import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0,3,20)
y = np.zeros(20)
a = np.random.normal(0,0.3,size=2E1)
for i in range(20):
    y[i] = x[i]**2 + a[i]
means = np.zeros(20)
stds = np.zeros(20)
for i in range(20):
    means[i] = np.mean(y[:i])
    stds[i] = np.std(y[:i])
plt.plot(x, y, 'bo-', lw = 1, label=u'Function')
plt.plot(x, means, lw = 1, label=u'Average')
plt.errorbar(x, means, stds, label=u'Std')
plt.legend(loc='best')
plt.title(u'Plots')
plt.xlabel('X')
plt.ylabel('Y')
plt.grid()
plt.show()

import numpy as np
import matplotlib.pyplot as plt
from math import *
x = np.linspace(0,3,20)
y = np.zeros(20)
a = np.random.normal(0,0.3,size=2E1)
for i in range(20):
    y[i] = x[i]**2 + a[i]
A = np.vstack([x, np.ones(len(x))]).T
m, c = np.linalg.lstsq(A, y)[0]
import matplotlib.pyplot as plt
plt.plot(x, y, 'bo-', lw = 1, label=u'Function')
plt.plot(x, m*x + c, 'r', label='Average')
std = np.zeros(20)
for i in range(20):
    std[i] = (sqrt((y[i] - (m*x[i] + c))**2))
plt.errorbar(x, y, std, label=u'Std')
plt.legend(loc='best')
plt.title(u'Plots')
plt.xlabel('X')
plt.ylabel('Y')
plt.grid()
plt.show()