REGRESSION AND HUMAN POPULATIONS

By: Gillian Constantino, 12.7.11

What is world population? The world population is the total

number of human beings living on earth.

The U.S. Census bureau predicts that by 2050 the world population will be around 7.5 to 10.5 billion.

Death by illness, natural disasters, and accidents have a great impact on how populations increase and decrease. Deaths per year: 57 million

WORLD POPULATION DATAU.S. Census Bureau

Year, t Population (in Billions)

2001, t = 1 6.17

2002, t = 2 6.25

2003, t = 3 6.32

2004, t = 4 6.40

2005, t = 5 6.48

2006, t = 6 6.55

2007, t = 7 6.63

2008, t = 8 6.71

2009, t = 9 6.79

World Population

Assuming that

the data is linear,

Our function is as

follows:

f(x)=.0772x+6.0919

The linear

correlation is

strong with

coefficient

r = .99989

0 1 2 3 4 5 6 7 8 9 105.8

6

6.2

6.4

6.6

6.8

7

f(x) = 0.077166666666667 x + 6.09194444444445R² = 0.999793234251601

World Population (in Billions)

Population (in Billions)Linear (Popula-tion (in Bil-lions))

World PopulationAssuming that

the

data is exponential,

our function will

be as follows:

with correlation

coefficient

r = .99989

0 1 2 3 4 5 6 7 8 9 105.8

6

6.2

6.4

6.6

6.8

7

f(x) = 6.10019619988 exp( 0.01191665213 x )R² = 0.999821540828519

World Population (in Billions)

Population (in Billions)Exponential (Population (in Billions))

World Population

However if we were to assume that the world population grows logistically then we must consider the world population beyond 100 years before obtaining the logistic growth pattern of the given graph. Assuming that this is true, the function would be given by:

Facts of U.S population The United States is the third most populous

country in the world.

California and Texas are the most populous states in the U.S

New York City is the most populated city of the U.S, with Los Angeles being the second.

U.S populationU.S. Census Bureau

Year, t Population (in Millions)

1900, t = 0 76.212

1910, t = 10 92.228

1920, t = 20 106.022

1930, t = 30 123.203

1940, t = 40 132.165

1950, t = 50 151.326

1960, t = 60 179.323

1970, t = 70 203.302

1980, t = 80 226.542

1990, t = 90 248.710

2000, t = 100 281.422

U.S populationAssuming that

the

population grows

linearly, then function

is as follows:

f(x) = 2.019x + 64.546

The data has a strong

linear relationship as

illustrated with a

Correlation coefficient

given by r = .9907.

0 20 40 60 80 100 1200

50

100

150

200

250

300

f(x) = 2.01899454545455 x + 64.5461818181818R² = 0.981434841681941

Series1Linear (Series1)

U.S populationAssuming that

the populations

grows

exponentially, the

function is given

by:f(x)=

80.563e0.0128x

The graph shows

a strong

correlation with

r = .9975

0 20 40 60 80 100 1200

50

100

150

200

250

300

f(x) = 80.5632075184932 exp( 0.0128040764924403 x )R² = 0.995033990619672

Series1Exponential (Series1)

U.S populationMany

demographers

assume that the U.S.

population will

continue to grow but

in a logistic manner as

the graph indicates.

The logistic function is

give by:

ConclusionIn conclusion, while the given set of

data showsstrong linear and exponential

correlations, it isassumes that the U.S. population will

grow in alogistic manner.