How has GDP Per Capita Changed Over Time?
1.
Does the GDP per capita seem to change by a constant difference, a constant second difference, or a constant ratio in each 5-year period? Explain. 2.
Three regression models for this data and their equations are shown below. Do you think a linear model, a quadratic model, or an exponential model fits the data best? Explain. !
" = −6844.79 + 200.530
!
" = 6579.89 − 183.040 + 1.7840
!
!
" = 1914.704(1.0149)
"
3.
Interpret the meaning of 1914.704 in the exponential regression equation. 4.
Interpret the meaning of 1.0149 in the exponential regression equation. 5.
Use the exponential model to predict the GDP per capita for the year 1830. 6.
Imagine if we took all the data values for GDP and found the log of them. Use your calculator to fill in the selected values in the table. 7.
What do you think the scatterplot will look like when plotting Years since 1800 and Log(GDP per capita)? Explain your reasoning. Years since 1800 GDP per capita Log(GDP per capita) 0 $2545.59 50 $3631.82 100 $8037.57 150 $15240.00 200 $45886.47 Gross Domestic Product (GDP) is a measure of a country’s total economic activity—the value of all goods and services produced over a given time period. GDP per capita divides this measure by the population to get a per person unit of wealth. Data about the U.S. GDP per capita is given in the spreadsheet for the years 1800 to 2020. Key
GDP
seems
to
be
changing
at
a
constant
ratio
of
about
1.
03
in
the
early
1800
's
.
The
differences
in
GDP
are
not
constant
.
The
exponential
model
seems
to
fit
best
,
especially
for
the
years
1800
-
1920
.
j=aob
×
g.
estimated
The
estimated
GDP
per
capita
for
the
year
1800
is
$
1914.704
.
=
in
Filed
y=yqsgY
¥
Tde
"
"
The
estimated
growth
factor
in
Gpp
per
capita
iÉ49
'
factor
transformed
I
=
1914.704
(
1.0149
)
"
=
$
2984.003
g
data
3.
4058
3.
5601
3.
9051
4.
1830
4.
6617
I
think
the
scatter
plot
will
look
linear
because
a
log
takes
inputs
that
grow
proportionally
+
produces
outputs
that
grow
linearly
.
