Tugas Mg 6 Progres ETS
Nova
2026-03-10
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summary(cars)## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00#Library
library(readr) ## Warning: package 'readr' was built under R version 4.5.2library(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, unionlibrary(stats)
library(ggplot2) ## Warning: package 'ggplot2' was built under R version 4.5.2library(corrplot) ## Warning: package 'corrplot' was built under R version 4.5.2## corrplot 0.95 loadedlibrary(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':
##
## recodelibrary(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.numericlibrary(Metrics) ## Warning: package 'Metrics' was built under R version 4.5.2data <- read.csv("C:/Users/Msi user/Downloads/StudentPerformanceFactors.csv")
print("Data Awal:")## [1] "Data Awal:"head(data)## Hours_Studied Attendance Parental_Involvement Access_to_Resources
## 1 23 84 Low High
## 2 19 64 Low Medium
## 3 24 98 Medium Medium
## 4 29 89 Low Medium
## 5 19 92 Medium Medium
## 6 19 88 Medium Medium
## Extracurricular_Activities Sleep_Hours Previous_Scores Motivation_Level
## 1 No 7 73 Low
## 2 No 8 59 Low
## 3 Yes 7 91 Medium
## 4 Yes 8 98 Medium
## 5 Yes 6 65 Medium
## 6 Yes 8 89 Medium
## Internet_Access Tutoring_Sessions Family_Income Teacher_Quality School_Type
## 1 Yes 0 Low Medium Public
## 2 Yes 2 Medium Medium Public
## 3 Yes 2 Medium Medium Public
## 4 Yes 1 Medium Medium Public
## 5 Yes 3 Medium High Public
## 6 Yes 3 Medium Medium Public
## Peer_Influence Physical_Activity Learning_Disabilities
## 1 Positive 3 No
## 2 Negative 4 No
## 3 Neutral 4 No
## 4 Negative 4 No
## 5 Neutral 4 No
## 6 Positive 3 No
## Parental_Education_Level Distance_from_Home Gender Exam_Score
## 1 High School Near Male 67
## 2 College Moderate Female 61
## 3 Postgraduate Near Male 74
## 4 High School Moderate Male 71
## 5 College Near Female 70
## 6 Postgraduate Near Male 71#Ubah nilai kolom menjadi numerik
kolom <- c("Hours_Studied","Sleep_Hours","Previous_Scores","Attendance","Exam_Score")
# cek missing value
colSums(is.na(data[kolom]))## Hours_Studied Sleep_Hours Previous_Scores Attendance Exam_Score
## 0 0 0 0 0# Tangani missing value (hapus baris yang mengandung NA pada kolom tersebut)
data <- data[complete.cases(data[kolom]), ]
cat("\nData Setelah Hapus Missing Value:\n")##
## Data Setelah Hapus Missing Value:colSums(is.na(data[kolom]))## Hours_Studied Sleep_Hours Previous_Scores Attendance Exam_Score
## 0 0 0 0 0#Cek Outlier
# Menentukan kolom yang dianalisis
kolom <- c("Hours_Studied","Sleep_Hours","Previous_Scores","Attendance","Exam_Score")
# Boxplot sebelum hapus 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))## Hours_Studied Sleep_Hours Previous_Scores Attendance Exam_Score
## 43 0 0 0 104# 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: 6607cat("Jumlah data setelah hapus outlier:", nrow(data_clean), "\n")## Jumlah data setelah hapus outlier: 6473# Boxplot setelah hapus outlier
boxplot(data_clean[kolom],
main = "Boxplot Setelah Hapus Outlier",
col = "lightgreen")
# Korelasi Pearson
cat("\nKorelasi Pearson\n")##
## Korelasi Pearsoncorr_matrix <- cor(data_clean[kolom], method = "pearson")
print(corr_matrix)## Hours_Studied Sleep_Hours Previous_Scores Attendance
## Hours_Studied 1.00000000 0.013696082 0.01332368 -0.03018724
## Sleep_Hours 0.01369608 1.000000000 -0.01795715 -0.01632872
## Previous_Scores 0.01332368 -0.017957149 1.00000000 -0.02798273
## Attendance -0.03018724 -0.016328718 -0.02798273 1.00000000
## Exam_Score 0.49499117 -0.009930772 0.19797068 0.67894473
## Exam_Score
## Hours_Studied 0.494991169
## Sleep_Hours -0.009930772
## Previous_Scores 0.197970684
## Attendance 0.678944734
## Exam_Score 1.000000000# Heatmap korelasi
library(ggplot2)
