How to create a linear regression plot with distribution curves (e.g., normal distribution) that indicate the frequency at the X-Y axes in Python?

Question

I’m trying to generate a linear regression plot with additional distribution curves on the X and Y axes in Python that indicate the distribution of values in each of these dimensions. See attached figure.

Example of this type of figure

I know how to create the linear plot, but have not been able to find a method to generate the distribution curves to appear on the axes themselves in Python.

Asked By: jankma15

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Answer 1

There is a good section of this on the matplotlib documentation, and with some modifications you can get something close-ish:

https://matplotlib.org/stable/gallery/lines_bars_and_markers/scatter_hist.html#sphx-glr-gallery-lines-bars-and-markers-scatter-hist-py

The main component that I personally think is a great learning point is matplotlib’s gridspec. It allows control of where the graphs are located which allows for stronger customization.

import numpy as np
import matplotlib.pyplot as plt

# Fixing random state for reproducibility
np.random.seed(19680801)

# some random data
x = np.random.randn(1000)
y = np.random.randn(1000)


def scatter_hist(x, y, ax, ax_histx, ax_histy):
    # no labels
    ax_histx.tick_params(axis="x", labelbottom=False)
    ax_histy.tick_params(axis="y", labelleft=False)

    # the scatter plot:
    ax.scatter(x, y)

    # now determine nice limits by hand:
    binwidth = 0.25
    xymax = max(np.max(np.abs(x)), np.max(np.abs(y)))
    lim = (int(xymax/binwidth) + 1) * binwidth

    bins = np.arange(-lim, lim + binwidth, binwidth)
    ax_histx.hist(x, bins=bins)
    ax_histy.hist(y, bins=bins, orientation='horizontal')

# Start with a square Figure.
fig = plt.figure(figsize=(6, 6))
# Add a gridspec with two rows and two columns and a ratio of 1 to 4 between
# the size of the marginal axes and the main axes in both directions.
# Also adjust the subplot parameters for a square plot.
gs = fig.add_gridspec(2, 2,  width_ratios=(4, 1), height_ratios=(1, 4),
                      left=0.1, right=0.9, bottom=0.1, top=0.9,
                      wspace=0.00, hspace=0.00)
# Create the Axes.
ax = fig.add_subplot(gs[1, 0])
ax_histx = fig.add_subplot(gs[0, 0], sharex=ax)
ax_histy = fig.add_subplot(gs[1, 1], sharey=ax)

# Remove Axis Lines
ax_histy.spines[['right', 'top', 'bottom']].set_visible(False)
ax_histx.spines[['right', 'top', 'left']].set_visible(False)

# Remove Ticks
ax_histy.set_xticks([])
ax_histx.set_yticks([])

# Draw the scatter plot and marginals.
scatter_hist(x, y, ax, ax_histx, ax_histy)

Answered By: Nick

How to create a linear regression plot with distribution curves (e.g., normal distribution) that indicate the frequency at the X-Y axes in Python?

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