Matplotlib: World population

Consider the following world population estimates going back in time.

The data is from https://www.worldometers.info/world-population/world-population-by-year/. (2020-03-09)

Year Population -5000 5000000 -4000 7000000 -3000 14000000 -2000 27000000 -1000 50000000 -500 100000000 -200 150000000 200 190000000 600 200000000 700 210000000 800 220000000 900 240000000 1000 275000000 1100 320000000 1200 360000000 1400 350000000 1500 450000000 1600 500000000 1700 610000000 1760 770000000 1804 1000000000 1850 1200000000 1900 1600000000 1927 2000000000 1951 2584034261 1960 3034949748 1970 3700437046 1980 4458003514 1990 5327231061 2000 6143493823 2010 6956823603 2020 7794798739

Here is the Python code [#1]

import math
import matplotlib.pyplot as plt
import rsPlot
import numpy as np
from sklearn.linear_model import LinearRegression
dataList1= [
	[-5000,5000000],
	[-4000,7000000],
	[-3000,14000000],
	[-2000,27000000],
	[-1000,50000000],
	[-500,100000000],
	[-200,150000000],
	[200,190000000],
	[600,200000000],
	[700,210000000],
	[800,220000000],
	[900,240000000],
	[1000,275000000],
	[1100,320000000],
	[1200,360000000],
	[1400,350000000],
	[1500,450000000],
	[1600,500000000],
	[1700,610000000],
	[1760,770000000],
	[1804,1000000000],
	[1850,1200000000],
	[1900,1600000000],
	[1927,2000000000],
	[1951,2584034261],
	[1960,3034949748],
	[1970,3700437046],
	[1980,4458003514],
	[1990,5327231061],
	[2000,6143493823],
	[2010,6956823603],
	[2020,7794798739],
	]
xData0 = []
yData0 = []
yData3 = []
for year1,count1 in dataList1:
	xData0.append(year1)
	yData3.append(math.log(float(count1),10))
	yData0.append(count1)
xData1 = np.array(xData0).reshape(-1, 1)
yData1 = np.array(yData0).reshape(-1, 1)
yData2 = np.array(yData3).reshape(-1, 1)
plot1 = rsPlot.plot("log31-1",1,0,72,640,480)
color1 = "#006600"
ax1 = plot1.ax1
ax1.plot(xData1,yData1,color=color1)
plot1.save()
# do a simple linear regression
reg1 = LinearRegression()
reg1.fit(xData1,yData1)
slope1 = float(reg1.coef_)
coef1 = float(reg1.coef_)
intercept1 = float(reg1.intercept_)
equation1 = "count = {0:1.1f} * year + {1:0.2f}".format(slope1,intercept1)
print("")
print("Regression line:")
print("")
print("\t{0:s}".format(equation1))
print("")
print("\tSlope: {0:0.2f}".format(slope1))
print("\tIntercept: {0:0.2f}".format(intercept1))
print("\tCorrelation coefficient: {0:0.2f}".format(coef1))
print("")
print("Linear predictions: (every 10)")
print("")
print("\t{0:>5} {1:>5} {2:>5}-actual".format("year", "count", "count"))
for dataPos1,tuple1 in enumerate(dataList1):
	year1,count1 = tuple1
	y1 = slope1 * year1 + intercept1
	if (dataPos1 % 10) == 0:
		print("\t{0:5.1f} {1:5.1f} {2:5.1f}".format(year1,y1,count1))
print("")
yPredict1 = reg1.predict(xData1)
ax1.plot(xData1,yPredict1,color="#000099",label=equation1)
ax1.legend(fontsize=10)
plot1.save()
# now try a log regression
reg2 = LinearRegression()
reg2.fit(xData1,yData2)
slope2 = float(reg2.coef_)
coef2 = float(reg2.coef_)
intercept2 = float(reg2.intercept_)
equation2 = "count = {0:1.1f} * year + {1:0.2f}".format(slope2,intercept2)
print("")
print("Regression line:")
print("")
print("\t{0:s}".format(equation2))
print("")
print("\tSlope: {0:0.2f}".format(slope2))
print("\tIntercept: {0:0.2f}".format(intercept2))
print("\tCorrelation coefficient: {0:0.2f}".format(coef2))
print("")
print("Log-linear predictions: (every 10)")
print("")
print("\t{0:>5} {1:>5} {2:>5}-actual".format("year", "count", "count"))
for dataPos2,tuple2 in enumerate(dataList1):
	year2,count2 = tuple2
	y2 = 10.0**(slope2 * year2 + intercept2)
	if (dataPos2 % 10) == 0:
		print("\t{0:5.1f} {1:5.1f} {2:5.1f}".format(year2,y2,count2))
yPredict2 = reg2.predict(xData1)
plot1 = rsPlot.plot("log31-1",1,0,72,640,480)
ax1 = plot1.ax1
ax1.plot(xData1 ,yData2,color=color1)
ax1.plot(xData1,yPredict2,color="#000099")
plot1.save()

Here is the output of the Python code.

(module rsPlot imported)

Here is the world population plotted over time. Note: The y-axis uses an exponential notation.

A linear fit for the world population plotted over time is not a good fit.

A log-linear fit for the world population plotted over time is a better fit.