Implications of Fitting a Regression and Pearson Correlation Models in the
Relationship Between Food Production, Production of Wood Products, CO2
Emissions and Climate: An Analysis of Time Series Data
Epule Terence Epule,
Balgah Sounders Nguh
This study investigates the most significant determinants of food production
in Canada from among the following variables: Production of wood products, CO2
emissions from agriculture and forestry, CO2 emissions from fossil
fuels, rainfall and temperature. It also verifies the relationship between food
production, production of wood products, CO2 emissions from agriculture
and forestry, CO2 emissions from fossil fuels, rainfall and temperature
in Canada. The data for the analysis was essentially time series data spanning
the period 1961-2010. The data on food production and production of wood products
was obtained from FAOSTAT. The data on CO2 emissions from agriculture
and forestry and fossil fuels was obtained from FAOSTAT and the US Department
of Energy. The data on rainfall and temperature was obtained from Environment
Canada, 2012. Data analysis was performed in the SPSS platform in which both
multiple linear regression and bivariate linear correlations were used to fit
the models. The results show that CO2 emissions generally increase
with food production. Food production and CO2 emissions from agriculture
and forestry have a correlation of about 0.87 while food production at the same
time has a correlation of 0.84 with CO2 emissions from fossil fuels.
Both CO2 emissions from agriculture and forestry and fossil fuels
have a correlation of 0.94 which shows that they reinforce each other. The most
significant variable that significantly correlates with food production is CO2
emissions from agriculture and forestry with a t-value of 2.63 and a p-value
to cite this article:
Epule Terence Epule, Changhui Peng, Laurent Lepage, Zhi Chen and Balgah Sounders Nguh, 2013. Implications of Fitting a Regression and Pearson Correlation Models in the
Relationship Between Food Production, Production of Wood Products, CO2
Emissions and Climate: An Analysis of Time Series Data. Research Journal of Environmental Sciences, 7: 1-14.
Received: January 21, 2013;
Accepted: March 12, 2013;
Published: May 24, 2013
With the global increase in human population and a parallel increase in standards
of living especially in the North, the need to produce more food remains urgent
(Kissinger, 2013; Chameides et
al., 1994). The results of this have been the development of agricultural
technologies or inputs that can result in high yields (Chameides
et al., 1994). For a long time, most advanced nations have laid emphasis
on fossil fuels to run the industrial systems that produce the expected farm
inputs as well as run farm machineries (Kissinger, 2013;
Chameides et al., 1994). Globally, the relationship
between food production, fossil fuel burning, cutting of forests to create farmlands
and their resultant CO2 emissions are more pronounced in North America,
Europe and parts of Asia (Chameides et al., 1994).
As such, CO2 emissions from food production are becoming central
in the entire food production debate (Kissinger, 2012).
Canada has for a long time been a net producer and exporter of a wide range
of food products such as legumes, cereals, oils, meat and fruits inter alia
(Kissinger, 2013; FAO, 2012).
In 2006, Canada produced over 75 million tons of agricultural and food commodities
out of which about 55% was exported (FAO, 2012). A look
at Canadas food consumption charts shows that most of Canadas staple
food comes from domestic sources; there is however a growing chunk of Canadas
food supply spread all over the world (Statistics Canada,
2008a; b). For example, about 15% of meat and 35%
of oils consumed in Canada are currently imported (FAO, 2012).
As a result, in recent literature, the concept of food miles has evolved. This
has to do with the distance a food commodity travels from the point of production
along the chain with related energy and CO2 emissions along the way
(Paxton, 1994; Kissinger, 2012).
Considering the fact that in 2006 55% of the 75 million tons of food produced
in Canada was exported, there is reason to verify the relationship between food
production and CO2 emissions from agriculture and forestry and from
Theoretically, this schematic representation is driven by the desire to increase
production either through farmland expansion or agricultural technologies. In
the farmland expansion scenario (Fig. 1) it is expected that
due to sufficient rainfall and adequate temperature, food production will be
high. However, the desire to cultivate more crops is often at the expense of
forests which equally leads to increase farmlands, increase yields in the short
run and increase atmospheric CO2. Also, reduced forests will mean
less rainfall in the long run and ultimately reduced food production (Epule
et al., 2011, 2012a). Increase atmospheric
CO2 will equally reduce production in the long run. Reduction in
forests will also directly increase atmospheric CO2 and will increase
temperatures. The second scenario is based on agricultural technology such as
mechanization and use of fertilizers inter alia (Fig. 1).
