import matplotlib.pyplot as plt
import numpy as np
from math import *
x=np.array([6,7,12,4,13,18])
y=np.array([8,9,14,2,16,20])
#y=-0.5*x+14
x2=x**2
y2=y**2
xy=x*y
n=len(x)
moyx=sum(x)/n
moyy=sum(y)/n
moyx2=sum(x2)/n
moyy2=sum(y2)/n
moyxy=sum(xy)/n
varx=moyx2-moyx**2
vary=moyy2-moyy**2
covxy=moyxy-moyx*moyy
sx=sqrt(varx)
sy=sqrt(vary)
r=covxy/(sx*sy)
print(round(r,2))
#droite d'ajustement y = a x + b
a=covxy/varx
b=moyy-a*moyx
y2=[a*t+b for t in x]
lab="y = "+str(round(a,2))+"x +"+str(round(b,2))
#nuage de points
plt.plot(x,y,'ob')
plt.plot(x,y2,'r-',label=lab)
plt.legend()
plt.show()