File:Catagolue still life scatterplot b3s23 C1.png

Script:

#!/usr/bin/python3

import numpy as np
import matplotlib.pyplot as plt
import statsmodels.api as sm

# read data file
datafile=open("xs_scatterplot.dat","rb")
x, y=np.loadtxt(datafile,delimiter="\t",skiprows=1,unpack=True)

# generate a scatter plot
fig, ax=plt.subplots()
ax.scatter(x, y, label='Count')
ax.set_yscale('symlog', linthreshy=1)
ax.set_xlabel('Population', fontsize=15)
ax.set_ylabel("Count", fontsize=15)
ax.set_title('Total still lifes by population', fontsize=20)
plt.ylim(ymin=0)
#plt.xlim(xmin=4)
ax.grid(True)
fig.tight_layout()

# plot linear fit
logy=np.log(y)
coefficients=np.polyfit(x, logy, 1)
polynomial=np.poly1d(coefficients)
ys=polynomial(x)
plt.plot(x, np.exp(ys), label='Linear fit')

# plot LOWESS fit
lowess=sm.nonparametric.lowess
z=lowess(logy, x, frac=0.3, it=3, return_sorted=False)
plt.plot(x, np.exp(z), label=r'LOWESS fit, $\alpha=0.3$')

# add legend
plt.legend(loc='upper right')

# save plot to file
fig.set_size_inches(8, 8)
plt.savefig("xs_scatterplot.png", dpi=80)

Input data:

Population	Count
4	59226634956040
5	8300152601291
6	36287875579390
7	9589041751021
8	1831061627671
9	9752130654
10	6648614605
11	1966944907
12	296645053864
13	250781922
14	113637861417
15	672983961
16	4250963305
17	223747639
18	799747551
19	28055058
20	100004321
21	2322435
22	14770842
23	722422
24	651844
25	333072
26	226630
27	48939
28	4663087
29	14302
30	69920
31	27084
32	11145
33	290
34	458
35	40
36	82
37	11
38	608
39	8
40	8048
41	2
42	102
45	1
46	1
56	1