Linear regression plot on log scale in Python

Question

I want to do linear regression to the data given by x and y. Everything seems to be fine when I use a linear plot, but when I want to plot it on a log scale the line does not look straight. I think I should divide the interval into finer grids rather than only six points. But I couldn't do that.

How can I do line fitting on a log scale for the below script?

import numpy as np
import matplotlib.pyplot as plt

x = np.array([1560., 526., 408., 226., 448., 288.])
y = np.array([0.118, 0.124, 0.131, 0.160, 0.129, 0.138])

f = np.multiply(x,y**2)

coefs = np.polyfit(x, f, 1)

pred_f = coefs[1] + np.multiply(sorted(x), coefs[0])

fig, ax1 = plt.subplots(1, 1, figsize=(8,6))

ax1.scatter(x, f)
ax1.plot(sorted(x), pred_f, 'k--')
ax1.set_xscale('log')
ax1.set_yscale('log')

plt.show()

ForceBru · Accepted Answer · 2022-02-25 13:46:51Z

2

Indeed, "straight lines" (linear functions) don't look straight on log-log plots:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0.1, 10)
y = 2*x+3 # LINEAR!

plt.plot(x, y)
plt.xscale('log')
plt.yscale('log')
plt.show()

Result:

To fit on the log scale, run your regression on loagrithms of the original data:

coefs = np.polyfit(np.log(x), np.log(f), 1)

# Now work with logarithms everywhere!
pred_f = coefs[1] + np.multiply(sorted(np.log(x)), coefs[0])

fig, ax1 = plt.subplots(1, 1, figsize=(8,6))
ax1.scatter(np.log(x), np.log(f)) # logs here too!
ax1.plot(sorted(np.log(x)), pred_f, 'k--') # pred_f is already in logs
plt.show()

Plot:

Or have Matplotlib draw log ticks. Then you'll need to exponentiate pred_f to put it on the same scale as the data:

fig, ax1 = plt.subplots(1, 1, figsize=(8,6))
ax1.scatter(x, f) # original scale!
ax1.plot(sorted(x), np.exp(pred_f), 'k--') # exponentiate pred_f
ax1.set_xscale('log')
ax1.set_yscale('log')
plt.show()

The plot is the same, but it now uses the original scale of your data:

edited Feb 25, 2022 at 13:46

answered Feb 25, 2022 at 13:00

ForceBru

45k10 gold badges71 silver badges104 bronze badges

Sign up to request clarification or add additional context in comments.

8 Comments

Lynx Over a year ago

Thank you for your answer. When I do that, I get an odd figure. Excuse my ignorance, I am a newbie as you might guess.

ForceBru Over a year ago

@Lynx, what exactly is "odd" about that figure?

Lynx Over a year ago

The line doesn't cross across the data points.

ForceBru Over a year ago

Could you please post the plot you're getting?

Lynx Over a year ago

Here it is: imgur.com/a/ECQBz8c

|

Collectives™ on Stack Overflow

Linear regression plot on log scale in Python

1 Answer 1

8 Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

8 Comments

Your Answer

Sign up or log in

Post as a guest

Related