RPubs link information

• Rpubs link comes here: http://rpubs.com/juliaHuynh/assignment4

Introduction

• In this presentation, we will analyze one of critical issues caused Climate Change or Global Warming in recent years. It is about whether the release of CO2 from industry impacts on the increase of temperature changes in global surface.
• In addition, we can see the upward trend of global temperature changes as well as the CO2 mole fraction in the air from 1958 to 2016.
• We will use Linear Regression Analysis in order to discover the correlation between CO2 and Global temperature.

Problem Statement

• There are some insights which can be discovered in this presentation:
  –The trend of CO2 and Global Temperature in recent years.
  – Can the CO2 mole fraction be used to predict the average change of Global Temperature anually ?
  
• In order to answer this question, Linear Regression is used to analyze the relationship between the annual mean of CO2 mole fraction and annual average change of global temperature.

Data

• Data is collected from website https://climate.nasa.gov/vital-signs/global-temperature/ and https://climate.nasa.gov/vital-signs/carbon-dioxide/
• There are three variables in sample data:
  – Year : Year
  – Global_Temperature_avg (Census degree) : the average change of global surface temperature anually
  – CarbonDioxide_avg (micromol/mol as ppm): the mean CO2 mole fraction in the air anually which are transformed by the author in website (ftp://aftp.cmdl.noaa.gov/products/trends/co2/co2_mm_mlo.txt). In the dataset, CO2 is collected monthly. However, in this report, we calculate the average of CO2 amongs months in a year.
  

climate_change <- read.csv(file = "climateChange_sample.csv")
climate_change

Descriptive Statistics and Visualisation

• Variables Summary

summaryTable <- climate_change %>%  summarise(variable = "Global Temperature",
                              Mean = mean(Global_Temperature_avg, na.rm = TRUE),
                              Min = min(Global_Temperature_avg, na.rm = TRUE),
                              Max = max(Global_Temperature_avg, na.rm = TRUE),
                              Median = median(Global_Temperature_avg, na.rm = TRUE),
                              Q1 = quantile(Global_Temperature_avg, probs = .25, na.rm = TRUE),
                              Q3 = quantile(Global_Temperature_avg, probs = .75, na.rm = TRUE),
                              SD = sd(Global_Temperature_avg, na.rm = TRUE),
                              n = n(),
                              Missing = sum (is.na(Global_Temperature_avg)))
summaryTable <- rbind(summaryTable, climate_change %>%  summarise(variable = "CO2",
                              Mean = mean(CarbonDioxide_avg, na.rm = TRUE),
                              Min= min(CarbonDioxide_avg, na.rm = TRUE),
                              Max= max(CarbonDioxide_avg, na.rm = TRUE),
                              Median= median(CarbonDioxide_avg, na.rm = TRUE),
                              Q1 = quantile(CarbonDioxide_avg, probs = .25, na.rm = TRUE),
                              Q3 = quantile(CarbonDioxide_avg, probs = .75, na.rm = TRUE),
                              SD = sd(CarbonDioxide_avg, na.rm = TRUE),
                              n = n(),
                              Missing = sum(is.na(CarbonDioxide_avg))))
knitr::kable(summaryTable)

• Boxplot Charts:

boxplot(x = climate_change$Global_Temperature_avg, main = "The change in global surface temperature",
        ylab = "Temperature Change (Census degree)")

boxplot(x = climate_change$CarbonDioxide_avg, main = "Carbon Dioxide",
        ylab = "CO2 (parts per million)")

Decsriptive Statistics Cont.

