Manual Gradient descent for given X and y with starting m and c values for an equation y= mX + c

gradient_descent.py

# Takes in X, y, current m and c (both initialised to 0), num_iterations, learning rate
# returns gradient at current m and c for each pair of m and c

def gradient(X, y, m_current=0, c_current=0, iters=1000, learning_rate=0.01):
    N = float(len(y))
    gd_df = pd.DataFrame( columns = ['m_current', 'c_current','cost'])
    for i in range(iters):
        y_pred = (m_current * X) + c_current
        cost = sum([data**2 for data in (y-y_pred)]) / N
        m_gradient = -(2/N) * sum(X * (y - y_pred))
        c_gradient = -(2/N) * sum(y - y_pred)
        m_current = m_current - (learning_rate * m_gradient)
        c_current = c_current - (learning_rate * c_gradient)
        gd_df.loc[i] = [m_current,c_current,cost]
    return(gd_df)