Analisis Regresi Linear Berganda (MLR)

Pipeline Data Processing dan Prediksi

Repository ini berisi implementasi lengkap pipeline analisis regresi linear berganda menggunakan metode Ordinary Least Squares (OLS) untuk prediksi dan analisis error.

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📊 Alur Data Processing

Input Awal

📁 pre-prosesing/
└── data.csv                    # Dataset mentah

Pipeline Processing

graph TD
    A[data.csv] --> B[Data Cleaning]
    B --> C[data_cleaned.csv]
    C --> D[Data Splitting]
    D --> E[train.csv]
    D --> F[test.csv]
    E --> G[Polynomial Features - Train]
    F --> H[Polynomial Features - Test]
    G --> I[train_polynomial.csv]
    H --> J[test_polynomial.csv]
    I --> K[Data Scaling - Train]
    J --> L[Data Scaling - Test]
    K --> M[train_scaled.csv]
    L --> N[test_scaled.csv]
    M --> O[OLS Training]
    O --> P[train_olsCoefficients.csv]
    P --> Q[MLR Prediction]
    N --> Q
    Q --> R[mlr_error_analysis.png]
    Q --> S[test_mlr.csv]

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🔄 Tahapan Processing

1. Data Cleaning 📝

File: pre-prosesing/cleaning.py

• Input: data.csv
• Output: data_cleaned.csv
• Fungsi:
  • Menghapus baris yang mengandung nilai: '-', '8888', '9999'
  • Membersihkan data missing/invalid
  • Reset index data

2. Data Splitting ✂️

File: pre-prosesing/spliting.py

• Input: data_cleaned.csv
• Output:
  • input_data/train.csv (70% data)
  • input_data/test.csv (30% data)
• Fungsi:
  • Split data secara berurutan (sequential split)
  • Rasio default: 70:30 (training:testing)

3. Polynomial Features 🔢

File: pre-prosesing/polynomial_features.py

• Input:
  • input_data/train.csv
  • input_data/test.csv
• Output:
  • polynomial_data/train_polynomial.csv
  • polynomial_data/test_polynomial.csv
• Fungsi:
  • Membuat fitur polynomial (X₁², X₁×X₂, dll.) untuk meningkatkan kompleksitas model
  • Degree default: 2 (quadratic features)
  • Menangani interaksi antar variabel independent
  • Mengonversi categorical wind direction ke numerical values

4. Data Scaling 📏

File: pre-prosesing/scaleing.py

• Input:
  • polynomial_data/train_polynomial.csv
  • polynomial_data/test_polynomial.csv
• Output:
  • output_data/train_scaled.csv
  • output_data/test_scaled.csv
• Fungsi:
  • Normalisasi data menggunakan standardization (z-score)
  • Formula: (x - mean) / std
  • Memastikan semua fitur dalam skala yang sama

5. OLS Training 🎯

File: prosesing/ols.py

• Input: output_data/train_scaled.csv
• Output: train_olsCoefficients.csv
• Fungsi:
  • Estimasi koefisien menggunakan metode OLS
  • Formula: β = (X'X)⁻¹X'y
  • Menghitung intercept dan slope untuk setiap variabel

6. MLR Prediction & Analysis 📈

File: prosesing/mlr.py

• Input:
  • train_olsCoefficients.csv (koefisien model)
  • output_data/test_scaled.csv (data test)
• Output:
  • test_mlr.csv (hasil prediksi)
  • mlr_error_analysis.png (visualisasi error analysis)
• Fungsi:
  • Prediksi menggunakan model MLR
  • Analisis error: MAE, MSE, RMSE, R²
  • Visualisasi perbandingan actual vs predicted

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📁 Struktur File Output

Pre-processing Results

📁 pre-prosesing/
├── data_cleaned.csv           # Data setelah cleaning
├── 📁 input_data/
│   ├── train.csv             # Data training (70%)
│   └── test.csv              # Data testing (30%)
├── 📁 polynomial_data/
│   ├── train_polynomial.csv  # Data training dengan polynomial features
│   └── test_polynomial.csv   # Data testing dengan polynomial features
└── 📁 output_data/
    ├── train_scaled.csv      # Data training yang sudah di-scale
    └── test_scaled.csv       # Data testing yang sudah di-scale

