#------------------------------------------

#Bootstrap test for significance

#------------------------------------------

import numpy as np

import matplotlib.pyplot as plt

x = compositeL # some numpy vector

y = compositeF # another numpy vector

# we will fill this vector with the regression coefficient as we find them

b1_vector = np.zeros(5000)

#bootstraping

for i in np.arange(5000):

index = np.random.randint(0,len(x),len(x))

#pull out the (x,y) pair for each index

sample_x = x[index]

sample_y = y[index]

#calculate the b1 value and store it in the b_vector

b_values = np.polyfit(sample_x,sample_y,1)

#b1 is the first element result of polyfit

b1=b_values[0]

b1_vector[i]=b1

plt.figure(6)

plt.hist(b1_vector,50)

In this example there is 99.96% confidence that the regression coefficient is positive.