###### Creating Resilient Supply Chains and Procurement

January 6, 2024###### Hannah Arendt & theory applied to the climate change and human relations with the natural environment

January 9, 2024## Multiple linear regression analysis

Linear regression is utilized to predict the value of one variable depending on the other variable. The value of the variable which wanted to predict from the analysis is known as the dependent variable and the variable that is used to predict the value of the dependent variable is known as the independent variable. The coefficient of a linear equation can be estimated through the linear equation (Raggad, 2018). A straight line or area has been fitted by linear regression that reduces the inconsistency between the actual results and the predicted values.

The general form of a multiple regression model is represented in the equation 1.

= + + + + … + _{i , }i= 1, 2, 3, … n

Where

_{i }= Error term

= Intercept of the equation of a straight line

= dependent variable

= independent variable, where j= 1, 2, 3, … k

… = Coefficient of each independent variable.

n = number of observations.

**Assumption of multiple linear regressions**

- The independent variables do not have any random value.

## Hypothesis development

For the regression analysis For CO_{2} and economics variables, four independent variables have been chosen. The dependent variable for this analysis is CO_{2 } emission. Of these four variables, two are economic variables and two are social variables. The economic variables are GDP (Gross Domestic Product) and energy_per_gdp, other two independent variables are populations and primary_energy_consumption. First, the relationships among variables have been established through regression for all the countries and after that, the regression analysis has been performed for Australia, USA, India, and China individually. The regression model for this analysis is represented through the equation 1.

CO_{2} emission = + gdp + energy_per_gdp + primary_energy_consumption + populations + (1)

Here = constant for all the regression analyses

and = constant for all the respective independent variables.

= the error term

For this analysis, the null hypothesis () has been developed.

: and > 0

: Any one of is not > 0

In this analysis, the null hypothesis will be rejected if the p-value or the probability value is greater than 5 percent. Otherwise, the null hypothesis will be accepted. The hypothesis testing with p-value can be achieved by making a Type I error.

## Regression analysis results

**Figure 1: Regression analysis of all 10 countries**

(Source: self-created in MS Excel)

The above figure 1 represents the regression analysis results for all 10 countries for all the independent variables. From the above figure, it has been seen that the p-value for all the variables is less than 5%, hence the null hypothesis would not be rejected. The p-value for the independent variable population is 2.34987E-37, for GDP, it is 2.22667E-06, for energy_per_gdp p-value is 1.5036E-05, and for primary_energy_consumption the value is 6.6047E-135. The coefficients (such as and ) of all these independent variables are 6.23004E-07 for population, -7.54977E-11 for GDP, 97.46566427 for energy_per_gdp, and for primary_energy_consumption the value is 0.266561051. The Standard Error for all these independent variables is 4.4794E-08 for population, 1.57676E-11 for GDP, 22.29480149 for energy_per_gdp, and for primary_energy_consumption the value 0.007669536. The R square value of this regression analysis is 0.970024751, and the value of Adjusted R Square is 0.969782526.

**Figure 2: Regression analysis for Australia**

(Source: self-created in MS Excel)

The above diagram 2 represents the regression analysis results for Australia. From the above figure, it has been seen that the p-value for the variable population and primary_energy_consumption are not less than 5%, hence these variables do not have any significance. The p-value for the independent variable primary_energy_consumption the value is 0.552015931. The coefficients of all these independent variables are -6.1011E-06 for population, -1.62787E-10 for GDP, for energy_per_gdp the value is 80.48430328, and 0.381429083 for primary_energy_consumption. The Standard Error for all these independent variables is 4.71E-06 for population, 4.85818E-11 for GDP, 19.43255608 for energy_per_gdp, and for primary_energy_consumption the value is 0.029651258. The R square value of this regression analysis is 0.98440876, and the value of Adjusted R Square is 0.983022872.

**Figure 3: Regression analysis for China**

(Source: self-created in MS Excel)

The above figure 3 represents the regression analysis results for China. The R square value of this regression analysis is 0.996132019, and the value of Adjusted R Square is 0.995780384. The p-value for all the variables is less than 5% except variable energy_per_gdp, hence it has no level of significance in this analysis. The p-value for the independent variable for energy_per_gdp p-value is 0.552015932. The coefficients of all these independent variables are 4.9668E-07 for population, -1.64303E-10 for GDP, 141.6802921 for energy_per_gdp, and for primary_energy_consumption the value is 0.343943593.

