Generate some graphs and projections of the population of Greenville

greenville_population.py

"""
Graph the population of Greenville County over time.

Data from wikipedia.
https://en.wikipedia.org/wiki/Greenville_County,_South_Carolina

Need to `pip install sklearn` and `pip install matplotlib` first.
"""
import matplotlib.pyplot as plt
import math
from sklearn import linear_model

population_by_year = {
    1790: 6503,
    1800: 11504,
    1810: 13133,
    1820: 14530,
    1830: 16476,
    1840: 17839,
    1850: 20156,
    1860: 21892,
    1870: 22262,
    1880: 37496,
    1890: 44310,
    1900: 53490,
    1910: 68377,
    1920: 88498,
    1930: 117009,
    1940: 136580,
    1950: 168152,
    1960: 209776,
    1970: 240546,
    1980: 287913,
    1990: 320167,
    2000: 379616,
    2010: 451225,
    2020: 532486,
}

years = list(population_by_year.keys())
populations = population_by_year.values()
log_populations = [math.log(population) for population in populations]

start_year, end_year = 1789, 2051
regression = linear_model.LinearRegression()
regression.fit([[year] for year in years], log_populations)
slope = regression.coef_[0]
intercept = regression.intercept_
predictions_by_year = {
    year: regression.predict([[year]])[0] for year in range(start_year, end_year)
}

# Print Model
print("Linear least squares fit of the log of the population.")
print(f"Intercept: {intercept:.5}")
print(f"Slope: {slope:.5}")
print(f"Years to Double: {math.log(2) / slope:.3}")
# e^{slope * x} = e^{slope * 0} * 2  # doubles when x years pass
# e^{slope * x} = 1 * 2
# e^{slope * x} = 2
# slope * x = log(2)
# x = log(2) / slope

# Make graphs
plt.rcParams.update({"text.usetex": True})
plt.plot(years, log_populations, label="$\\log(population)$")
plt.plot(
    predictions_by_year.keys(),
    predictions_by_year.values(),
    label=f"$y = {slope:.3}x {intercept:.3}$".replace("-", "- "),
)
plt.legend()
plt.title("Greenville Population (log)")
plt.savefig("greenville-population-log.png")
plt.close()

plt.plot(years, populations, label="$population$")
plt.plot(
    predictions_by_year.keys(),
    [math.exp(prediction) for prediction in predictions_by_year.values()],
    label=f"$population = ({math.exp(intercept):.4E}) e^{{{slope:.3}year}}$".replace(
        "E-", "$E-$"
    ),
)
plt.legend()
plt.title("Greenville Population")
plt.savefig("greenville-population.png")
plt.close()

# Print population table.
print("| Year | Projected Population | Population |")
print("|------|----------------------|------------|")
for year, prediction in predictions_by_year.items():
    population = (
        f"{population_by_year[year]:10,d}" if year in population_by_year else " " * 10
    )
    print(f"| {year} | {int(math.exp(prediction)):20,d} | {population} |")

