implementation-Linear-Regression-normal-equation-from-scratch.: A Jupyter Notebook repository from rezamosavi8740

Normal Linear Regression

This repository contains an implementation of Normal Linear Regression in Python. Normal Linear Regression is a supervised learning algorithm used for predicting numeric values based on a linear relationship between the input features and the target variable.

Class: NormalLinearRegression

The NormalLinearRegression class provides a simple and efficient implementation of Normal Linear Regression. It includes the following methods:

`init(self)`

The constructor initializes the attributes of the class:

X: Input/feature matrix.
Y: Target matrix.
theta: Array of the optimal values of weights.

`fit(self, x, y)`

This method trains the Normal Linear Regression model on the provided input data x and target values y. It returns the optimal values of weights (theta) that best fit the data.

x: Input/feature matrix.
y: Target matrix.

`predict(self, x)`

The predict() method makes predictions using the trained model on new input data x. It returns the predicted target values based on the learned weights (theta).

x: Test input/feature matrix.

`calculate_theta(self)`

This internal method is used by the fit() method to calculate the optimal values of weights (theta) using the Normal Equation. The Normal Equation allows finding the weights directly without using an iterative optimization algorithm like gradient descent.

Usage

# Import the necessary libraries
import numpy as np

# Create a NormalLinearRegression object
model = NormalLinearRegression()

# Prepare your training data - x and y are NumPy arrays with input features and target values
x = ...
y = ...

# Train the model and obtain the optimal weights
optimal_weights = model.fit(x, y)

# Make predictions on new data
new_data = ...
predictions = model.predict(new_data)

Example

Here's a simple example using the NormalLinearRegression class:

import numpy as np

# Create sample data
x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 5, 4, 5])

# Create a NormalLinearRegression object
model = NormalLinearRegression()

# Train the model and obtain the optimal weights
optimal_weights = model.fit(x, y)

# Make predictions on new data
new_data = np.array([6, 7, 8])
predictions = model.predict(new_data)

print("Optimal Weights:", optimal_weights)
print("Predictions:", predictions)

Contribution

Contributions to this repository are welcome! If you find any bugs, have feature requests, or want to optimize the code, feel free to submit issues or pull requests.

Dependencies

The implementation relies on NumPy for efficient numerical computations. Ensure you have NumPy installed before using the code:

pip install numpy

License

This project is licensed under the MIT License - see the LICENSE file for details.

Explore the world of Normal Linear Regression and build powerful predictive models! Happy coding!

rezamosavi8740/implementation-Linear-Regression-normal-equation-from-scratch.