This document presents the results of a regression analysis examining the relationship between forest area percentage and carbon emissions. The analysis finds a strong negative correlation between forest area and emissions. After addressing outliers and multicollinearity issues, the regression shows forest area percentage is a statistically significant indicator of carbon emissions. However, some other variables like urban population and energy production are not statistically significant predictors. This suggests that while forest area capture carbon, energy usage is a more important driver of emissions levels than other factors.

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Derek Applegate Economics major
Psych minor
Cell: 518-852-1648
Home: 518-355-1824
Econ/Finc classes:
Econ 101,102,
201,202, 210, 300,340
and 430
Career Goals: I want
to possibly be a
market analyst or
work in the emerging
green sector. I also
wouldn’t mind
opening up my own
business at some
point down the road if
I get the opportunity
and capital to do so.

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Can forest area be used an indicator of carbon emissions?
Hypotheses and inspiration: Countries with higher percentage of forest will have lower carbon
emissions during the year of 2005. I want to see if having a large body of forests in a country is
an indicator of low carbon emissions for each individual country. I decided to do this regression
because I had heard of the carbon capture concept in Professor Booker’s class and wanted to see
if the data would hold up in a regression. This data is arithmetical in how the carbon capture is
calculated but it is still worth it in determining forest area’s role in carbon emissions.
Variables
1. Forestry (percent of land area): Forest area is land under natural or planted stands of trees
of at least 5 meters in situ, whether productive or not, and excludes tree stands in
agricultural production systems (for example, in fruit plantations and agroforestry
systems) and trees in urban parks and gardens
2. Urban population: Urban population refers to people living in urban areas as defined by
national statistical offices. It is calculated using World Bank population estimates and
urban ratios from the United Nations World Urbanization Prospects.
3. Energy Use per Capita: Energy use refers to use of primary energy before transformation
to other end-use fuels, which is equal to indigenous production plus imports and stock
changes, minus exports and fuels supplied to ships and aircraft engaged in international
transport.
4. Energy Production per capita: Energy production refers to forms of primary energy—

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petroleum (crude oil, natural gas liquids, and oil from nonconventional sources), natural
gas, solid fuels (coal, lignite, and other derived fuels), and combustible renewables and
waste--and primary electricity, all converted into oil equivalents.
5. C02 Emissions per capita: Carbon dioxide emissions are those stemming from the
burning of fossil fuels and the manufacture of cement. They include carbon dioxide
produced during consumption of solid, liquid, and gas fuels and gas flaring.
Initial run
Model Summaryb
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .907a
.823 .813 .0027021
a. Predictors: (Constant), Energy Production Per Capita, Urban Population, Forest Area
(percentage of land area), Motor Vehicles (per 100 people), Energy Use Per Capita
b. Dependent Variable: C02 Emissions per capita (kt)
Coefficientsa
Model Unstandardized Coef f icients Standardized
Coef f icients
t Sig.
B Std. Error Beta
1 (Constant) .001 .001 2.400 .018
Motor Vehicles (per 100 people) 8.853E-007 .000 .032 .450 .654
Forest Area (percentage of land area) -2.372E-005 .000 -.080 -1.736 .086
Urban Population 2.200E-012 .000 .025 .569 .571
Energy Use Per Capita 1.842E-006 .000 .771 8.687 .000

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Energy Production Per Capita .084 .035 .151 2.394 .019
a. Dependent Variable: C02 Emissions per capita (kt)
In my initial run I found the R squared to be .823 and only two of variables to have passed the T-
test. I am not going to be discounting these values yet as I have to still correct for any outliers
and determine if there is any multicollinearity, auto correlation, or Heteroschadisticity between
my explanatory variables which would throw off the T-stat.
Casewise Diagnosticsa
Case Number Std. Residual C02 Emissions per
capita (kt)
Predicted Value Residual
86 -6.297 .0074 .024443 -.0170160
114 2.120 .0244 .018624 .0057273
144 -2.496 .0092 .015909 -.0067454
185 -2.009 .0057 .011137 -.0054281
a. Dependent Variable: C02 Emissions per capita (kt)
In my first run, I found that there is a significant outlier in my regression. I checked my data and
found that Iceland was throwing out my data due to emitting lower C02 per capita than the rest
of my data. After conducting some research I found that Iceland gets 81% of its energy from
renewable resources and derives 19% of its energy from oil and other fossil fuels. This 19%
percent energy use in fossil fuels is what accounts for the.0074 C02 emissions per capita. I will
be taking Iceland out of my regression and running the regression anew. I realized that this tells
me something about the rest of the data in my regression. This means that most of the countries