library(reshape2)## Warning: package 'reshape2' was built under R version 4.5.2corr_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()
# Interpretasi korelasi dengan Exam_Score
cat("\nKorelasi dengan Exam_Score:\n")##
## Korelasi dengan Exam_Score:variabel <- c("Hours_Studied","Sleep_Hours","Previous_Scores","Attendance")
for (var in variabel) {
test <- cor.test(data_clean$Exam_Score, data_clean[[var]], method = "pearson")
r <- round(test$estimate, 3)
p <- round(test$p.value, 4)
cat(var, "r =", r, "p =", p, "\n")
}## Hours_Studied r = 0.495 p = 0
## Sleep_Hours r = -0.01 p = 0.4244
## Previous_Scores r = 0.198 p = 0
## Attendance r = 0.679 p = 0# Mendefinisikan variabel dependen (Y)
Y <- data_clean$Exam_Score
# Mendefinisikan variabel independen (X)
X <- data_clean[, c("Hours_Studied","Sleep_Hours","Previous_Scores","Attendance")]
# Menambahkan konstanta (intercept)
X <- cbind(constant = 1, X)# Model Regresi Linear
model <- lm(Exam_Score ~ Hours_Studied + Sleep_Hours + Previous_Scores + Attendance,
data = data_clean)
# Ringkasan model
summary(model)##
## Call:
## lm(formula = Exam_Score ~ Hours_Studied + Sleep_Hours + Previous_Scores +
## Attendance, data = data_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.4833 -1.0532 -0.0159 1.0624 5.3878
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.024811 0.207477 202.552 <2e-16 ***
## Hours_Studied 0.287595 0.003333 86.277 <2e-16 ***
## Sleep_Hours -0.003841 0.013110 -0.293 0.77
## Previous_Scores 0.047404 0.001339 35.411 <2e-16 ***
## Attendance 0.197106 0.001675 117.658 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.549 on 6468 degrees of freedom
## Multiple R-squared: 0.7713, Adjusted R-squared: 0.7712
## F-statistic: 5453 on 4 and 6468 DF, p-value: < 2.2e-16# Mengambil koefisien model
coef_model <- coef(model)
b0 <- coef_model["(Intercept)"]
b1 <- coef_model["Hours_Studied"]
b2 <- coef_model["Sleep_Hours"]
b3 <- coef_model["Previous_Scores"]
b4 <- coef_model["Attendance"]
cat("\nPersamaan Model:\n")##
## Persamaan Model:cat(sprintf("Y = %.3f + (%.3f)X1 + (%.3f)X2 + (%.3f)X3 + (%.3f)X4\n",
b0, b1, b2, b3, b4))## Y = 42.025 + (0.288)X1 + (-0.004)X2 + (0.047)X3 + (0.197)X4# Mengambil nilai R-square dan Adjusted R-square
r2 <- summary(model)$r.squared
adj_r2 <- summary(model)$adj.r.squared
cat(sprintf("\nR-square = %.3f\n", r2))##
## R-square = 0.771cat(sprintf("Adjusted R-square = %.3f\n", adj_r2))## Adjusted R-square = 0.771# Interpretasi R-square
cat("\nInterpretasi R-square:\n")##
## Interpretasi R-square:cat(sprintf("Nilai R-square sebesar %.3f menunjukkan bahwa %.2f%% variasi nilai ujian mahasiswa ",
r2, r2*100))## Nilai R-square sebesar 0.771 menunjukkan bahwa 77.13% variasi nilai ujian mahasiswacat("dapat dijelaskan oleh variabel Hours_Studied, Sleep_Hours, Previous_Scores, dan Attendance secara bersama-sama, ")## dapat dijelaskan oleh variabel Hours_Studied, Sleep_Hours, Previous_Scores, dan Attendance secara bersama-sama,cat(sprintf("sedangkan sisanya sebesar %.2f%% dijelaskan oleh faktor lain di luar model.\n",
(1-r2)*100))## sedangkan sisanya sebesar 22.87% dijelaskan oleh faktor lain di luar model.# Uji Asumsi Klasik
# =========================
# 1. Normalitas (Shapiro-Wilk)
residual <- resid(model)
shapiro_test <- shapiro.test(sample(residual, 5000))
print(shapiro_test)##
## Shapiro-Wilk normality test
##
## data: sample(residual, 5000)
## W = 0.99966, p-value = 0.5896if (shapiro_test$p.value > 0.05){
cat("Residual berdistribusi normal sehingga asumsi normalitas terpenuhi.")
} else {
cat("Residual tidak berdistribusi normal sehingga asumsi normalitas tidak terpenuhi.")
