Shading background based on groups above/below a line

Question

Suppose I have a scatterplot with some kind of line (least squares regression line, knn regression line, etc.) through it, like this. I want to shade the upper region of the plot reddish, and the lower region of the plot blueish, to give an indication of how my line is doing as a classifier for the points. Similar to my mimic example with this effect is this plot from Elements of Statistical Learning (Hastie et al), (Chapter 2, page 13).

How can I achieve this effect with Matplotlib?

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I know how to set rectangular regions of a plot to be different colors with axhspan and axvspan (see this answer), but have been struggling to set different plot colors based on regions above and below a line.

Code to replicate my current mock plot

import numpy as np
import matplotlib.pyplot as plt

plt.style.use('seaborn-notebook')

np.random.seed(17)
grp1_x = np.random.normal(1, 1, 100)
grp1_y = np.random.normal(3, 1, 100)

grp2_x = np.random.normal(1.2, 1, 100)
grp2_y = np.random.normal(1.2, 1, 100)

########################################
## least squares plot

plt.scatter(grp1_x, grp1_y,
            lw         = 1,
            facecolors = 'none',
            edgecolors = 'firebrick')
plt.scatter(grp2_x, grp2_y,
            lw         = 1,
            facecolors = 'none',
            edgecolors = 'steelblue')
plt.tick_params(
    axis        = 'both',
    which       = 'both',
    bottom      = 'off',
    top         = 'off',
    labelbottom = 'off',
    right       = 'off',
    left        = 'off',
    labelleft   = 'off')

full_x = np.concatenate([grp1_x, grp2_x])
full_y = np.concatenate([grp1_y, grp2_y])
m, c = np.linalg.lstsq(np.vstack([full_x,
                                  np.ones(full_x.size)]).T,
                       full_y)[0]
plt.plot(full_x, m*full_x + c, color='black')
plt.show()

Answer 1

First I would recommend sorting the x values, such that the line looks smooth.

x = np.sort(full_x)
plt.plot(x, m*x + c, color='black')

Then you can use fill_between to fill the region above (below) the line up to (from) the upper (lower) plot limits.

xlim=np.array(plt.gca().get_xlim())
ylim=np.array(plt.gca().get_ylim())
plt.fill_between(xlim, y1=m*xlim + c, y2=[ylim[0],ylim[0]], 
                 color="#e0eaf3", zorder=0 )
plt.fill_between(xlim, y1=m*xlim + c, y2=[ylim[1],ylim[1]], 
                 color="#fae4e4", zorder=0 )
plt.margins(0)

Or use some hatching for the background:

fb1 = plt.fill_between(xlim, y1=m*xlim + c, y2=[ylim[0],ylim[0]], 
                 facecolor="w", edgecolor="#e0eaf3", zorder=0 )
fb1.set_hatch("//")
fb2 = plt.fill_between(xlim, y1=m*xlim + c, y2=[ylim[1],ylim[1]], 
                  facecolor="w", edgecolor="#fae4e4", zorder=0 )
fb2.set_hatch("\\\\")