📈 Linear Regression from Scratch with Python

In this project, we manually implemented a Linear Regression model using Python and compared it against Scikit-learn’s LinearRegression model. 🛠 Files Structure

LinearRegression.py

    A custom LinearRegression class built from scratch.

    fit() method trains the model.

    predict() method makes predictions.

LogisticModel.py

    Generates random data.

    Trains the custom model.

    Compares the custom model with Scikit-learn's model.

    Calculates and prints error metrics.

main.py

    (Currently empty or supports running the LogisticModel.py.)

📚 Project Flow

Data Generation

    We create 100 random samples between 0 and 2:

X = 2 * np.random.rand(100, 1)
y = 4 + 3 * X + np.random.randn(100, 1)

y is generated based on a linear relation with added noise.

Training the Model

Using fit(X_train, y_train), the custom model is trained.

If the data is not a numpy.ndarray, it is converted.

For each feature (column):

    Calculates SxxSxx​ (sum of squared differences for X).

    Calculates SxySxy​ (sum of cross products between X and y).

    Updates the model's intercept and coefficients accordingly.

Making Predictions

The custom model predicts values using:

    y_head = np.dot(self.coeff_, X_test.T) + self.intercept_

Comparing with Scikit-learn

    The Scikit-learn LinearRegression model is trained on the same data.

    We calculate the Mean Squared Error (MSE) for both models.

    Plotting the predicted vs real values using matplotlib.

📊 Outputs and Metrics

Custom Model:

    Intercept value

    Coefficients

    Deviation from the real sample

    Custom calculated Mean Squared Error (MSE)

Scikit-learn Model:

    Automatically fitted intercept and coefficients

    Scikit-learn calculated MSE

✅ Results show that our custom model performs similarly to Scikit-learn's implementation! 📈 Example Plot

After training, the following plot is displayed:

Red line: Model's predicted linear fit.

Dots: The actual randomly generated data points.

⚙️ Requirements

Python 3.x

Libraries:

    numpy

    pandas

    matplotlib

    scikit-learn

Install the requirements using:

pip install numpy pandas matplotlib scikit-learn

🚀 How to Run

python LogisticModel.py

Would you also like me to generate a little fancier version with badges (like Python version, license, etc.)? 🚀 (If you want, I can add that too!)