(TIỂU LUẬN) the dependent variable (DV) CO2 emissions (metric tons per capita) y

********** BUSINESS STATISTICS - ECON1193 ********** Group Team - Assignment 3A - CO2 Teacher - Sung Yong Park Class - 11:30 am on Tuesday Group Members: First name Student ID Truong Quynh Tam Nguyen Thi Hong An Do Ngoc Thien Thanh Le Khiet Nhi S3804730 S3803533 S3797589 S3803532 Parts contributed Contribution % Signature Part 1+2 Part 3+4 Part 3+4 Part 1+2 25% 25% 25% 25% Tam An Thanh Nhi Part 1: Multiple Regression The dependent variable (DV): CO2 emissions (metric tons per capita) - Y The independent variable (IV): ● GNI per capita, Atlas method (current US$) - X1 ● Renewable electricity output (% of total electricity output) - X2 ● Air transport, freight (million ton-km) - X3 ● Air transport, passengers carried - X4 Part 1.5: The final regression model: ★ The final regression model of data set I - All countries: a The final regression output: Figure 1: Regression output of all countries b The regression equation: ŷ = 3.746 + 0.00017*X1 - 0.045*X2+ 0.00063*X3 - 2.57E-08*X4 ŷ: CO2 emissions (metric tons per capita) X1: GNI (current US$) X2: Renewable electricity output (% of total electricity output) X3: Air transport, freight (million ton-km) X4: Air transport, passengers carried c Interpret the regression coefficient of the significant independent variables: - b1 = 0.00017 indicates that CO2 emissions will increase by 0.00017 metric tons per capita for every U.S dollar increases in the GNI per capita, considering renewable electricity output, air transport, freight and air transport, passenger carried as constant - b2 = - 0.045 means that CO2 emissions will decrease by 0.045 metric tons per capita for every percentage increases in renewable electricity output, considering GNI, air transport, freight and air transport, passenger carried as constant - b3 = 0.00063 shows that CO2 emissions will increase by 0.00063 metric tons per capita for every million ton-km increases in the air transport, freight, considering GNI, renewable electricity output and air transport, passenger carried as constant - b4 = - 2.57E-08 means that CO2 emissions will decrease by 2.57E-08 metric tons per capita for million ton-km increases in air transport, passengers carried, considering GNI, renewable electricity output and air transport, freight as constant d Interpret the coefficient of determination: R-squared = 0.521, meaning that 52.1% of variation in CO2 emission can be explained by variations in renewable electricity output and GNI per capita, and the remaining 47.9% may be caused by other factors ★ The final regression model of data set II - Low income countries: a The regression output: Figure 2: Regression output of low-income countries For LI group countries, we cannot find its linear model because all P-values are greater than 0.05 CO2 emissions of low-income countries may be caused by the other variables which we have to research more to find out ★ The final regression model of data set III - Middle income countries: a The final regression output: Figure 3: Regression output of middle-income countries b The regression equation: ŷ = 1.705 + 0.00049*X1 - 0.035*X2 ŷ: CO2 emissions (metric tons per capita) X1: GNI (current US$) X2: Renewable electricity output (% of total electricity output) c Interpret the regression coefficient of the significant independent variables: - b1 = 0.00049 illustrates that CO2 emissions will increase by 0.00049 metric tons per capita for every U.S dollar increases in the GNI per capita, considering renewable electricity output as constant - b2 = - 0.035 means that CO2 emissions will decrease by 0.035 metric tons per capita for every percentage increases in renewable electricity output, considering GNI as constant d Interpret the coefficient of determination: R-squared = 0.506, meaning that 50.6% of variation in CO2 emission can be explained by variations in renewable electricity output and GNI per capita, and the remaining 49.4% is due to other reasons ★ The final regression model of data set IV - High income countries: a The final regression output: Figure 4: Regression output of high-income countries b The regression equation: ŷ = 7.146 + 0.00015*X1 - 0.096*X2 ŷ: CO2 emissions (metric tons per capita) X1: GNI (current US$) X2: Renewable electricity output (% of total electricity output) c Interpret the regression coefficient of the significant independent variables: - b1 = 0.00015 indicates that CO2 emissions will increase by 0.00015 metric tons per capita for every U.S dollar increases in the GNI per capita, considering