 231 76 63.18841
## 232 46 44.79330
## 233 67 80.32550
## 234 92 79.59160
## 235 83 76.93353
## 236 80 72.41213
## 237 63 64.60338
## 238 64 61.63093
## 239 54 52.33997
## 240 84 76.08059
## 241 73 64.14599
## 242 80 78.59615
## 243 56 53.38825
## 244 59 49.66697
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## 247 89 72.20237
## 248 58 65.82302
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## 250 68 57.47572
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## 253 60 66.34716
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## 270 71 71.15410
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## 275 88 76.56633
## 276 83 73.09320
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## 278 59 63.62235
## 279 65 79.53929
## 280 73 56.21819
## 281 53 49.98135
## 282 45 48.72383
## 283 73 76.55241
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## 285 37 47.57093
## 286 81 76.40940
## 287 97 77.98181
## 288 67 81.79278
## 289 88 72.15006
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## 291 76 67.17125
## 292 86 69.42474
## 293 63 57.17576
## 294 65 70.73509
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## 296 67 60.46310
## 297 46 42.55424
## 298 71 68.12883
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## 300 90 78.80540
## 301 81 73.84152
## 302 56 53.75494
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## 304 80 69.58168
## 305 74 72.63631
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## 307 99 79.02958
## 308 51 50.50549
## 309 53 67.48564
## 310 49 55.48430
## 311 73 73.77478
## 312 66 58.52399
## 313 67 60.63497
## 314 68 64.35574
## 315 59 64.19880
## 316 71 64.07925
## 317 77 78.76802
## 318 83 70.94484
## 319 63 68.00977
## 320 56 62.97866
## 321 67 75.20418
## 322 75 79.27722
## 323 71 76.65704
## 324 43 53.44056
## 325 41 46.78472
## 326 82 85.51406
## 327 61 60.41079
## 329 82 71.06390
## 330 41 54.06932
## 331 71 59.57227
## 332 47 39.50011
## 333 62 53.82168
## 334 90 75.18975
## 335 83 87.50548
## 336 61 65.49422
## 337 76 66.08509
## 338 49 49.66697
## 340 35 55.07971
## 341 58 57.79010
## 342 61 67.59026
## 343 69 70.85414
## 344 67 66.71386
## 345 79 68.63854
## 346 72 74.77024
## 347 62 59.10044
## 348 77 86.73370
## 349 75 68.95292
## 350 87 71.57361
## 351 52 64.55107
## 352 66 55.48430
## 353 63 73.57946
## 354 46 57.37109
## 355 59 68.27184
## 356 61 68.84829
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# =========================
# Plot grafik Aktual vs Prediksi
# =========================
plot(Y, type="l", col="blue", lwd=2,
ylab="Math Score",
xlab="Observasi",
main="Aktual vs Prediksi")
lines(data_clean$prediksi_math_score, col="red", lwd=2)
legend("topleft",
legend=c("Aktual","Prediksi"),
col=c("blue","red"),
lwd=2)
