import numpy as np
import matplotlib.pyplot as plt
 
def estimate_coef(x, y):
    # number of observations/points
    n = np.size(x)
 
    # mean of x and y vector
    m_x, m_y = np.mean(x), np.mean(y)
 
    # calculating cross-deviation and deviation about x
    SS_xy = np.sum(y*x - n*m_y*m_x)
    SS_xx = np.sum(x*x - n*m_x*m_x)
 
    # calculating regression coefficients
    b_1 = SS_xy / SS_xx
    b_0 = m_y - b_1*m_x
 
    return(b_0, b_1)
 
def plot_regression_line(x, y, b):
    # plotting the actual points as scatter plot
    plt.scatter(x, y, color = "m",marker = "o", s = 30)
 
    # predicted response vector
    y_pred = b[0] + b[1]*x
 
    # plotting the regression line
    plt.plot(x, y_pred, color = "g")
 
    # putting labels
    plt.xlabel('x')
    plt.ylabel('y')
 
    # function to show plot
    plt.show()
 

    # observations
y = np.array([9, 8, 6, 5, 4, 4, 4, 3, 2, 1])
x = np.array([9, 8, 7, 5, 7, 5, 4, 3, 2, 2])
#x = np.random.random_integers(0,100,1000)
#y = np.random.random_integers(0,100,1000)
 
    # estimating coefficients
b = estimate_coef(x, y)
print("Estimated coefficients:\nb_0 = {}  \nb_1 = {}".format(b[0], b[1]))
 
    # plotting regression line
plot_regression_line(x, y, b)