Visualize 3D correlations, inspired by Paul Graham's analysis in _Why Nerds Are Unpopular_

3d-corr-vis.py

# -*- coding: utf-8 -*-

import numpy as np
import matplotlib.pylab as pl
from mpl_toolkits.mplot3d import Axes3D

xx = np.array([0, 10]) # smart
yy = np.array([0, 10]) # nerd
zz = np.array([0, 10]) # unpopular  

means = [xx.mean(), yy.mean(), zz.mean()]
stds = [xx.std() / 3, yy.std() / 3, yy.std() / 3]

xy_corr = 0.6
yz_corr = -0.8
xz_corr = -0.6

covs = [
        [stds[0]**2,                stds[0]*stds[1]*xy_corr,    stds[0]*stds[2]*xz_corr],
        [stds[1]*stds[0]*xy_corr,   stds[1]**2,                stds[1]*stds[2]*yz_corr],
        [stds[2]*stds[0]*xz_corr,   stds[2]*stds[1]*yz_corr,    stds[2]**2]
        ]

m = np.random.multivariate_normal(means, covs, 1000).T
fig = pl.figure()
ax = Axes3D(fig)

ax.scatter(m[0], m[1], m[2], s=15, facecolor='red', edgecolors='black')

pl.title('Why Nerds Are Unpopular', fontstyle='italic')

ax.set_xlabel('Smarts')
ax.set_ylabel('Nerdiness')
ax.set_zlabel('Unpopularity')

pl.grid(True)
pl.legend()
pl.show()