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import numpy as np
import random
from sklearn.datasets.samples_generator import make_regression 
import pylab
from scipy import stats

def gradient_descent_2(alpha, x, y, numIterations):
    m = x.shape[0] # number of samples
    theta = np.ones(2)
    x_transpose = x.transpose()
    for iter in range(0, numIterations):
        hypothesis = np.dot(x, theta)
        loss = hypothesis - y
        J = np.sum(loss ** 2) / (2 * m)  # cost
        print #"iter %s | J: %.3f" % (iter, J)      
        gradient = np.dot(x_transpose, loss) / m         
        theta = theta - alpha * gradient  # update
    return theta

if __name__ == '__main__':

    x, y = make_regression(n_samples=100, n_features=1, n_informative=1, 
                        random_state=0, noise=35) 
    m, n = np.shape(x)
    x = np.c_[ np.ones(m), x] # insert column
    alpha = 0.01 # learning rate
    theta = gradient_descent_2(alpha, x, y, 1000)

    # plot
    for i in range(x.shape[1]):
        y_predict = theta[0] + theta[1]*x 
    pylab.plot(x[:,1],y,'o')
    pylab.plot(x,y_predict,'k-')
    pylab.show()
   # print "Done!"


    

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