renewable electricity output as constant - b2 = - 0.096 means that CO2 emissions will decrease by 0.096 metric tons per capita for every percentage increases in renewable electricity output, considering GNI as constant d Interpret the coefficient of determination: R-squared = 0.257, meaning that 25.7% of variation in CO2 emission can be explained by variations in renewable electricity output and GNI per capita, and the remaining 74.3% may be caused by other factors Part 2: Team Regression Conclusion: Data sets Significant independent variables R-square 0.521 All GNI Renewable electricity output Air transport, freight Air transport, passengers carried LI Not available MI GNI Renewable electricity output 0.506 HI GNI Renewable electricity output 0.257 Not available To sum up, all models have different significant variables that affect CO2 emissions In all data sets, there are two independent variables that have a significant relationship with CO2 emissions, including GNI per capita and renewable electricity output High-income countries (HI) appear two significant variables which are GNI per capita and renewable electricity output Similarly, the middle-income countries (MI) have two significant variables, including GNI per capita and renewable electricity output In contrast, low-income countries (LI) have no significant variable GNI per capita appears in three categories of countries as the significant variable, which are all countries, middle-income countries and high-income countries Likewise, renewable electricity output also is known as the significant independent variables that also has an impact on CO2 emissions of all countries, middle-income countries and high-income countries categories The regression model of middle-income countries will provide the most accurate assessment of the level of CO2 emissions This is due to its R-squared value has the largest number (0.506) out of other countries, which means 50.6% (more than half of the sample size) of CO2 emissions depends on two variables - GNI per capita and renewable electricity output In addition, the variation in CO2 emission can be described in the regression models by the increase in the quality of significant independent variables According to Bilan et al, they found that LI and MI want to join the EU tend to have a higher rate of economic growth without the ability to develop renewable energy technologies, hence, the amount of CO2 emissions depends more on GNI per capita (MPDI, 2019) Part 3: Time Series: Noted: - (LI) Low Income - (MI) Medium Income - (HI) - High Income - LIN : Linear Model - QUA : Quadratic Model - EXP: Exponential Model - X : GNI per capita, Atlas method (current US$) Country Trend Model Chad (LI) LIN Analyses Description Regression output Figure 5: Regression output for Chad’s CO2 emissions of Linear Model Trend model formula ŷ= b0 + b1*T Hypothesis testing: - Using α = 0.05 -Null hypothesis (H0): β1 = (There is no trend model) - Alternative hypothesis (H1): β1 ≠ (There is a trend model) -According to output summary, p-value = 0.000 < α (0.05) -> we reject H0 -As H0 is rejected so we are 95% confidence that there is linear trend model Trend model equation ŷ= 0.013 + 0.001*T ŷ: CO2 emissions (metric tons per capita) T: trend QUA Regression output Figure 6: Regression output for Chad’s CO2 emissions of Quadratic Model Trend model formula ŷ= b0 + b1*T + b2*T^2 Hypothesis testing: - Using α = 0.05 - Null hypothesis (H0): β2 = (There is no trend model) - Alternative hypothesis (H1): β2 ≠ (There is a trend model) - According to output summary, p-value of Time period square= 0.000 < α (0.05) -> we reject H0 - As H0 is rejected, thus we are 95% confidence that there is quadratic trend model Trend model equation ŷ= 0.031 - 0.002*T+0.0001*T^2 ŷ: CO2 emissions (metric tons per capita) T: trend EXP Regression output Figure 7: Regression output for Chad’s CO2 emissions of Exponential Model Trend model formula ŷ= (b0) (b1^T) (Linear form) Or log (Y)= log(b0)+ log(b1 )*T (Non-linear form) Using α =0.05 Null hypothesis (H0): β1 = Alternative hypothesis (H1): β1 ≠ According to output summary, p-value of T = 0.000 < α (0.05) => we reject H0 As H0 is rejected, thus we are 95% confidence that there is an exponential trend model Trend model equation: log (Y) = -1.827 + 0.016 * X ŷ= 10 ^-1.827 + 10 ^ 0.016X ŷ: CO2 emissions (metric tons per capita) T: trend Prediction of CO2 emissions: Model LIN QUA EXP 0.043 0.052 0.254 0.044 0.056 0.258 ŷ2013 ŷ2014 0.046 0.06 0.262 ŷ2015 Bolivia (MI) LIN Regression output Figure 8: Regression output for Bolivia’s CO2 emissions