linear_regression.py

class LinearRegression:
    
    def __init__(self, order):
        self.W = np.random.randn((order+1))
    
    def fit(self, X, Y, alpha=1e-5, epochs=1000):
        X = np.vstack((X, np.ones_like(X))).T
        Y = Y.T
        
        for _ in range(epochs):
            err = self.perdict(X) - Y  # (Y_hat - Y)
            dL = X.T.dot(err)          # 2 X^T (Y_hat - Y), absorbing 2 into alpha
            self.W -= alpha*dL         # W <- W - alpha * dL/dW
    
    def perdict(self, X):
        return X.dot(self.W)
    
    def coeff(self):
        return self.W.ravel()
    
    
if __name__ == '__main__':
    
    x = np.linspace(0,25,100)
    epsilon = 3*np.random.randn(len(x))
    y = 3*x + 1 + epsilon

    lr = LinearRegression(order=1)
    lr.fit(x,y)
    w, b = lr.coeff()

    plt.plot(x, y, 'bo')
    plt.plot(x, w*x+b, 'r')
    plt.xlabel("x")
    plt.ylabel("y")
    plt.show()

    print("Equation of the line is y = {:.0f}x + {:.0f}".format(w, b))