linear_regression.py

import numpy as np
from sklearn.preprocessing import add_dummy_feature


class LinearRegression:
    def __init__(self):
        self.X = None
        self.y = None
        self.theta = None
        self.coaf_ = None
        self.intercept_ = None

    def predict(self, X):
        '''
        With the input X the functions uses the model to makes predictions
        :param X: The independent variables.
        :return: A numpy array containing the predicted values.
        '''
        predictions = np.array([])

        for element in X:
            predictions = np.append(predictions, element * self.coaf_ + self.intercept_)

        return predictions

    def fit(self, X, y, epoch=1000, learning_rate=0.1):
        '''
        train the linear regressor using the Batch Gradient Descent algorithm
        :param X: The independent variables.
        :param y: The dependent variables.
        :return: the trained model.
        '''

        self.X = X
        self.y = y
        self.X = add_dummy_feature(self.X)

        np.random.seed(42)
        self.theta = np.random.randn(self.X.shape[1]) # Random initialisation
        self.theta = self.theta.reshape(-1, 1)

        m = self.X.shape[0] # The number of items
        for i in range(epoch):
            predictions = (self.X @ self.theta).reshape(-1, 1)
            gradient = 2 / m  * self.X.T @ (predictions - self.y)
            self.theta = self.theta - learning_rate * gradient

        self.coaf_ = self.theta[1:]
        self.intercept_ = self.theta[0]

        return self


    def score(self, X, y):
        '''
        Evaluates the model on the test data using Mean Squared Error
        :param X: independent variables.
        :param y: dependent variables.
        :return: Mean Squared Error value
        '''

        predictions = self.predict(X)
        m = predictions.shape[0] # the size of the test data.
        mae = 0
        for i in range(m):
            mae = mae + (y[i] - predictions[i]) ** 2

        mae = mae / m
        return mae

main.py

import linear_regression.linear_regression as LinearRegression
import numpy as np
import matplotlib.pyplot as plt

np.random.seed(45)

number_of_instances = 100
X = np.random.randn(number_of_instances,1)
Y = 4 + 3 * X + np.random.randn(number_of_instances, 1)

plt.scatter(X, Y)

linear_regression = LinearRegression.LinearRegression()
regressor = linear_regression.fit(X, Y)

print(f"coaf: {linear_regression.coaf_}")
print(f"intercept: {linear_regression.intercept_}")

plt.plot(X, X @ regressor.coaf_ + regressor.intercept_, color='red')

print(f"predict: {linear_regression.predict([0])}")
print(f"score: {linear_regression.score([0], [4.07535703])}")

plt.show()