These intensive farming technologies are often run from fossils fuels. If this
obtains, then on the positive side there will be higher yields in the short
run but increase CO2 emissions which ultimately will increase temperatures.
|| Schematic causal loop representation of the key variables
It has been argued that the food supply/production landscape of Canada is shaped
by factors such as climate, wood production, CO2 emissions, soils,
slope, standards of living that are extremely high, commercial marketing and
ethnic diversity inter alia (Agriculture and Agri-Food Canada,
2009; Kissinger, 2012; Kissinger,
2013). However, this study is restricted to analyzing only the relationship
between food productions, production of wood products, CO2 emissions
from agriculture and forestry, CO2 emissions from fossil fuels, rainfall
and temperatures because these have not been verified. This is because all the
variables that affect food production cannot be brought into the equation at
the same time; however, those selected here are some of the very important ones
that are currently steering much of the debates on food production.
MATERIALS AND METHODS
Data Sources and properties: This study is a national scale study
that covers data for the whole of Canada. The two main objectives are to determine
from a number of pre-determined variables, the variable(s) that affects food
production most and the level of bivariate correlation between these variables.
The variables under consideration are subdivided as follows: food production
in tons (the dependent variable in objective one), production of wood products
in tons, CO2 from agriculture and forestry in million metric tons,
CO2 emissions from fossil fuels in thousand metric tons, average
annual rainfall in mm and average annual temperature in °C (independent
variables). Lobell and Field (2007) and Almaraz
et al. (2008) have also used similar techniques. All the data used
in this study was time series data covering the period 1961-2010. The data on
food production, production of wood products, CO2 emissions from
agriculture and forestry was obtained from the Food and Agricultural Organization
FAOSTAT data base (FAO, 2012). Data on CO2
emissions from fossil fuels was obtained from the U.S Department of Energy carbon
dioxide information analysis centre (Boden et al.,
2011). The data on average annual rainfall and temperature was culled from
Environment Canadas official climate data website (http://www.climate.weatheroffice.gc.ca/climateData/canada_e.html).
Statistical analysis and empirical model specification: The data was
analyzed using the Statistical Package for the Social Sciences (SPSS) version
19. In the case of objective one, the emphasis was to determine the variables
that affect food production in Canada. The multiple linear regression approach
was used to fit the model as specified by Motulsky (1999).
This method was used to verify which of the independent variable(s) (production
of wood products, CO2 emissions from agriculture and forestry, CO2
emissions from fossil fuels, rainfall and temperature) affects the dependent
variable (food production) more. The equation used to fit such a model is given
y = β0+ β1x1+ β2x2+
where, y is the dependent variable (food production), β0 is the intercept, β1+ β2+ β3+ β4 are the partial regression coefficients, x1+x2+x3+x4 are the independent variables, ε is the error term and t is time (i.e., year).
To achieve the second objective, the bivariate correlation between all the
variables (dependent and independent) was calculated using the Pearson correlation
statistical tool (Motulsky, 1999). The equation used
to run a Pearson correlation is given as follows:
where, r is the Pearson correlation coefficient, x is the independent variable, y is the dependent variable and μ is the mean of both variables. Both methods were selected because of their suitability in exploring the relationship between dependent and independent variables.
In addition, three period running averages were used to smooth out short-term
fluctuations in the time series data and highlight long term trends or to verify
the link between the actual trends in the data and the simulated.
RESULTS AND DISCUSSION
In Canada, it has been observed that between 1961 and 2010, the production of wood products exceeded food production. The actual and simulated 3 period running averages shows that food production is generally below 20 million tons while by 1969 the production of wood products exceeded 20 million tons and this situation has been the same all through (Fig. 2). This is a reflection of the possible long term effects of too much deforestation and food production.
Observations of the trends of actual and simulated CO2 emissions
from agriculture and forestry show that emissions from agriculture and forestry
are generally higher throughout the simulation and at the end in 2010 (>15
million metric tons) (Fig. 3a, b). Those
from fossil fuels are generally lower throughout the simulation (<160 thousand
tons) (Fig. 3a, b).
The trends for actual and simulated temperature show that generally average
annual temperatures are generally close to 0°C. Their range is about 2°C
(MAX-MIN= -4- - 6 = 2). Average annual rainfall is highly variable and has a
range of 250 mm (450- 200 = 250) between 1961 and 2010 (Fig. 4a,
After a multiple linear regression model was fitted to the time series data
to verify the most significant variables affecting food production, it was found
that CO2 emissions from agriculture and forestry had a t-value of
2.62 and a p-value of 0.12. The implication here is that this variable is more
closely related to food production than do the other variables. The p-value
of 0.12 denotes a 12% possibility of obtaining a difference as large as observed,
meaning this variable is fairly reliable (Table 1).
