How to achieve a straight regression line in a log-log sns.regplot

Question

I am trying to recreate this plot created with R in Python:

This is where I got:

This is the code I used:

from matplotlib.ticker import ScalarFormatter

fig, ax = plt.subplots(figsize=(10,8))

sns.regplot(x='Platform2',y='Platform1',data=duplicates[['Platform2','Platform1']].dropna(thresh=2), scatter_kws={'s':80, 'alpha':0.5})
plt.ylabel('Platform1', labelpad=15, fontsize=15)
plt.xlabel('Platform2', labelpad=15, fontsize=15)
plt.title('Sales of the same game in different platforms', pad=30, size=20)

ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xticks([1,2,5,10,20])
ax.set_yticks([1,2,5,10,20])
ax.get_xaxis().set_major_formatter(ScalarFormatter())
ax.get_yaxis().set_major_formatter(ScalarFormatter())
ax.set_xlim([0.005, 25.])
ax.set_ylim([0.005, 25.])

plt.show()

I think I am missing some conceptual knowledge behind the logarithmic values I plotted here. Since I did not change the values themselves but the scale of the graph I think I am doing something wrong. When I tried changing the values themselves I was not successful.

What I wanted was to show the regression line like the one in the R plot and also show the 0s in the x and y axes. The logarithmic nature of the plot does not allow me to add the 0 limits in the x and y axes. I found this StackOverflow entry: LINK but I was not able to make it work. Maybe if someone can rephrase it or if someone has any suggestions on how to move forward it would be great!

Thanks!

Answer 1

Seaborn's regplot creates either a line in linear space (y ~ x), or (with logx=True) a linear regression of the form y ~ log(x). Your question asks for a linear regression of the form log(y) ~ log(x).

This can be accomplished by calling regplot with the log of the input data. However, this will change the data axes showing the log of the data instead of the data themselves. With a special tick formatter (taking the power of the value), these tick values can be converted again to the original data format.

Note that both the calls to set_xticks() and set_xlim() will need their values converted to log space for this to work. The calls to set_xscale('log') need to be removed.

The code below also changes most plt. calls to ax. calls, and adds the ax as argument to sns.regplot(..., ax=ax).

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

sns.set()
p1 = 10 ** np.random.uniform(-2, 1, 1000)
p2 = 10 ** np.random.uniform(-2, 1, 1000)
duplicates = pd.DataFrame({'Platform1': 0.6 * p1 + 0.4 * p2, 'Platform2': 0.1 * p1 + 0.9 * p2})

fig, ax = plt.subplots(figsize=(10, 8))

data = duplicates[['Platform2', 'Platform1']].dropna(thresh=2)
sns.regplot(x=np.log10(data['Platform2']), y=np.log10(data['Platform1']),
            scatter_kws={'s': 80, 'alpha': 0.5}, ax=ax)
ax.set_ylabel('Platform1', labelpad=15, fontsize=15)
ax.set_xlabel('Platform2', labelpad=15, fontsize=15)
ax.set_title('Sales of the same game in different platforms', pad=30, size=20)

ticks = np.log10(np.array([1, 2, 5, 10, 20]))
ax.set_xticks(ticks)
ax.set_yticks(ticks)
formatter = lambda x, pos: f'{10 ** x:g}'
ax.get_xaxis().set_major_formatter(formatter)
ax.get_yaxis().set_major_formatter(formatter)
lims = np.log10(np.array([0.005, 25.]))
ax.set_xlim(lims)
ax.set_ylim(lims)

plt.show()

To create a jointplot similar to the example in R (to set the figure size, use sns.jointplot(...., height=...), the figure will always be square):

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

sns.set()
p1 = 10 ** np.random.uniform(-2.1, 1.3, 1000)
p2 = 10 ** np.random.uniform(-2.1, 1.3, 1000)
duplicates = pd.DataFrame({'Platform1': 0.6 * p1 + 0.4 * p2, 'Platform2': 0.1 * p1 + 0.9 * p2})

data = duplicates[['Platform2', 'Platform1']].dropna(thresh=2)
g = sns.jointplot(x=np.log10(data['Platform2']), y=np.log10(data['Platform1']),
                  scatter_kws={'s': 80, 'alpha': 0.5}, kind='reg', height=10)

ax = g.ax_joint
ax.set_ylabel('Platform1', labelpad=15, fontsize=15)
ax.set_xlabel('Platform2', labelpad=15, fontsize=15)

g.fig.suptitle('Sales of the same game in different platforms', size=20)

ticks = np.log10(np.array([.01, .1, 1, 2, 5, 10, 20]))
ax.set_xticks(ticks)
ax.set_yticks(ticks)
formatter = lambda x, pos: f'{10 ** x:g}'
ax.get_xaxis().set_major_formatter(formatter)
ax.get_yaxis().set_major_formatter(formatter)
lims = np.log10(np.array([0.005, 25.]))
ax.set_xlim(lims)
ax.set_ylim(lims)
plt.tight_layout()
plt.show()