library(plotly)
temp <- climate_change %>% select("Year", "Global_Temperature_avg")
plot_ly(temp, x = ~Year, y = ~Global_Temperature_avg, x.format= "%Y")  %>%  add_lines(y = ~Global_Temperature_avg) %>% 
  layout(xaxis = list(title = "Year"),
         yaxis = list(title = "Temperature Anomaly (C)"),
         title = "Fig1: The change in global surface temperature between 1958-2016 ")

carb <- climate_change %>% select("Year", "CarbonDioxide_avg")
plot_ly(carb, x = ~Year, y = ~CarbonDioxide_avg, x.format= "%Y")  %>%  add_lines(y = ~CarbonDioxide_avg) %>% 
  layout(xaxis = list(title = "Year"),
         yaxis = list(title = "CO2 (parts per million)"),
         title = "Fig2 : The anual average of CO2 mole fraction between 1958-2016")

plot_ly(climate_change, x = ~CarbonDioxide_avg, y = ~Global_Temperature_avg, type = 'scatter') %>% 
  layout(xaxis = list(title= "CO2 (parts per million)"),
         yaxis = list(title = "The change of global surface temperature (C)"),
         title = "Fig 3: The relationship between Global Temperature and CO2")

Hypothesis Testing

• Applying F-test to test the overal linear regression model for this question.
• In this case, the response variable y is Global_Temperature_avg. The predictor variable x is CarbonDioxide_avg

model <- lm(Global_Temperature_avg ~ CarbonDioxide_avg, data = climate_change)
model %>% summary()

## 
## Call:
## lm(formula = Global_Temperature_avg ~ CarbonDioxide_avg, data = climate_change)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.20603 -0.06850 -0.01029  0.07641  0.18567 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       -3.3364046  0.1659795  -20.10   <2e-16 ***
## CarbonDioxide_avg  0.0103374  0.0004703   21.98   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09447 on 57 degrees of freedom
## Multiple R-squared:  0.8945, Adjusted R-squared:  0.8926 
## F-statistic: 483.1 on 1 and 57 DF,  p-value: < 2.2e-16

• The p-value for F-test is very small, F(1,57) = 483.1, p <0.001.
• It implies that the model is statistically significant

Hypthesis Testing Cont .

plot(model)

- Residual vs Fitted : The trend line seems to flat
- Normal Q-Q plot : the model seems to follow a normal distribution, except in the extreme tails

Intepreting

model %>% summary()

## 
## Call:
## lm(formula = Global_Temperature_avg ~ CarbonDioxide_avg, data = climate_change)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.20603 -0.06850 -0.01029  0.07641  0.18567 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       -3.3364046  0.1659795  -20.10   <2e-16 ***
## CarbonDioxide_avg  0.0103374  0.0004703   21.98   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09447 on 57 degrees of freedom
## Multiple R-squared:  0.8945, Adjusted R-squared:  0.8926 
## F-statistic: 483.1 on 1 and 57 DF,  p-value: < 2.2e-16

model %>% confint()

##                          2.5 %      97.5 %
## (Intercept)       -3.668772837 -3.00403629
## CarbonDioxide_avg  0.009395619  0.01127923

• The Intercept of the regression was statistically significant, a= -3.34, p-value <0.0001, 95% CI (-3.67, -3.004)
• The slope of the regrestion for Carbon Dioxide was statistically significant in which a = 0.01, p-value < 0.0001, 95% CI (0.009, 0.011)

cor(climate_change$Global_Temperature_avg, climate_change$CarbonDioxide_avg, use="complete.obs")

## [1] 0.9457604

• The correlation coefficient between CarbonDioxide_avg and Global_Temperature_avg is 0.946. It means that this is a strong correlation between two these variable

Discussion

• To sum up, there was a statistically significant positive linear relationship between CarbonDioxide_avg and Global_Temperature_avg.
  
• It implies that CO2 release impacts significantly on the change of global surface temperature on the earth. It also helps to answer why the Earth become hotter in recent years due to the release of CO2 into the air by manufactures.
• In the future, we can use other factors such as sea level, arctic sea ice minimum or land ice to evaluate their changes caused by the relase of CO2 or the increase of Global Temperature.

References

• https://climate.nasa.gov
• ftp://aftp.cmdl.noaa.gov/products/trends/co2/co2_mm_mlo.txt