问题
I want to create a regplot with a linear regression in Seaborn and scale both axes equally by log, such that the regression stays a straight line.
An example:
import matplotlib.pyplot as plt
import seaborn as sns
some_x=[0,1,2,3,4,5,6,7]
some_y=[3,5,4,7,7,9,9,10]
ax = sns.regplot(x=some_x, y=some_y, order=1)
plt.ylim(0, 12)
plt.xlim(0, 12)
plt.show()
What I get:
If I scale the x and y axis by log, I would expect the regression to stay a straight line. What I tried:
import matplotlib.pyplot as plt
import seaborn as sns
some_x=[0,1,2,3,4,5,6,7]
some_y=[3,5,4,7,7,9,9,10]
ax = sns.regplot(x=some_x, y=some_y, order=1)
ax.set_yscale('log')
ax.set_xscale('log')
plt.ylim(0, 12)
plt.xlim(0, 12)
plt.show()
How it looks:
回答1:
The problem is that you are fitting to your data on a regular scale but later you are transforming the axes to log scale. So linear fit will no longer be linear on a log scale.
What you need instead is to transform your data to log scale (base 10) and then perform a linear regression. Your data is currently a list. It would be easy to transform your data to log scale if you convert your list to NumPy array because then you can make use of vectorised operation.
Caution: One of your x-entry is 0
for which log is not defined. You will encounter a warning there.
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
some_x=np.array([0,1,2,3,4,5,6,7])
some_y=np.array([3,5,4,7,7,9,9,10])
ax = sns.regplot(x=np.log10(some_x), y=np.log10(some_y), order=1)
Solution using NumPy polyfit where you exclude x=0 data point from the fit
import matplotlib.pyplot as plt
import numpy as np
some_x=np.log10(np.array([0,1,2,3,4,5,6,7]))
some_y=np.log10(np.array([3,5,4,7,7,9,9,10]))
fit = np.poly1d(np.polyfit(some_x[1:], some_y[1:], 1))
plt.plot(some_x, some_y, 'ko')
plt.plot(some_x, fit(some_x), '-k')
来源:https://stackoverflow.com/questions/53972754/how-to-scale-the-x-and-y-axis-equally-by-log-in-seaborn