Cubic Regression
Immigration The number of foreign-born immigrants in the United States has fluctuated over
the last one-hundred years. Below is a table that gives the number of immigrants (in millions) for
years since 1900. Source: Center for Immigration Studies
Years since 1900, t
0
10
20
30
40
50
10.3
13.5
13.9
14.2
11.6
10.3
Years since 1900
60
70
80
90
100
Immigrant Population, P
(in millions)
9.7
9.6
14.1
19.8
31.1
Immigrant Population, P
(in millions)
a)
Use a graphing utility to create a scatter plot for the data. Let t represent the year, with t = 0
corresponding to 1900.
b)
Use the regression feature of a graphing utility to find a cubic model for the data. Graph
your equation along with the scatter plot on the same screen. How does your model compare
with the scatter plot?
c) Use your model to predict the immigration population in 2010?
d) According to the Federation for American Immigration Reform, the immigrant population in
2010 was 39,955,854. How does this compare to your estimation? What might it imply
about your model?