Dotted line style from non-evenly distributed data - matplotlib

Question

I'm new to Python and MatPlotlib.
This is my first posting to Stackoverflow - I've been unable to find the answer elsewhere and would be grateful for your help.
I'm using Windows XP, with Enthought Canopy v1.1.1 (32 bit).
I want to plot a dotted-style linear regression line through a scatter plot of data, where both x and y arrays contain random floating point data.
The dots in the resulting dotted line are not distributed evenly along the regression line, and are "smeared together" in the middle of the red line, making it look messy (see upper plot resulting from attached minimal example code).
This does not seem to occur if the items in the array of x values are evenly distributed (lower plot).
I'm therefore guessing that this is an issue with how MatplotLib renders dotted lines, or with how Canopy interfaces Python with Matplotlib.
Please could you tell me a workaround which will make the dots on the dotted line type appear evenly distributed; even if both x and y data are non-evenly distributed; whilst still using Canopy and Matplotlib?
(As a general point, I'm always keen to improve my coding skills - if any code in my example can be written more neatly or concisely, I'd be grateful for your expertise).
Many thanks in anticipation
Dave
(UK)
import matplotlib.pyplot as plt
import numpy as np
from scipy import stats
#generate data
x1=10 * np.random.random_sample((40))
x2=np.linspace(0,10,40)
y=5 * np.random.random_sample((40))
slope, intercept, r_value, p_value, std_err = stats.linregress(x1,y)
line = (slope*x1)+intercept
plt.figure(1)
plt.subplot(211)
plt.scatter(x1,y,color='blue', marker='o')
plt.plot(x1,line,'r:',label="Regression Line")
plt.legend(loc='upper right')
slope, intercept, r_value, p_value, std_err = stats.linregress(x2,y)
line = (slope*x2)+intercept
plt.subplot(212)
plt.scatter(x2,y,color='blue', marker='o')
plt.plot(x2,line,'r:',label="Regression Line")
plt.legend(loc='upper right')
plt.show()

Answer 1

Welcome to SO.
You have already identified the problem yourself, but seem a bit surprised that a random x-array results in the line be 'cluttered'. But you draw a dotted line repeatedly over the same location, so it seems like the normal behavior to me that it gets smeared at places where there are multiple dotted lines on top of each other.
If you don't want that, you can sort your array and use that to calculate the regression line and plot it. Since its a linear regression, just using the min and max values would also work.
x1_sorted = np.sort(x1)
line = (slope * x1_sorted) + intercept
or
x1_extremes = np.array([x1.min(),x1.max()])
line = (slope * x1_extremes) + intercept
The last should be faster if x1 becomes very large.
With regard to your last comment. In your example you use whats called the 'state-machine' environment for plotting. It means that specified commands are applied to the active figure and the active axes (subplots).
You can also consider the OO approach where you get figure and axes objects. This means you can access any figure or axes at any time, not just the active one. Its useful when passing an axes to a function for example.
In your example both would work equally well and it would be more a matter of taste.
A small example:
# create a figure with 2 subplots (2 rows, 1 column)
fig, axs = plt.subplots(2,1)
# plot in the first subplots
axs[0].scatter(x1,y,color='blue', marker='o')
axs[0].plot(x1,line,'r:',label="Regression Line")
# plot in the second
axs[1].plot()
etc...