Year	Projected Population	Population
1789	7,120
1790	7,257	6,503
1791	7,396
1792	7,537
1793	7,682
1794	7,829
1795	7,979
1796	8,132
1797	8,287
1798	8,446
1799	8,608
1800	8,773	11,504
1801	8,941
1802	9,112
1803	9,287
1804	9,465
1805	9,646
1806	9,831
1807	10,019
1808	10,211
1809	10,407
1810	10,606	13,133
1811	10,809
1812	11,016
1813	11,227
1814	11,442
1815	11,662
1816	11,885
1817	12,113
1818	12,345
1819	12,581
1820	12,822	14,530
1821	13,068
1822	13,318
1823	13,573
1824	13,833
1825	14,098
1826	14,368
1827	14,644
1828	14,924
1829	15,210
1830	15,501	16,476
1831	15,798
1832	16,101
1833	16,410
1834	16,724
1835	17,044
1836	17,371
1837	17,704
1838	18,043
1839	18,388
1840	18,741	17,839
1841	19,100
1842	19,465
1843	19,838
1844	20,218
1845	20,606
1846	21,000
1847	21,403
1848	21,813
1849	22,231
1850	22,656	20,156
1851	23,091
1852	23,533
1853	23,984
1854	24,443
1855	24,911
1856	25,389
1857	25,875
1858	26,371
1859	26,876
1860	27,391	21,892
1861	27,915
1862	28,450
1863	28,995
1864	29,551
1865	30,117
1866	30,694
1867	31,282
1868	31,881
1869	32,491
1870	33,114	22,262
1871	33,748
1872	34,395
1873	35,054
1874	35,725
1875	36,409
1876	37,107
1877	37,818
1878	38,542
1879	39,281
1880	40,033	37,496
1881	40,800
1882	41,582
1883	42,378
1884	43,190
1885	44,017
1886	44,860
1887	45,720
1888	46,596
1889	47,488
1890	48,398	44,310
1891	49,325
1892	50,270
1893	51,233
1894	52,214
1895	53,215
1896	54,234
1897	55,273
1898	56,332
1899	57,411
1900	58,511	53,490
1901	59,632
1902	60,774
1903	61,938
1904	63,125
1905	64,334
1906	65,566
1907	66,822
1908	68,102
1909	69,407
1910	70,736	68,377
1911	72,091
1912	73,472
1913	74,880
1914	76,314
1915	77,776
1916	79,266
1917	80,785
1918	82,332
1919	83,909
1920	85,517	88,498
1921	87,155
1922	88,824
1923	90,526
1924	92,260
1925	94,027
1926	95,829
1927	97,664
1928	99,535
1929	101,442
1930	103,385	117,009
1931	105,366
1932	107,384
1933	109,441
1934	111,538
1935	113,674
1936	115,852
1937	118,071
1938	120,333
1939	122,638
1940	124,987	136,580
1941	127,382
1942	129,822
1943	132,309
1944	134,843
1945	137,426
1946	140,059
1947	142,742
1948	145,476
1949	148,263
1950	151,103	168,152
1951	153,998
1952	156,948
1953	159,954
1954	163,018
1955	166,141
1956	169,324
1957	172,568
1958	175,873
1959	179,242
1960	182,676	209,776
1961	186,175
1962	189,742
1963	193,376
1964	197,081
1965	200,856
1966	204,704
1967	208,625
1968	212,622
1969	216,695
1970	220,846	240,546
1971	225,076
1972	229,388
1973	233,782
1974	238,260
1975	242,825
1976	247,476
1977	252,217
1978	257,048
1979	261,972
1980	266,991	287,913
1981	272,105
1982	277,318
1983	282,630
1984	288,044
1985	293,562
1986	299,186
1987	304,917
1988	310,758
1989	316,711
1990	322,778	320,167
1991	328,961
1992	335,263
1993	341,685
1994	348,230
1995	354,901
1996	361,700
1997	368,629
1998	375,690
1999	382,887
2000	390,222	379,616
2001	397,697
2002	405,315
2003	413,079
2004	420,992
2005	429,057
2006	437,276
2007	445,653
2008	454,190
2009	462,890
2010	471,757	451,225
2011	480,794
2012	490,005
2013	499,391
2014	508,958
2015	518,707
2016	528,644
2017	538,770
2018	549,091
2019	559,610
2020	570,330	532,486
2021	581,255
2022	592,390
2023	603,738
2024	615,303
2025	627,090
2026	639,102
2027	651,345
2028	663,822
2029	676,539
2030	689,499
2031	702,707
2032	716,168
2033	729,887
2034	743,869
2035	758,118
2036	772,641
2037	787,442
2038	802,526
2039	817,900
2040	833,567
2041	849,535
2042	865,809
2043	882,395
2044	899,298
2045	916,525
2046	934,082
2047	951,976
2048	970,212
2049	988,797
2050	1,007,739