In [1]:
import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as plt

# print(plt.style.available) # uncomment to print all styles
import seaborn as sns
sns.set(font_scale=2)
plt.style.use('seaborn-whitegrid')
plt.rcParams['figure.figsize'] = (12,6.0)
%matplotlib inline
In [2]:
def f(x):
    return 0.8 - x + x**2
In [3]:
xx = np.linspace(0,1,1000)
plt.plot(xx, f(xx))
Out[3]:
[<matplotlib.lines.Line2D at 0x10f532e10>]

Add noise for some random samples

In [16]:
n = 25
t = np.random.rand(n)
y = f(t) + 0.1*np.random.randn(n)*f(t)
In [17]:
plt.plot(xx, f(xx))
plt.plot(t, y, 'ro')
Out[17]:
[<matplotlib.lines.Line2D at 0x10f84e5c0>]

Find a quadratic fit

In [18]:
A = np.zeros((n, 3))
A[:,0] = 1
A[:,1] = t
A[:,2] = t**2
In [19]:
ATA = np.dot(A.T, A)
ATb = np.dot(A.T, y)
x = la.solve(ATA, ATb)
print(x)

[ 0.83858842 -1.10526941  1.14293682]
In [20]:
x0,x1,x2 = x

plt.plot(xx, f(xx))
plt.plot(t, y, 'ro')
plt.plot(xx, x0 + x1*xx + x2*xx**2, 'g-', lw=3)
Out[20]:
[<matplotlib.lines.Line2D at 0x10f9d6d68>]