<jupyter_start><jupyter_text>What nonlinearities do to noiseNonlinear relationships are complicated because they (a) amplify small bits of noise and (b) there are so many different types of nonlinearities.In this notebook we'll explore the effect that nonlinearities have on noise<jupyter_code>import numpy as np
import matplotlib.pyplot as plt

#set up uniform noise on a 0-function
x = np.linspace(-10,10,1000)
y = 0 + np.random.uniform(-1.0,1.0,size=x.shape)
plt.scatter(x,y)
plt.hist(y)
z = 1/10 * y**2
plt.scatter(x,z)
plt.hist(z)
z = 1/10 * y**3
plt.scatter(x,z)
plt.figure()
plt.hist(z)<jupyter_output><empty_output>
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