Create OLS example image.

ols_plot.py

%matplotlib inline 

import numpy as np
import pandas as pd 
import seaborn as sns 
import matplotlib.pyplot as plt 

from sklearn.datasets import make_regression
from sklearn.preprocessing import StandardScaler 
from matplotlib.patches import Rectangle

sns.set_context('notebook')
sns.set_style('whitegrid')
sns.set_palette('deep')

_, ax = plt.subplots(figsize=(9,6))
X, y, coef = make_regression(n_samples=10, n_features=1, noise=35.0, coef=True, random_state=32)
X = X.ravel()

lims = (X.min()-0.5, X.max()+0.5)
xl = np.linspace(*lims)
yl = np.dot(xl,coef)
yp = np.dot(X,coef)
ax.plot(xl, yl, ls='--')

ax.scatter(X, y,)
# ax.set_xticklabels([])
# ax.set_yticklabels([])
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
ax.set_xlim(*lims)

for xi, yi, yhi in zip(X, y, yp):
    err = yhi - yi
    rect = Rectangle((xi,yi), err/100, err, alpha=0.3, ls='solid', fill=True, ec='r', fc='r')
    ax.add_patch(rect)
    
plt.savefig("figures/ordinary_least_squares.png")