||Trends in food production and production of wood products
and their simulated 3 period running averages for Canada between 1961-2010
||Results of the multiple linear regressions showing the most
significant determinants of food production and their respective t and p-values
|Dependent variable: Food production in tons, Independent variables
are: Production of wood in tons (represents the extraction of trees to produce
various wood products), average annual rainfall in mm and average annual
temperature in °C, CO2 emissions from agriculture and forestry
in million metric tons, CO2 emissions from fossil fuels in thousand
metric tons, Average (Avg), The total No. of observations = 50, r = 0.88,
r2 = 0.77, adjusted r2 = 0.75, f = 28.68
||Trends in CO2 emissions from (a) Agriculture and
forestry and (b) Fossil fuels and their simulated 3 period running averages
for Canada between 1961-2010
The least significant variable here is temperature with a t-value of -0.06
and a p-value of 0.96 depicting a 96% possibility of obtaining a difference
as large as observed (Table 1). These results are consistent
with reports that CO2 emissions from agriculture and forestry are
more dominant than those for fossils fuels.
In terms of correlations, it is observed that the highest bivariate correlations
exist between CO2 emissions from agriculture and forestry on the
one hand and CO2 emissions from fossil fuels. These variables have
a Pearson correlation of 0.94 or 94% which denotes a perfect positive correlation.
The parallel coefficient of determination (r2) is 0.88 which depicts
that there is about 88% of reliability in the observed trend (Table
2, 3, Fig. 5a-e).
In terms of the second most significant bivariate correlations, it is observed
that the bivariate correlations between food production and CO2 emissions from agriculture and forestry are significant.
||Trends in (a) Average annual temperature and (b) Rainfall
and their respective simulated 3 period running averages for Canada between
|| Results of the bivariate-pearson correlation and coefficient
|Food production in tons, production of wood in tons (represents
the extraction of trees to produce various wood products), average annual
rainfall in mm and average annual temperature in °C, CO2
emissions from agriculture and forestry in million metric tons, CO2
emissions from fossil fuels in thousand metric tons, Average (Avg)
The actual bivariate correlation here is 0.87 or 87% while the coefficient
of determination (r2) is 0.76 or 76% (Table 2,
3, Fig. 5a-e). The implication
of this relationship is that there is a strong positive correlation between
food production and CO2 emissions from agriculture and forestry.
||Scatter plots of the correlation between (a) Food production
and production of wood products, (b) Food production and CO2
emissions from agriculture and forestry (c) CO2 emissions from
fossil fuels and CO2 emissions from agriculture and forestry,
(d) Food production and CO2 emissions from fossil fuels and (e)
Average annual rainfall and food production
With the r2 of about 76%, it can be said that this model has 76%
reliability in explaining the observed trends.
Generally, when it is said that there is a perfect positive correlation between
CO2 emissions from agriculture and forestry and CO2 emissions
from fossil fuels on the one hand and food production and CO2 emissions
from agriculture and forestry it means as one increases so does the other.
|| Correlation matrix of all the variables under study
|The correlation matrix is a summary table of all the bivariate-pearson
correlations between all the variables under study
Actually, based on the data, both sets of variables have been increasing towards
the same direction. This is because as food production increases, more forests
are cut and as such more CO2 from agriculture and forestry is emitted.
The even higher correlation between CO2 emissions from agriculture
and forestry and CO2 emissions from fossil fuels further shows that
agriculture and forestry are not the only CO2 emission source. Increase
use of fossil fuels to power machines in mechanized farms has also contributed
intensely to the emissions. However, some of these emissions may be from other
industrialization processes. Therefore, the more the use of fossil fuels, the
more emissions from agriculture and forestry.
The relationship between food production and CO2 emissions from
fossil fuel (Table 2, 3, Fig.
5a-e) can be explained by the fact that the desire to
increase production through agricultural technologies leads to the exploitation
of fossil fuels which also has a daunting effect on global emissions. The rest
of the correlations are generally weak positive correlations, the reason why
the focus has been on the relationship between food production and CO2
emissions (Fig. 6a-e). As seen on
Fig. 7a and Table 4, average annual rainfall
is around 300 mm while the rainfall for the other seasons of the year is generally
below 300 mm. In the case of temperatures, it is observed that the average summer
temperatures are above 10°C while those for the other seasons are below
this threshold (Fig. 7b, Table 4). For a
complete picture of the trends in annual rainfall and temperature as well as
the raw data used in this study (Fig. 7a, b
and Table 4).
The results presented in this study are consistent with those of other studies
(Cumming et al., 2001; Hobson
et al., 2002; Van der Werf et al., 2009;
FAO, 2012; Kissinger, 2013).
Firstly, there is a lot of evidence to show that food production in Canada is
rising but this might not be forever. In 2006, about 75 million tons of agricultural
commodities were produced in Canada and consumed locally as well as exported
(FAO, 2012; Kissinger, 2013).
