FINALEXAM_Brandon_Gravett
Brandon Gravett
12/9/2019
Global CO[2] Emissions
GHGs include water vapor, Carbon dioxide, methane, Nitrous oxide, Ozone, Chlorofluorocarbons and Hydrofluorocarbons. These gases in the atmosphere help Earth hold on to some of the energy it receives from the Sun. So is carbon in the air a good thing? And why are we interested? CO[2] and other greenhouse gases are good but up to a point. CO[2] emissions are especially good at holding in heat from the Sun, that even a small increase in CO[2] in the atmosphere can cause Earth to get even warmer. Throughout history, whenever the amount of CO[2] in the atmosphere has gone up, the temperature of Earth has also gone up. At present, these gases are now out of balance and threaten to change drastically which living things can survice on this planet-and where.
## -- Attaching packages ------------------------ tidyverse 1.2.1 --## v ggplot2 3.2.1 v purrr 0.3.2
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## v readr 1.3.1 v forcats 0.4.0## -- Conflicts --------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()The Data
The Carbon Dioxide Information Analysis Center (CDIAC) has published a dataset containing ‘Per Country CO[2] Emissions from fossil-fuels annually since 1751 till 2014’. The total carbon emissions are broken down further into emissions from solid fuel consumption, liquid fuel consumption, gas fuel consumption, cement production, gas flaring, per capita carbon emissions, and bunker fuels (not included in total). The values for total carbon emissions are measured in million metric tons of Carbon.
Boden et al. (2013) estimated fossil fuel CO[2] emissions back to 1751 using publications that contained historical energy statistis. Furthermore, the 1950 to present CO[2] emission estimates were derived primarily from energy statistics published by the United Nations (2017) and using methods of Marland and Rotty (1984). Boden et al. established a list of the top 20 countries that emit CO[2], expressed in thousand metric tons of carbon, which identified China (Mainland), the United States of America, and India as the top three contributors of CO[2] into the atmosphere.
Notable figures from the data include the estimate for global fossil-fuel carbon emissions in 2014, 1823 million metric tons of carbon. This estimate is an all-time high and a 0.8% increase over 2013 emissions. Globally, liquid and solid fuels accounted for 75.1% of the emissions from the total emissions from fossil-fuel burning and cement production in 2014 (Boden et al. 2013).
Components of Emissions
## Standard deviations (1, .., p=6):
## [1] 134492.9766 43529.8143 11610.9494 3344.1490 2689.7340 924.8839
##
## Rotation (n x k) = (6 x 6):
## PC1 PC2 PC3
## Liquid.Fuel 0.2583734925 -0.754383701 -0.59317373
## Solid.Fuel 0.9535587404 0.251958356 0.07161969
## Gas.Fuel 0.0984004360 -0.592147104 0.79871398
## Cement 0.1187911493 0.115317485 0.05599797
## Gas.Flaring 0.0006388357 -0.009681343 0.03754106
## Bunker.fuels..Not.in.Total. 0.0132089369 -0.058242389 -0.02294382
## PC4 PC5 PC6
## Liquid.Fuel -0.06742171 -0.087985202 -0.002493142
## Solid.Fuel 0.01323180 0.146246319 0.023457813
## Gas.Fuel -0.01649681 -0.004991469 -0.037921986
## Cement -0.05626197 -0.969745980 -0.160879128
## Gas.Flaring -0.04767639 -0.159593381 0.985268210
## Bunker.fuels..Not.in.Total. 0.99477065 -0.070486812 0.037012135## [1] "0.6841" "0.2214" "0.0591" "0.0170" "0.0137" "0.0047"A multivariate analysis was performed in order to understand the variability among the samples. The total variability will be always 100% and all the PCs (PC1 + PC2 + PC3 + …. + PCn-1; where “n” is the number of continuous variables or samples (whichever is smaller) you have) will always sum 100%.
So, the first axis describes 68% of the variation and the second describes 22%. The two fuel types that are most heavily loading are Solid Fuel (PC1) and Liquid Fuel (PC2). This is verified due to the fact they accounted for 75.1% of the total emissions.
However, you cannot represent in 2 dimensions more than 4 axes (PC1, PC2, PC3 and PC4), for this reason you typically represent only the PC1 and PC2 (and sometimes with PC3 in a 3D graph). And why? Why typically PC1 vs. PC2. Simply because those axes (Principal Components) are ordered by the % of variability they explain, being PC1 always the axis that explain more variability among the samples included in the test. PC2 is the second axes explaining more variability, and so on. So, typically PC1 and PC2 will represent a “large” % of variability but never 100%.
Temporal Trends
## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2##
## Attaching package: 'GGally'## The following object is masked from 'package:dplyr':
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## nasa## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
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## Pearson's product-moment correlation
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## data: datacor5$Total and datacor5$Per.Capita
## t = 13.37, df = 218, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.5914538 0.7379673
## sample estimates:
## cor
## 0.6712145The data shows there is a very weak correlation between countries and total emissions from 1960 to 2010. The two countries that have the lowest correlation is the United States of America and Canada. The two countries that have the highest correlation is Germany and Japan.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
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## Call:
## lm(formula = Total ~ Year, data = datacor4)
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## Coefficients:
## (Intercept) Year
## -25005773 13243## [1] "coefficients" "residuals" "effects" "rank"
## [5] "fitted.values" "assign" "qr" "df.residual"
## [9] "xlevels" "call" "terms" "model"
This is not a good model and the residuals are not properly behaved.