Creating a Confidence Ellipses in a sccatterplot using matplotlib

How to creating a Confidence Ellipses in a sccatterplot using matplotlib?

The following code works until creating scatter plot. Then, does anyone familiar with putting Confidence Ellipses over the scatter plot?

import numpy as np
import matplotlib.pyplot as plt
x = [5,7,11,15,16,17,18]
y = [8, 5, 8, 9, 17, 18, 25]

plt.scatter(x,y)
plt.show()

Following is the reference for Confidence Ellipses from SAS.

http://support.sas.com/documentation/cdl/en/grstatproc/62603/HTML/default/viewer.htm#a003160800.htm

The code in sas is like this:

proc sgscatter data=sashelp.iris(where=(species="Versicolor"));
  title "Versicolor Length and Width";
  compare y=(sepalwidth petalwidth)
          x=(sepallength petallength)
          / reg ellipse=(type=mean) spacing=4;
run;

Solution 1:

The following code draws a one, two, and three standard deviation sized ellipses:

x = [5,7,11,15,16,17,18]
y = [8, 5, 8, 9, 17, 18, 25]
cov = np.cov(x, y)
lambda_, v = np.linalg.eig(cov)
lambda_ = np.sqrt(lambda_)
from matplotlib.patches import Ellipse
import matplotlib.pyplot as plt
ax = plt.subplot(111, aspect='equal')
for j in xrange(1, 4):
    ell = Ellipse(xy=(np.mean(x), np.mean(y)),
                  width=lambda_[0]*j*2, height=lambda_[1]*j*2,
                  angle=np.rad2deg(np.arccos(v[0, 0])))
    ell.set_facecolor('none')
    ax.add_artist(ell)
plt.scatter(x, y)
plt.show()

Solution 2:

After giving the accepted answer a go, I found that it doesn't choose the quadrant correctly when calculating theta, as it relies on np.arccos:

Taking a look at the 'possible duplicate' and Joe Kington's solution on github, I watered his code down to this:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse

def eigsorted(cov):
    vals, vecs = np.linalg.eigh(cov)
    order = vals.argsort()[::-1]
    return vals[order], vecs[:,order]

x = [5,7,11,15,16,17,18]
y = [25, 18, 17, 9, 8, 5, 8]

nstd = 2
ax = plt.subplot(111)

cov = np.cov(x, y)
vals, vecs = eigsorted(cov)
theta = np.degrees(np.arctan2(*vecs[:,0][::-1]))
w, h = 2 * nstd * np.sqrt(vals)
ell = Ellipse(xy=(np.mean(x), np.mean(y)),
              width=w, height=h,
              angle=theta, color='black')
ell.set_facecolor('none')
ax.add_artist(ell)
plt.scatter(x, y)
plt.show()