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in my regression heavily rely on fossil fuels because if they did not Iceland would be an outlier
and instead could possibly be the norm for this regression.
Second Run (without Case 86 or Iceland).
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .962a
.925 .921 .0017666
a. Predictors: (Constant), Motor Vehicles (per 1000 people), Urban Population, Forest
Area (percentage of land area), Energy Production Per Capita, Energy Use Per Capita
After taking out Iceland my R squared jumped to .925 which is a significant jump from the .823
that I had previously reported. This details that 92.5% of C02 emissions per capita is explained
by Motor Vehicles per 1000 people, Urban Population, Percentage of forest area, Energy
Production per capita, Energy Use per capita. The other interesting point I found was that the
adjusted R squared in this regression was only off by .004 in this regression as opposed to a
difference of .010 in the previous regression. This means that the variables in my regression are
pulling their weight in this regression stronger than they were previously.
Coefficientsa
Model Unstandardized Coef f icients Standardized
Coef f icients
t Sig.
B Std. Error Beta
1 (Constant) .001 .000 2.892 .005
Forest Area (percentage of land area) -3.187E-005 .000 -.106 -3.555 .001
Urban Population 6.988E-013 .000 .008 .276 .783
Energy Production Per Capita .003 .024 .006 .133 .894
Energy Use Per Capita 2.508E-006 .000 .980 16.567 .000

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Motor Vehicles (per 1000 people) -1.525E-006 .000 -.054 -1.169 .246
a. Dependent Variable: C02 Emissions per capita (kt)
This regression gave me back some very interesting values as far as the T- stat. The most
important difference I see is that Forest Area has passed the t-stat while in the first run it failed
that test. Energy use remained the same with the t-stat while urban population and energy
production per capita saw a more pronounced failing of the t-stat. There is a negative slope on
forest area which is what I expected out of the regression. Urban population has a positive slope
which is what I expected. Energy use also had a positive slow which is what I expected to occur.
I expected motor vehicles to have a negative slope and the data confirmed it. The only slope that
did not fall according to my data was energy production. I expected it to have a negative slope
but instead it had a positive slope. This makes sense in practicality because energy production
should increase with C02 emissions given my observance above of countries relying heavily on
fossil fuels that produce C02 emissions.
A more in depth look at these variables shows that percentage of forest area can be used
as an explanation for the C02 emissions since the data passes the 5% t-stat test as well as the 1%
test. I could still be off but the IPSS has only shown the number out to the thousandth’s place.
This means that forest area does have an impact on the C02 emissions per capita in a given
country.
Urban population failed the t-test with a sig value of .783. This means that if I were to
reject the null hypotheses for urban population I would be wrong 78.3% of the time. With this
knowledge I can safely say that urban population is not statistically significant in impacting C02
emissions per capita.
Energy production also failed the t-test with a sig value of .894. This means that if I were
to reject the null hypotheses I would be wrong 89.4% of the time. With this knowledge I can
suggest that energy production is not statistically significant in determining C02 emissions.

