Linear Model Project

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Economics

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Feb 20, 2024

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Curve-Fitting Project - Linear Model: United States Population by Year (LR-1) Purpose : To analyze the population in the United States using a linear model. Data : The data was retrieved from https://www.worldometers.info/world-population/us-population/ The data used is based off the total population reported in the United States, although more statistics are available per year and further back in time. DATA: United States Population by Year Year Population 1955 171,685,336 1960 186,720,571 1965 199,733,676 1970 209,513,341 1975 219,081,251 1980 229,476,354 1985 240,499,825 1990 252,120,309 1995 265,163,745 2000 281,710,909 2005 294,993,511 2010 309,011,475 2015 320,878,310 2020 331,002,651 (LR-2) SCATTERPLOT: 1950 1960 1970 1980 1990 2000 2010 2020 2030 0 50,000,000 100,000,000 150,000,000 200,000,000 250,000,000 300,000,000 350,000,000 United States Population Year Population Page 1 of 4

(LR-3) 1950 1960 1970 1980 1990 2000 2010 2020 2030 0 50,000,000 100,000,000 150,000,000 200,000,000 250,000,000 300,000,000 350,000,000 f(x) = 2444198.92 x − 4607017413.93 United States Population with Regression Line Year Population Line of Best Fit (Regression Line) y = 2444198.924x - 4607017414 where x = Year and y = Population (LR-4) The slope is 2444198.924 annotating an average rate of increase of 2,444,199 people to the population in the United States each year. The slope indicates that in general, the population increases by average at a rate of 2,444,199 people per year or 12,220,995 people every 5 years. Page 2 of 4

(LR-5) Values of r 2 and r : r 2 = 0.996615132 We know that the slope of the regression line is positive so the correlation coefficient r will be positive. If r = 1, then there is a perfect positive linear relationship between x and y. r = ¿ 0.998306131 A line is a good curve for this data as the rate of increase in population between the year 1955 and 2020 are generally similar as they do not fluctuate much higher or lower than previous years and is a steady set of data. The linear relationship is a very strong positive one as the r value is very close to 1 as is the r 2 value. (LR-6) Prediction : For the year of 2025 in the United States, substitute x = 2025 to get y = 2444198.924(2025) – 4607017414 = 342,485,407 The regression line predicts a population total of 342,485,407 people in the United States in the year of 2025. 1940 1960 1980 2000 2020 2040 2060 0 50,000,000 100,000,000 150,000,000 200,000,000 250,000,000 300,000,000 350,000,000 400,000,000 450,000,000 f(x) = 2444198.92 x − 4607017413.93 R² = 1 United States Population Predicition by Year 2050 Year Population Page 3 of 4

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(LR-7) Narrative: Overall, the data consisted of the total population in the United States from the year of 1955 to the year of 2020, covering a range of 65 total years. While these numbers can fluctuate greatly due to catastrophes and large world events that result in a large increase or decrease of the population in a specific region. Take for example World War 2, in 1940 the World Population was estimated to be around 2.3 billion people, and in 1940 estimated to be only 2.5 billion people, a very small increase due to the total loss of population in that time. What surprised me with this data, is that while the population in the United States continues to increase a steadily rate, the fertility rate almost cut in half between the year 1955 and 2020 in the United States, with the fertility rate being 3.31 in 1955, and 1.78 in 2020. Many factors could play a role in this decline such as temporary declines in the economy (i.e., the Great Depression or Oil Shocks) or even social factors such as postponement of marriage into older ages compared to past years resulting in childbearing into older ages. So many factors have a play in the overall population, but the data from the past 68 years has proven to be relatively steady. Page 4 of 4

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