Regression-Influential-Points-Identification-Python

Influential Points Detection using Cook’s Distance & Leverage Cutoff

---

📌 Overview

This Python script identifies influential data points in regression models using:

• Cook’s Distance: Measures the impact of a data point on the regression model.
• Leverage Values: Detects outliers in the predictor space.
• CSV Input Support: Reads a CSV file containing Cook’s Distance and Leverage values.
• From the Cook's DIstance and Leverage Values using reference (i & ii) it estimates a threshold point which is used to determine the infleuncial points.

The script is useful for data scientists, statisticians, and machine learning engineers working with regression models.

✅ Features

• ✔ Computes Cook’s Distance for each data point (Upcoming)
• ✔ Calculates Leverage values (Hat Matrix Diagonal) (Upcoming)
• ✔ Provides a sample CSV file to guide users for CSV Input Support
• ✔ CSV Input Support: Reads a CSV file containing Cook’s Distance and Leverage values
• ✔ Automatically determines cutoff values for Cook’s Distance and Leverage
• ✔ Identifies only influential data points based on statistical cut-offs
• ✔ Displays results in a formatted table for clarity
• ✔ Supports custom visualization of influential points (Upcoming Feature)

---

🔹 How It Works (Current)

1. Enter regression parameters (number of predictors (p), data points (n), and independent variables (d)).
2. Based on two references provided, the script automatically calculates cutoff values for:
   • Cook’s Distance (Two Methods)
   • Leverage Points
3. Reads Cook’s Distance and Leverage values from a CSV file.
4. Identifies and displays only influential points in a structured table.

---

📌 FUll DETAILS

Input CSV Format

The CSV file must have three columns:

Column Name	Description
Index	Row number of the data point
Cooks_Distance	Cook’s Distance value
Leverage	Leverage value

Example CSV File (data.csv):

Index,Cooks_Distance,Leverage
1,0.12,0.25
2,0.45,0.30
3,0.90,0.50

👉 The script will automatically filter and display only influential points.

---

🔧 Installation

Ensure you have Python 3+ installed, then install the required dependencies using:

pip install pandas scipy

2. Alternative: Clone from GitHub If you want to view or modify the source code, you can clone it:

   git clone https://github.com/REBELABS/Regression-Influential-Points-Identification-Python.git
cd Regression-Influential-Points-Identification-Python
python setup.py install

3. Install via PyPI You can install this package directly from PyPI:

   pip install influential_points

---

📌 How to Use

Method 1: Run script directly

1. Run the script:

   python script.py

2. Enter the required regression parameters:
   • P: Number of predictors (including the intercept).
   • n: Number of data points.
   • d: Number of independent variables (excluding the intercept).
3. Provide a CSV file containing Cook’s Distance and Leverage values.
4. The script automatically identifies and displays influential data points.

Method 2: Importing as a Python Module

1. After installing via pip install influential_points, you can import and use it in your scripts:

   from influential_points import calculate_influential_cutoffs
   #Usage Example
   cutoffs = calculate_influential_cutoffs(n=100, p=5)
   print("Influential Point Cutoffs:", cutoffs)

Method 3: Using the GitHub Version

1. Clone the repo:

   git clone https://github.com/REBELABS/Regression-Influential-Points-Identification-Python.git

2. Navigate to the project directory:

   cd Regression-Influential-Points-Identification-Python

3. Install dependencies:

   pip install -r requirements.txt

4. Run the script:

   python influential_points.py

---

📌 Example Output

 **Influential Data Points**
============================================================
Index     Cook’s Distance      Leverage         Status    
============================================================
3         0.90                0.50             Influential
5         1.10                0.45             Influential(i)
9         0.85                0.48             Influential(ii)
============================================================

✅ If no influential points are found, the script will notify the user.

---

📖 References

• (i) Kutner et al., 2004. Applied Linear Statistical Models
• (ii) Fox, 2016. Applied Regression Analysis and Generalized Linear Models

---

🚀 Upcoming Features

• Computes Cook’s Distance for each data point
• Compute Leverage values (Hat Matrix Diagonal) for each data point
• Visualization: Plot influential points for better understanding.
• Classification of High Cook’s Distance & High Leverage Points (separately from influential points).
• Batch Processing: Analyze multiple datasets at once.

---

📌 Contributing

Contributions are welcome! If you’d like to improve this script, feel free to fork the repository and submit a pull request.

📌 License

This project is licensed under the MIT License – feel free to use and modify it.