Processing Results

📁 prosesing/
├── train_olsCoefficients.csv  # Koefisien model OLS
├── test_mlr.csv              # Hasil prediksi MLR
└── mlr_error_analysis.png    # Visualisasi analisis error

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🚀 Cara Menjalankan

Otomatis (Recommended)

Jalankan seluruh pipeline dengan satu command:

./run_analysis.sh

Manual (Step by Step)

# 1. Aktifkan virtual environment
source ./regresi_env/bin/activate

# 2. Data Cleaning
python ./pre-prosesing/cleaning.py

# 3. Data Splitting
python ./pre-prosesing/spliting.py

# 4. Polynomial Features
python ./pre-prosesing/polynomial_features.py

# 5. Data Scaling
python ./pre-prosesing/scaleing.py

# 6. OLS Training
python ./prosesing/ols.py

# 7. MLR Prediction
python ./prosesing/mlr.py

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📊 Output dan Hasil

1. train_olsCoefficients.csv

Berisi koefisien model OLS dengan kolom:

• Variable: Nama variabel
• Coefficient: Nilai koefisien β
• Std_Error: Standard error
• t_value: Nilai t-statistik
• p_value: P-value untuk uji signifikansi

2. test_mlr.csv

Berisi hasil prediksi dengan kolom:

• Semua kolom input original
• Predicted_RR: Nilai prediksi dari model MLR
• Residual: Selisih antara actual dan predicted
• Abs_Residual: Absolute residual

3. mlr_error_analysis.png

Visualisasi yang menampilkan:

• Scatter Plot: Actual vs Predicted values
• Residual Plot: Error distribution
• Histogram: Distribusi residual
• Metrics: MAE, MSE, RMSE, R² score

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🎯 Tujuan Analisis

1. Data Preparation: Membersihkan dan mempersiapkan data untuk modeling
2. Feature Scaling: Menormalisasi data untuk performa model yang optimal
3. Model Training: Membangun model regresi linear berganda menggunakan OLS
4. Prediction: Melakukan prediksi pada data test
5. Error Analysis: Menganalisis performa model dengan berbagai metrik

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📈 Metrik Evaluasi

• MAE (Mean Absolute Error): Rata-rata absolute error
• MSE (Mean Squared Error): Rata-rata squared error
• RMSE (Root Mean Squared Error): Akar dari MSE
• R² Score: Koefisien determinasi (goodness of fit)

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🔧 Requirements

Lihat requirements.txt untuk dependencies:

• pandas
• numpy
• matplotlib
• seaborn
• scikit-learn
• openpyxl

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📝 Notes

• Dataset target variable: RR
• Split ratio: 70% training, 30% testing
• Scaling method: Z-score standardization
• Model: Multiple Linear Regression via OLS
• All paths menggunakan relative path untuk portabilitas

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📚 References

Data Sources

1. BMKG Data Online - Badan Meteorologi, Klimatologi, dan Geofisika
   • Link: https://dataonline.bmkg.go.id/data-harian
   • Sumber data cuaca dan iklim Indonesia

Academic References

2. Weather Prediction Using Multi Linear Regression Algorithm
   • Authors: N Anusha, M Sai Chaithanya, and Guru Jithendranath Reddy
   • Published: IOP Conference Series: Materials Science and Engineering, Volume 590
   • Conference: International Conference on Frontiers in Materials and Smart System Technologies
   • Date: 10 April 2019, Tamil Nadu, India
   • DOI: 10.1088/1757-899X/590/1/012034
   • Link: https://iopscience.iop.org/article/10.1088/1757-899X/590/1/012034/meta

Mathematical Background

3. Mathematical Foundation Document
   • Link: https://drive.google.com/file/d/1pVPWokZJRlGjps9rks7KxTspnGk0db4f/view?usp=sharing
   • Berisi teori matematika di balik implementasi MLR dan OLS

Textbook Reference

4. Numerical Methods for Engineers (6th Edition)
   • Authors: Steven C. Chapra and Raymond P. Canale
   • Publisher: McGraw-Hill Education
   • ISBN: 978-0073397924
   • Referensi utama untuk metode numerik yang digunakan

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Generated by MLR Analysis Pipeline - Metode Numerik 2025