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Energy use per capita passed the t-test with a .000. This means that I can reject the null
hypotheses and would be wrong 0% of the time. I could still be wrong on this but IPSS has only
reported out to the thousandth’s place. From this I can infer that energy use per capita does have
a statistically significant impact on C02 emissions.
Motor Vehicles per 1000 people failed the t-test with a value of .246. This means that if I
were to reject the null hypotheses I would be wrong 24.6% of the time. This means that motor
vehicles per 1000 people is not a statistically significant indicator of C02 emissions.
Practical significance is another issue entirely which is very intertwined in my regression.
It is not statistically significant that urban population affects C02 emissions yet in my regression
it is statistically significant for energy use to affect C02 emissions. This means that the urban
population does not matter but rather how that population uses energy influences C02 emissions.
To clarify, a population that uses a lot of energy per capita is going to be influencing the C02
emissions of that particular country more than a population that does not use a lot of energy per
capita. A high urban population will not matter if the people who are in that population do not
use a lot energy per capita. This logic can be applied to energy production per capita as well.
Producing more energy per capita does not in any way necessitate that the population will be
using the energy which is the key in how much C02 is produced. This essentially comes down to
how much a nation uses C02 producing energy will result in higher C02 emissions. This can also
apply to motor vehicles as well. Having more motor vehicles per 1000 people doesn’t suggest
that they will use those vehicles but rather the energy use per capita will be a indicator of how
much they use those vehicles. Using vehicles is simply a means of energy use which is why I
postulate that it fails the t-test by a smaller margin than energy production or urban population.
This is something that I had not initially thought about when running my regression. This
however leaves a gray area of forestry and how it falls into being practically significant given
that is the crux of my regression.

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Multicollinearity
After running a pearson correlation I found that there were two separate cases of
multicollinearity. The first case is between energy production per capita and energy use per
capita with a pearson correlation value of .661. Under Professor Trees rule of thumb anything
over .6 is considered a strong correlation. The other multicollinearity issue is with energy use per
capita and motor vehicles per 1000 people with a pearson correlation of .691. This a much more
problematic issue because they are not measured the same way and are therefore more
problematic to interpret. I am going to focus more on the energy use and energy production
problem instead.
I am going to run another regression using energy use and production to determine if
multicollinearity is still present.
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .781a .610 .607 1710.575
a. Predictors: (Constant), Energy Production Per Capita
This is a strong case for the existence of multicollinearity with these two variables. The major
problem with trying to correct for this by dividing all of the explanatory variables by energy
production or energy use is that it will be far more problematic as they are all measured
differently besides energy use per capita and energy production per capita. Instead I am going to
take out each variable individually to try to correct for multicollinearity. The first variable I am
going to remove is energy production.

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Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .962a
.925 .922 .0017569
a. Predictors: (Constant), Energy Use Per Capita, Urban Population, Forest Area
(percentage of land area), Motor Vehicles (per 1000 people)
Coefficientsa
Model Unstandardized Coef f icients Standardized
Coef f icients
t Sig. Fraction Mis
B Std. Error Beta
1 (Constant) .001 .000 2.907 .005
Urban Population 6.664E-013 .000 .008 .266 .791
Motor Vehicles (per 1000 people) -1.600E-006 .000 -.056 -1.367 .175
Forest Area (percentage of land area) -3.184E-005 .000 -.106 -3.572 .001
Energy Use Per Capita 2.522E-006 .000 .985 23.998 .000
a. Dependent Variable: C02 Emissions per capita (kt)
After examining my previous R squared with energy production in it. I can see that the R squared
has remained the same and I have successfully rid my regression of that particular
multicollinearity.
I am going to attempt to solve the multicollinearity issue with motor vehicles and energy use by
removing motor vehicles as that variable has failed it’s t-test.
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate

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1 .967a
.936 .934 .0018705
a. Predictors: (Constant), Energy Use Per Capita, Urban Population, Forest Area
(percentage of land area)
Coefficientsa
Model Unstandardized Coef f icients Standardized
Coef f icients
t Sig.
B Std. Error Beta
1 (Constant) .000 .000 1.376 .171
Urban Population -1.745E-013 .000 -.001 -.067 .946
Forest Area (percentage of land area) -1.914E-005 .000 -.061 -3.039 .003
Energy Use Per Capita 2.555E-006 .000 .958 47.517 .000
a. Dependent Variable: C02 Emissions per capita (kt)
Interestingly enough I have removed motor vehicles from the equation and the R squared has
jumped by .11. This shows that motor vehicles was not pulling its weight in this regression as
well as contributing to the problem of multicollinearity. There has been trend in each of these
tests as well. As I have removed a variable that has contributed to multicollinearity the t-stat on
my energy use variable has increased sharply with each test. There is another phenomenon that I
have noticed as well during this test, the t-stat on the forest area continues to move positively
after each variable that I have removed.
Autocorrelation