of Linear Model Trend model formula ŷ= b0 + b1*T Hypothesis testing: - Using α = 0.05 - Null hypothesis (H0): β1 = (There is no trend model) - Alternative hypothesis (H1): β1 ≠ (There is a trend model) - According to output summary, p-value = 0.000 < α (0.05) -> we reject H0 - As H0 is rejected so we are 95% confidence that there is a linear trend model Trend model equation ŷ= 0.63 + 0.037*T ŷ: CO2 emissions (metric tons per capita) T: trend QUA Regression output Figure 9: Regression output for Bolivia’s CO2 emissions of Quadratic Model Trend model formula ŷ= b0 + b1*T + b2*T^2 Hypothesis testing: - Using α = 0.05 - Null hypothesis (H0): β2 = (There is no trend model) - Alternative hypothesis (H1): β2 ≠ (There is a trend model) - According to output summary, p-value of time period square = 0.000 < α (0.005) => we reject H0 - As H0 is rejected, thus we are 95% confidence that there is quadratic trend model Trend model equation ŷ= 0.579 + 0.047*T - 0.0003*T^2 ŷ: CO2 emissions (metric tons per capita) T: trend EXP Regression output Figure 10: Regression output for Bolivia’s CO2 emissions of Exponential Model Trend model formula ŷ= (b0 ) (b1^T) (Linear form) Or log (Y)= log(b0 )+ log(b1 )*T (Non-linear form) Using α = 0.05 Null hypothesis (H0): β1 = Alternative hypothesis (H1): β1 ≠ According to output summary, p-value of T = 0.000 < α (0.005) => we reject H0 As H0 is rejected, thus we are 95% confidence that there is an exponential trend model Trend model equation log (Y) = -0.165 + 0.015 * X ŷ= 10 ^ -0.165 + 10 ^ 0.015*X ŷ: CO2 emissions (metric tons per capita) T: trend Prediction of CO2 emissions: Model LIN QUA EXP 1.674 1.649 1.276 1.711 1.678 1.295 1.748 1.707 1.314 ŷ2013 ŷ2014 ŷ2015 Equatorial Guinea (HI) LIN Regression output Figure 11: Regression output for Equatorial Guinea’s CO2 emissions of Linear Model 10 Trend model formula ŷ= b0 + b1*T Hypothesis testing: - Using α = 0.05 - Null hypothesis (H0): β1= (There is no trend model) - Alternative hypothesis (H1): β1 ≠ (There is a trend model) - According to output summary, p-value = 0.000 < α ( 0.005) -> we reject H0 - As H0 is rejected so we are 95% confidence that there is linear trend model Trend model equation ŷ= -1.145 + 0.263*T ŷ: CO2 emissions (metric tons per capita) T: trend QUA Regression output Figure 12: Regression output for Equatorial Guinea’s CO2 emissions of Quadratic Model Trend model formula ŷ= b0 + b1*T + b2*T^2 Hypothesis testing: - Using α = 0.05 - Null hypothesis (H0): β2 = (There is no trend model) - Alternative hypothesis (H1): β2 ≠ (There is a trend model) - According to output summary, p-value of time period square = 0.602 > α (0.05) => we not reject H0 - Therefore, there is no quadratic trend 11 EXP Regression output Figure 13: Regression output for Equatorial Guinea’s CO2 emissions of Exponential Model Trend model formula ŷ= (b0 ) (b1^T) (Linear form) Or log (Y)= log(b0 )+ log(b1 )*T (Non-linear form) Hypothesis testing: - Using α = 0.05 - Null hypothesis (H0): β1 = Alternative hypothesis (H1): β1 ≠ According to output summary, p-value of T = 0.000 < α (0.05) => we reject H0 As H0 is rejected, thus we are 95% confidence that there is an exponential trend model Trend model equation log (Y) = -0.984 + 0.068*X ŷ = 10 ^ -0.984 + 10 ^ 0.068*X ŷ: CO2 emissions (metric tons per capita) T: trend Prediction of CO2 emissions: Model LIN QUA EXP 6.223 6.002 2.482 6.486 6.195 2.655 ŷ2013 ŷ2014 12 6.75 6.382 2.841 ŷ2015 Countries Trend model Errors of the year (e) 2013 CHAD BOLIVIA EQUATORIAL GUINEA 2014 MAD SSE 2015 LIN 0.005 0.009 0.008 0.007 0.000154 QUA -0.004 -0.003 -0.205 0.005 0.00007 EXP -0.206 -0.205 -0.209 0.207 0.128 LIN 0.137 0.084 0.158 0.126 0.051 QUA 0.162 0.117 0.200 0.160 0.080 EXP 0.535 0.500 0.593 0.543 0.888 LIN -1.263 -1.690 -1.986 1.646 8.392 _ QUA _ _ _ _ EXP 2.479 2.141 1.923 2.181 14.430 Recommendation: ● For Chad, it is recommended to use Quadratic trend model to predict the CO2 emissions This is because it has the smallest values of MAD (0.005) and SSE (0.00007) compared to other trends As a result, it will provide a more accurate prediction for CO2 emissions ● For Bolivia and Equatorial Guinea, Linear trend model is suggested to predict the CO2 emissions The reason is that they have the smallest MAD (Bolivia=0.126 and Equatorial Guinea=1.646) and SSE (Bolivia=0.051 and Equatorial Guinea=8.392) Part 4: Time Series Conclusion: a The line chart of CO2 emissions over time from 1985 - 2015, including all three countries (Chad, Bolivia and Equatorial Guinea) 13 Figure 14: Line chart of CO2 emissions over time from 1986 - 2015 of