**Figure 4: Regression analysis for India**

(Source: self-created in MS Excel)

The above figure 4 represents the regression analysis results for India for all the independent variables as mentioned above. From the above figure, it has been seen that the p-value for the variable GDP is not less than 5%, hence this variable has no significance in this analysis. The p-value for the independent variable population is 0.000553251, for GDP, it is 0.376895275, for energy_per_gdp p-value is 0.009746073, and for primary_energy_consumption the value is 4.06087E-11. The R square value of this regression analysis is 0.999138228, and the value of Adjusted R Square is 0.999059885. The coefficients of all these independent variables are -4.88076E-07 for population, -2.88691E-11 for GDP, 40.00440131 for energy_per_gdp, and for primary_energy_consumption the value is 0.358585121. The Standard Error for all these independent variables is 1.3103E-07 for population, 3.23405E-11 for GDP, 14.80389215 for energy_per_gdp, and for primary_energy_consumption the value 0.041209976.

**Figure 5: Regression analysis for the USA**

(Source: self-created in MS Excel)

The above figure represents the regression analysis results for all 10 countries for all the independent variables. The R square value of this regression analysis is 0.972872614, and the value of Adjusted R Square is 0.970406488. From the above figure, it has been seen that the p-value is less than 5% for all variables except population, therefore this variable does not have any significance in this regression analysis. The p-value for the independent variable population is 0.006030972, for GDP, it is 0.600772933, for energy_per_gdp p-value is 5.27035E-25, and for primary_energy_consumption the value is 6.6047E-135. The coefficients of all these independent variables are -1.8221E-05 for population, 2.8502E-11 for GDP, 343.4758598 for energy_per_gdp, and for primary_energy_consumption the value is 0.290945919. The Standard Error for all these independent variables is 6.31445E-06 for population, 5.40734E-11 for GDP, 78.88075654 for energy_per_gdp, and for primary_energy_consumption the value is 0.013505554. The R square value of this regression analysis is 0.972872614, and the value of Adjusted R Square is 0.970406488.

## Discussion

The results of the regression analysis show that the indent variables have both negative and positive values for different countries. The positive relation between the dependent variable CO_{2} and the independent variables indicates that the carbon dioxide emission has increased with the increase of this variable, whereas the negative relation depicts the opposite results.

** **

**Figure 6: CO _{2 } emission vs. gdp**

(Source: self-created in MS Excel)

The above graph shows the variation of CO_{2} emission with the GDP of all the countries. From the above graph, it can be said that carbon dioxide emission has increased over the increment of GDP in different countries.

**Figure 7: co _{2 }vs. energy_per_gdp _{ }**

(Source: self-created in MS Excel)

The above graph represents the variation of the emission of carbon dioxide with energy_per_gdp. Like the variable GDP, it also shows the same trend that the carbon dioxide emission is increased with increased energy_per_gdp.

## References

**Journals**

Boateng, F.K., 2020. Effects of economic growth, trade openness, and urbanization on carbon dioxide emissions in Ghana, 1960 to 2014. *Applied Economics and Finance*, *7*(2), pp.9-17.

Osobajo, O.A., Otitoju, A., Otitoju, M.A. and Oke, A., 2020. The impact of energy consumption and economic growth on carbon dioxide emissions. *Sustainability*, *12*(19), p.7965.

Raggad, B., 2018. Carbon dioxide emissions, economic growth, energy use, and urbanization in Saudi Arabia: evidence from the ARDL approach and impulse saturation break tests. *Environmental Science and Pollution Research*, *25*(15), pp.14882-14898.

Sasana, H. and Aminata, J., 2019. Energy subsidy, energy consumption, economic growth, and carbon dioxide emission: Indonesian case studies. *International Journal of Energy Economics and Policy*, *9*(2), p.117.

Tong, T., Ortiz, J., Xu, C. and Li, F., 2020. Economic growth, energy consumption, and carbon dioxide emissions in the E7 countries: a bootstrap ARDL bound test. *Energy, Sustainability and Society*, *10*(1), pp.1-17.

Wen, J., Mughal, N., Zhao, J., Shabbir, M.S., Niedbała, G., Jain, V. and Anwar, A., 2021. Does globalization matter for environmental degradation? Nexus among energy consumption, economic growth, and carbon dioxide emission. *Energy Policy*, *153*, p.112230.

Yaw Naminse, E. and Zhuang, J., 2018. Economic Growth, Energy Intensity, and Carbon Dioxide Emissions in China. *Polish Journal of Environmental Studies*, *27*(5).