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Autocorrelation is not a particular issue for cross-sectional analysis but it is worth going
over to check to see if my regression suffers from it. The test I will be conducting is the Durbin-
Watson.
Model Summaryb
Model R R Square Adjusted R Square Std. Error of the
Estimate
Durbin-Watson
1 .962a
.925 .921 .0017666 1.679
a. Predictors: (Constant), Motor Vehicles (per 1000 people), Urban Population, Forest Area (percentage of land
area), Energy Production Per Capita, Energy Use Per Capita
b. Dependent Variable: C02 Emissions per capita (kt)
I found the value of my DL to be 1.69261 and Du to be 1.76991. My DL-4 equals -2.3079 and
my Du-4 equals 2.2009. My Durbin Watson is 1.679 which means that I do have autocorrelation
but I have cross-sectional data which means I still do not have autocorrelation.
Heteroscedasticity
As a means to test for Heteroscedasticity I will be graphing the unstandardized residual against
the unstandardized predicted value to determine if I have hetero for this regression.

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Based on this graph there seems to be a moderate degree of heteroscedasticity.

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This graph indicates that there is a small amount of heteroscedasticity

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This graph indicates that there is a little heteroscedasticity.

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This graph indicates that there is a large degree of heteroscedasticity.

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This graph indicates that there is little heteroscedasticity.

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This graph indicates that there is little heteroscedasticity.
Heteroscedasticity test 2: Glejser test.
To be certain that I do not have heteroscedasticity I will be performing the glejser test on all of
my explanatory variables. I have taken all of the residual values that I had previous attained by
my first heteroscedasticity test ran them through excel using the the heteroscedasticity absolute
value function. The only data that makes me question my original findings is energy use per
capita which had a graph that had a strong indication of heteroscedasticity. I am going to start

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simply by running energy use as an explanatory variable while absolute value of the residuals
will be the dependent.
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .000a
.000 -.011 .00172780
a. Predictors: (Constant), Energy Use Per Capita
Coefficientsa
Model Unstandardized Coef f icients Standardized
Coef f icients
t Sig.
B Std. Error Beta
1 (Constant) -1.220E-018 .000 .000 1.000
Energy Use Per Capita .000 .000 .000 .000 1.000
a. Dependent Variable: Unstandardized Residual
The R squared on this regression is zero and the t-stat is zero. This would suggest that there is
no heteroscedasticity. I am going to run another regression with the absolute value of the residual
as dependent and square root of energy use per capita as explanatory variable. This test will be
the second part of determining if energy use per capita has heteroscedasticity.
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .075a
.006 .001 .0010145
a. Predictors: (Constant), square root of energy us per capita

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Coefficientsa
Model Unstandardized Coef f icients Standardized
Coef f icients
t Sig.
B Std. Error Beta
1 (Constant) .001 .000 5.621 .000
square root of energy us per capita -2.856E-006 .000 -.075 -1.087 .278
a. Dependent Variable: Abs. residual
The R squared in this case is still below zero and doesn’t explain the absolute value of the
residuals enough to suggest that there is heteroscedasticity. From this test as well I can suggest
that there is no heteroscedasticity in this regression.
The final test I will be running to determine if I have heteroscedasticity will be using energy use
per capita divided by one and the absolute value of the residual.
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .051a
.003 -.003 .0009679
a. Predictors: (Constant), 1/energy use per capita
Coefficientsa
Model Unstandardized Coef f icients Standardized
Coef f icients
t Sig.
B Std. Error Beta
1 (Constant) .000 .000 5.677 .000
1/energy use per capita -.009 .014 -.051 -.655 .513
a. Dependent Variable: Abs. residual

