%matplotlib inline
import matplotlib.pyplot as plt

# Some nice default configuration for plots
plt.rcParams['figure.figsize'] = 10, 7.5
plt.rcParams['axes.grid'] = True
plt.gray()

import numpy as np
import pandas as pd

# a simulated sin wave
X = np.random.uniform(2, 10, 100)
y = np.sin(X) + np.random.normal(0, 0.2, 100)

# high bias estimate
est_bias = np.zeros(100)
est_bias[:50] = np.mean(y[np.argsort(X)[:50]])
est_bias[50:] = np.mean(y[np.argsort(X)[50:]])

# high variance estimate
def movingaverage(values, window):
    '''calculate simple moving average'''
    weigths = np.repeat(1.0, window)/window
    #including valid will REQUIRE there to be enough datapoints.
    #for example, if you take out valid, it will start @ point one,
    #not having any prior points, so itll be 1+0+0 = 1 /3 = .3333
    smas = np.convolve(values, weigths, 'valid')
    return smas

est_var = movingaverage(y[np.argsort(X)], 3) # MA(3)

plt.scatter(X, y)

# plot high bias estimate
plt_bias, = plt.plot(np.insert(X[np.argsort(X)], 50, np.nan), 
                     np.insert(est_bias, 50, np.nan), # insert discontinuous point
                     color='g', linewidth=2)

# plot high variance estimate
plt_var, = plt.plot(X[np.argsort(X)][2:], est_var, color='r')

plt.xlabel("Predictor")
plt.ylabel("Outcome")
plt.legend([plt_bias, plt_var], ['High bias model', 'High variance model'])