}## Residual berdistribusi normal sehingga asumsi normalitas terpenuhi.# =========================
# 2. Multikolinearitas (VIF)
# =========================
library(car)
vif_values <- vif(model)
cat("\nUji Multikolinearitas (VIF):\n")##
## Uji Multikolinearitas (VIF):print(vif_values)## Hours_Studied Sleep_Hours Previous_Scores Attendance
## 1.001249 1.000787 1.001286 1.001945if (all(vif_values < 10)) {
cat("Interpretasi: Tidak terdapat multikolinearitas antar variabel bebas.\n")
} else {
cat("Interpretasi: Terdapat multikolinearitas pada beberapa variabel bebas.\n")
}## Interpretasi: Tidak terdapat multikolinearitas antar variabel bebas.# =========================
# 3. Heteroskedastisitas (Breusch-Pagan)
# =========================
library(lmtest)
bp_test <- bptest(model)
cat("\nUji Heteroskedastisitas (Breusch-Pagan):\n")##
## Uji Heteroskedastisitas (Breusch-Pagan):print(bp_test)##
## studentized Breusch-Pagan test
##
## data: model
## BP = 4.6751, df = 4, p-value = 0.3223if (bp_test$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 = 1.9736, p-value = 0.1439
## alternative hypothesis: true autocorrelation is greater than 0dw_value <- dw_test$statistic
cat("Nilai DW =", dw_value, "\n")## Nilai DW = 1.973566if (dw_value > 1.5 & dw_value < 2.5) {
cat("Interpretasi: Tidak terdapat autokorelasi pada residual.\n")
} else if (dw_value <= 1.5) {
cat("Interpretasi: Terdapat autokorelasi positif.\n")
} else {
cat("Interpretasi: Terdapat autokorelasi negatif.\n")
}## Interpretasi: Tidak terdapat autokorelasi pada residual.#Prediksi
data_clean$prediksi_exam_score <- predict(model)#Evaluasi Model
# Nilai aktual
Y <- data_clean$Exam_Score
# Nilai prediksi
pred <- data_clean$prediksi_exam_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 = 1.548074cat("MAE =", mae, "\n")## MAE = 1.242287cat("MAPE =", mape, "%\n")## MAPE = 1.857014 %cat("\nInterpretasi Evaluasi Model:\n")##
## Interpretasi Evaluasi Model:cat(sprintf("RMSE sebesar %.3f menunjukkan rata-rata besar kesalahan prediksi dalam satuan yang sama dengan variabel nilai ujian siswa (Exam_Score).\n", rmse))## RMSE sebesar 1.548 menunjukkan rata-rata besar kesalahan prediksi dalam satuan yang sama dengan variabel nilai ujian siswa (Exam_Score).cat(sprintf("MAE sebesar %.3f menunjukkan rata-rata kesalahan absolut antara nilai ujian aktual dengan nilai ujian hasil prediksi model.\n", mae))## MAE sebesar 1.242 menunjukkan rata-rata kesalahan absolut antara nilai ujian aktual dengan nilai ujian 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 1.86% menunjukkan model memiliki akurasi sangat baik.# Menampilkan hasil prediksi
hasil <- data_clean[, c("Exam_Score","prediksi_exam_score")]
cat("\nTabel Hasil Prediksi:\n")##
## Tabel Hasil Prediksi:print(hasil)## Exam_Score prediksi_exam_score
## 1 67 68.62999
## 2 61 62.87000
## 3 74 72.53034
## 4 71 72.52235
## 5 70 68.68106
## 6 71 69.02266
## 7 67 70.11854
## 8 66 66.93609
## 9 69 69.21114
## 10 72 71.29082
## 11 68 66.82322
## 12 71 70.13429
## 13 70 68.99156
## 14 66 64.15820
## 15 65 63.75218
## 16 64 63.60468
## 17 60 60.92034
## 18 65 66.01340
## 19 67 66.38640
## 20 66 62.98143
## 21 69 70.41312
## 22 72 70.96148
## 23 66 66.55078
## 24 66 65.27229
## 25 63 63.26190
## 26 64 62.82164
## 27 65 67.94349
## 28 71 69.14462
## 29 66 67.09991
## 30 64 62.61274
## 31 63 65.66509
## 32 69 67.83944
## 33 67 65.89708
## 34 61 60.22848
## 35 68 66.27373
## 36 61 64.34070
## 37 64 65.16307
## 38 67 66.36428
## 39 63 63.61878
## 40 64 65.49874
## 41 67 64.95418
## 42 65 67.06315
## 43 64 64.33588
## 44 70 69.58971
## 45 68 68.35728
## 46 65 65.03861
## 47 68 66.43669
## 48 64 64.82098
## 49 68 68.68920
## 50 63 62.47313
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## 54 67 68.62430
## 55 66 65.09909
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## 144 72 70.71829
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## 6590 70 70.76522
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## 6598 70 67.95300
## 6599 64 64.77217
## 6600 70 71.62640
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## 6603 68 66.39081
## 6604 69 67.42854
## 6605 68 68.57444
## 6606 68 66.14258
## 6607 64 63.96624# Plot grafik Aktual vs Prediksi
plot(Y, type="l", col="blue", lwd=2,
ylab="Exam Score",
xlab="Observasi",
main="Aktual vs Prediksi")
lines(data_clean$prediksi_exam_score, col="red", lwd=2)
legend("topleft",
legend=c("Aktual","Prediksi"),
col=c("blue","red"),
lwd=2)
# Plot Grafik Residual
plot(data_clean$prediksi_exam_score, residual,
xlab = "Nilai Prediksi",
ylab = "Residual",
main = "Scatter Plot Residual",
pch = 19)
abline(h = 0, col = "red", lwd = 2)