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As I have state before the R squared is not enough to explain the possible heteroscedasticity. The
t-stat is also below 2 which would indicate that there is no heteroscedasticity.
From these two tests I can easily see that it simply a graphing anomaly that explains why
the graph was indicating that I had heteroscedasticity when all of the numbers in the regressions
point to heteroscedasticity being very small or non-existent in the overall regression. I am going
to assume that heteroscedasticity plays a negligible role in my regression.
Conclusion and final runs:
I am still at a loss for how forest area fits into the practical significance of my original hypothese
despite it confirming my original hypotheses. To illuminate forest area more I am going to run a
few more regressions.
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .971a
.942 .941 .0017760
a. Predictors: (Constant), Energy Production Per Capita, Rural Population, Forest Area
(percentage of land area), Energy Use Per Capita
Coefficientsa
Model Unstandardized Coef f icients Standardized
Coef f icients
t Sig.
B Std. Error Beta
1 (Constant) .001 .000 2.118 .036

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Forest Area (percentage of land area) -1.700E-005 .000 -.054 -2.828 .005
Energy Use Per Capita 2.284E-006 .000 .856 28.111 .000
Rural Population 3.034E-013 .000 .004 .188 .851
Energy Production Per Capita .076 .018 .131 4.305 .000
a. Dependent Variable: C02 Emissions per capita (kt)
I ran this regression without motor vehicles and instead of using urban population I ran the
regression with rural population. What I have found here is that is different from the rest of the
regression run up to this point is that energy production has passed the t-stat and my R squared is
significantly higher than I have previously reported. I am going to do away with rural population
in this regression and run it with GDP per capita instead.
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .975a
.950 .949 .0016798
a. Predictors: (Constant), GDP per Capita, Energy Production Per Capita, Forest Area
(percentage of land area), Energy Use Per Capita
Coefficientsa
Model Unstandardized Coef f icients Standardized
Coef f icients
t Sig.
B Std. Error Beta
1 (Constant) .001 .000 2.507 .013
Forest Area (percentage of land area) -1.644E-005 .000 -.052 -2.812 .006
Energy Use Per Capita 2.220E-006 .000 .827 27.210 .000
Energy Production Per Capita .103 .018 .171 5.676 .000

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GDP per Capita -3.046E-009 .000 -.007 -.400 .689
a. Dependent Variable: C02 Emissions per capita (kt)
My R squared is higher than it was before but GDP per capita still fails it t-test. It is also worth
noting that in these two regressions that I have multicollinearity for energy use and production. I
also noticed that the beta2hat for gdp per capita is negative which is opposite of what I was
expecting. This means that the less gdp per capita a nation has the more C02 emissions will be
produced by that nation.
I think I figured out that possibly my hypotheses was wrong not because the data doesn’t
confirm it but rather that the relationship my data is telling me is a far more compelling story. I
have noticed that after I solved for multicollinearity the t-stat on energy use and forest area
would both move positively the more I corrected for multicollinearity. Statistically this makes a
lot sense to correct for multicollinearity but it tells me something even deeper about the nature of
energy use and forest area. The t-stat was always being reported as less than it actually was
which was understating the effects of energy use and increasing the role forest area played into
C02 emissions. This essentially means that energy use tends to fluctuate with forest area but why
would that matter? This would matter because it is essentially suggesting that countries with
higher energy use tend to adopt policies that will decrease the area of forests. This inverse
relationship tells me that the smaller the forest area percentage is in a country the more energy
use. My initial hypothesis was wrong because forest area contributes to the rise of C02 emissions
through its relationship with energy use. Without the relationship with energy use, forest area is
not itself an indication of C02 emissions.
Another alternative to this is that the less forest area a nation has can also be an indicator
of the amount deforestation that occurs as well. For instance, forest area is negatively sloped
with C02 emissions which can suggest that the more a nation uses energy the more likely that

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nation is also taking a pro-deforestation stance since it requires the use of fossil burning fuels at
greater amounts to cut down forests that could contribute to higher C02 emissions.