countries b Comment: This chart shows the CO2 emissions over time from 1986 to 2015 of countries: Chad, Bolivia BOL and Equatorial Guinea GNQ As for LI and MI country like Chad and Bolivia BOL did not have much of fluctuation It means that every year, between 0.05 and metric tons per capita CO2 emissions in these countries were released steadily In other words, LI and MI countries will lead to less factories and transportation activities that can generate CO2 emissions compared to HI country (Tucker, 2016) After 29 years, Equatorial Guinea’s CO2 emissions have doubled since 1986, rising from 0.03 to nearly metric tons/capita Equatorial Guinea country had the highest rate of CO2 discharge (approximately metric tons/capita) Based on the chart, for the beginning, it is at a moderate level (from 1986 to 2000): however, it increased dramatically between 2001 to 2015 Overall, all countries have upward trends in CO2 emissions c ● Both Bolivia and Equatorial Guinea countries are following the linear trend model ● As calculated above, the results of Chad’s Quadratic trend model has the smallest MAD (0.005) and SSE (0.00007), which indicates the trend model has the least error compared to other countries Therefore, it can be considered as the best CO2 trend predictor Part 5: Overall Team Conclusion: CO2 emission and country income are proved to be related to each other by all country regression model above Being specific, due to the positive coefficient of GNI per capita in almost all types of countries, it shows that there is a correlation between the amount of CO2 emissions emitted and GNI In terms of other categories, GNI per capita has become the significant independent variable of three out of four regression model Since the R-squared of the models differ from each other, thus the degree of GNI impact is different 14 GNI per capita and renewable electricity output are two main factors that will determine the CO2 emissions In part 1, we have indicated that they are significant independent variables of majority of types countries, including: all countries, middle-income countries and high-income countries In particular, the coefficient of determination (Rsquared) of the middle-income level model can be considered as the most reliable model because more than half of the variation in CO2 emissions can be caused by variations in GNI per capita and renewable electricity output And this finding has indicated the much greater effect of these two independent variables - GNI and renewable electricity output compared to other factors - air transport, freight and air transport, passengers carried On the contrary, the amount of CO2 emissions of every country is not always affected by GNI and renewable electricity output because in lowincome level group, these variables are insignificant After being compared, Chad, the country has the smallest MAD and SSE, is chosen to be the model country: - Chad’s Quadratic trend model equation: ŷ= 0.031 - 0.002*T+0.0001*T^2 - Predicted Value of CO2 emissions in 2020: ŷ= 0.031 - 0.002*35+0.0001*35^2= 0.0835 → As Chad’s Quadratic model is identified as the best predictor, it can be used to predict the trend of CO2 emissions in 2020 which is 0.0835 It means after years, the CO2 emissions will increase 0,03 metrics tons per capita from 2015 (0.05 metrics tons per capita) And based on the line chart above, there is an upward trend in CO2 emissions, hence the CO2 emissions may go up United Nations seems not to achieve its goal of reducing the CO2 emissions by 2030 Based on the upward linear trend chart, it is likely to continuously increase in the future REFERENCES: MDPI 2019, Linking between Renewable Energy, CO2 Emissions, and Economic Growth: Challenges for Candidates and Potential Candidates for the EU Membership, MDPI, Switzerland, viewed January 2020, 15 Davey, T (2016), Developing Countries Can’t Afford Climate Change - Future of Life Institute, Future of Life Institute, viewed January, 2020, APPENDICES: 16 17 18 ... Regression The dependent variable (DV): CO2 emissions (metric tons per capita) - Y The independent variable (IV): ● GNI per capita, Atlas method (current US$) - X1 ● Renewable electricity output... tons per capita) And based on the line chart above, there is an upward trend in CO2 emissions, hence the CO2 emissions may go up United Nations seems not to achieve its goal of reducing the CO2. .. carried On the contrary, the amount of CO2 emissions of every country is not always affected by GNI and renewable electricity output because in lowincome level group, these variables are insignificant