# Anscombe's quartetΒΆ

Anscombe's quartet is a group of datasets (x, y) that have the same mean, standard deviation, and regression line, but which are qualitatively different.

It is often used to illustrate the importance of looking at a set of data graphically and not only relying on basic statistic properties.

import matplotlib.pyplot as plt
import numpy as np

x = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]
y1 = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68]
y2 = [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74]
y3 = [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73]
x4 = [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8]
y4 = [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89]

datasets = {
'I': (x, y1),
'II': (x, y2),
'III': (x, y3),
'IV': (x4, y4)
}

fig, axs = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(6, 6),
gridspec_kw={'wspace': 0.08, 'hspace': 0.08})
axs[0, 0].set(xlim=(0, 20), ylim=(2, 14))
axs[0, 0].set(xticks=(0, 10, 20), yticks=(4, 8, 12))

for ax, (label, (x, y)) in zip(axs.flat, datasets.items()):
ax.text(0.1, 0.9, label, fontsize=20, transform=ax.transAxes, va='top')
ax.tick_params(direction='in', top=True, right=True)
ax.plot(x, y, 'o')

# linear regression
p1, p0 = np.polyfit(x, y, deg=1)  # slope, intercept
ax.axline(xy1=(0, p0), slope=p1, color='r', lw=2)

# add text box for the statistics
stats = (f'$\\mu$ = {np.mean(y):.2f}\n'
f'$\\sigma$ = {np.std(y):.2f}\n'
f'$r$ = {np.corrcoef(x, y)[0][1]:.2f}')
bbox = dict(boxstyle='round', fc='blanchedalmond', ec='orange', alpha=0.5)
ax.text(0.95, 0.07, stats, fontsize=9, bbox=bbox,
transform=ax.transAxes, horizontalalignment='right')

plt.show()


References

The use of the following functions, methods, classes and modules is shown in this example:

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