import matplotlib.pyplot as plt

u = [-2, 0, 2, 1, -1]
y = [4, 6, 8, 7, 5]

N=len(u)

def avg(a):
    suma = 0
    for element in a:
        suma+=element
    return suma/len(a)

def theta1(u,y):
    u_avg= avg(u)
    y_avg = avg(y)

    theta_licznik = 0
    theta_mianownik = 0

    for un, yn in zip(u,y):
        theta_licznik+=1/N * ((yn*un)-u_avg*y_avg)
        theta_mianownik+= 1/N * (un**2-u_avg**2)
    return (theta_licznik/theta_mianownik)

def theta0(u,y):
    return avg(y) - theta1(u,y)*avg(u)

plt.scatter(u,y, s=5, c='red')
t1 = theta1(u,y)
t0 = theta0(u,y)

y2=[]
for el in u:
    y2.append(t1*el+t0)

u, y2 = (list(x) for x in zip(*sorted(zip(u, y2))))

plt.plot(u,y2, linewidth=0.5, c='blue')
plt.show()