It is however argued that much of this increase in food production has been
due to two reasons. These are increase forest loss and agricultural expansion
to create more cropland or pasture (Van der Werf et
al., 2009). For example, the agricultural sector in Western Canada in
general and around the Saskatchewan-Manitoba border is heavily unregulated.
As a result of this, a lot of forests in these areas have been transformed into
farmland for the production of cereal, oilseeds and cattle (Hobson
et al., 2002). Between 1966 and 1996, the area referred to above
experienced a total of 4368 km2 of forest loss; this is equivalent
to -0.8% in terms of annual rate of forest cover change (Hobson
et al., 2002). Again, between 1966 and 1996, the amount of land not
used for agriculture in 39 municipalities of the same area above decreased from
about 44219 to 17646 km2 (Hobson et al.,
2002). According to the FAO (1999), although much
of the deforestation in the region occurred around the era of the Second World
War, the rate quantified for the period between 1966-1996 was higher than the
global average of 0.3% per year.
|| Raw data of the various variables used in running the models
||Scatter plots of the correlation between (a) Production of
wood products and CO2 emissions from agriculture and forestry,
(b) Production of wood products and CO2 emissions from fossil
fuel, (c) Production of wood products and average annual rainfall, (d) CO2
emissions from agriculture and forestry and average annual rainfall and
(e) CO2 emissions from fossil fuel and average annual rainfall
||Average annual, winter, spring, summer and autumn (a) Rainfall
and (b) Temperature for Canada between 1961-2010
In the south of the Saskatchewan-Manitoba border, very little forest is left
with most of the land converted to cereal and cattle production. In other parts
of Canadas boreal and the global temperate forests, similar findings have
been obtained showing rates of deforestation of about 0.8-1.7% per year (Cumming
et al., 2001).
However, it is necessary to state that, not all forest lost in the boreal of
Canada is as a result of agricultural expansion. Lightening, droughts and insects
have also been reported responsible for huge forest loss in the boreal forest
(Weber and Stocks, 1998; Peng
et al., 2011; McCullough et al., 1998).
A key repercussion of the increase clearance of forests in favor of farmland
is CO2 accumulation in the atmosphere (Adams
and Piovesan, 2002; Fang et al., 2001).
In fact, it has been argued that deforestation is the second largest anthropogenic
source of carbon dioxide to the atmosphere because carbon emissions from deforestation
account for about 20% of the global anthropogenic CO2 emissions (Van
der Werf et al., 2009). It is now reported that the amount of CO2
in the atmosphere is currently increasing at a rate of 0.5-3 parts per million
(ppm) per year (Keeling and Whorf, 2001; Adams
and Piovesan, 2002). Whatever the case, it is pertinent to argue that a
good fraction of this annual CO2 input into the atmosphere is linked
to the burning of fossil fuels (Falkowski et al.,
2000; Van der Werf et al., 2009). Today,
food production systems all over the world depend a lot on fossil fuels. As
a result of this, machines and various agricultural inputs such as fertilizers
have been produced to enhance food production (Epule et
al., 2012b; Tomczak, 2005). While the objective
of increasing food production has been attained from the use of fossil fuels
and increase deforestation, there has been a parallel increase in CO2
emissions which heralds long run food declines (Timmer,
1975). In addition to the emissions of CO2, the production of
fertilizers to enhance food production has been responsible for increase use
of fossil fuels and the seepage of pollutants into rivers as well as general
flora and fauna degradation (Epule et al., 2012b;
Maeda et al., 2003).
This study has shown that, among the set of factors under consideration, CO2 emissions from agriculture and forestry and fossil fuels have the strongest correlations with food production. This is obvious because when forests are cut in favor of farmlands and fossil fuels are burnt to produce agricultural inputs as well as run intensive farming systems, a myriad of CO2 emissions are spurred into the atmosphere. As seen in the discussion, these findings are consistent with other studies that have studied the relationship between food production and CO2 emissions.
A major question now is, will food production keep rising with rising CO2
emissions from these sources? Obviously, with rising CO2 emissions
and the resultant negative feedbacks that this will have on long run food production,
much has to be done. The long run effects of deforestation on the other hand
are food and water scarcity (Epule et al., 2012c).
This study is therefore proposing that more investments be made in the area
of renewable energy sources such as bio-fuels, wind to name but these. Deforestation
in favor of farmlands could be adverted through the enactment of policies that
encourage farmers to farm intensively against the backdrop of renewable energies
and organic fertilizers.
It would however be necessary to carry out further research by bringing in several other variables not used here into the regression function. Again, regional scale studies over different parts of Canada could be carried out to test for regional disparities.
We are thankful to the NSERC Canada Discovery grant and the FARE merit based scholarship board of the University of Quebec for funding this study.
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