The impact of green energy development on the economic component of Sustainable Development in Germany

. The paper presents the results of the correlation and regression analysis of Germany's green energy development factors on business activity. The article presents possible predictions for the development of the economic component of Germany’s sustainable development, taking into account the use of RES. The research paper discusses the importance of using the green energy for the achievements the Sustainable Development Goals and mitigation of the consequences of the COVID-19 pandemic.


Introduction
Relevance of the topic of the study.One of the key global trends of our time is the energy transition.The energy transition refers to the gradual replacement of fossil fuel-based energy with alternative ways of generating energy from renewable and environmentally friendly sources.
The COVID-19 pandemic has intensified the need for an early green energy transition.The need to replace fossil fuels with RES has increased significantly from 2020.One factor in this has been the drop in demand for oil and gas for the first time in 11 years [3].The G7 countries have also felt the need to develop green energy.
The G7 is an association of the world's most economically developed countries.These countries have the largest economies in the world in terms of GDP and human development index.By the end of 2019, the share of the G7 in global industrial output was 29.37 % [4].The decline of the world economy at the end of 2020 exceeded both the consequences of the financial crisis of 2008 and the Great Depression of the 1930s [9].Given the influence of the economic activity of the G7 countries on the world economy, it can be expected that the representatives of this association will determine the direction of the world development, including the speed of implementation of the Sustainable Development Goals.
One of the brightest representatives of this association is Germany.In addition, Germany has been the leader among the G7 countries in the Global Green Economy Index [7] for the entire period of publication of this study.Thus, the study of the impact of green energy development on business activity in this country is important.It will make it possible to assess the potential of renewable and alternative energy sources as a driver of global sustainable development.

Materials and methods
This research proposes to perform the correlation and regression analysis of Germany's green energy development factors on business activity using MS Excel.This will help to identify patterns of implementation of environmental security in Germany and their role in the implementation of the concept of sustainable development.
In particular, it is proposed to use the following statistical indicators as quantitative indicators of the state of green energy in Germany:  Primary energy consumption from RES, TWh. Investments for the development of RES, billion EUR.
Energy consumption from RES involves the use of hydropower, solar, wind geothermal, wave (tidal) energy, and bioenergy.Energy consumption is based on primary energy equivalents rather than final energy consumption [1].
Investment for the development of RES is the amount of money spent on the development of RES [2].
As an indicator of economic activity in the country, it is proposed to use the value of GDP for the 2002-2021 years.
GDP is a macroeconomic indicator that reflects the market value of all final goods and services produced in the country.Its use is conditioned by the fact that it will be an indicator of the state of development of the economic component of the concept of sustainable development in the country [5].
The sources of these indicators will be data from the World Bank and the International Energy Agency, data from The Federal Ministry for Economic Affairs and Climate Action, etc.
The implementation of the above study involves six stages:  Calculation of pairwise Pearson correlation coefficients in order to detect the phenomena of autocorrelation and multicollinearity between the explanatory variables.Interpretation of the results. Performing the construction of equations of the multiple linear and power functions using the «Data Analysis» MS Excel package. Calculation of descriptive statistics of regression equations to determine the degree of adequacy of the obtained function.Selection of the most adequate dependence.Interpretation of indicators of the significance of the selected function. Check the significance of the equation as a whole at the level of α = 0.05 using Fisher's criterion. Calculation of equation parameters using MS Excel.Interpretation of estimates of its parameters. Constructing a prediction using the resulting equation.Interpretation of the results.

Results
To calculate pairwise correlation coefficients Pearson correlation coefficients, we imported the original data (Table 1) into MS Excel.This will assess the degree of closeness of the relationship between the selected indicators and its direction.
The "Correlation" function in the "Data Analysis" MS Excel package allowed us to obtain the following values of pairwise Pearson correlation coefficients (Table 2).Based on the calculated correlation indicators, the following was found:  The relationship between the amount of primary energy consumption from RES (x 1 ) and the amount of Germany's GDP (y) is strong and direct.This shows that an increase in the consumption of energy from RES leads to an increase for GDP. The relationship between the amount of investment in the development of RES (x 2 ) and Germany's GDP (y) is medium and direct.This indicates that an increase in investment in renewable energy development leads to an increase for GDP.The "Regression" function in the "Data Analysis" MS Excel package allowed us to obtain the following values of descriptive statistics of regression equations for linear and power functions (Table 3).Based on comparison of descriptive statistics of regression equations we can conclude that the most adequate is the dependence, represented as a multiple power function of dependence of business activity in Germany on factors of green energy development in the country.
The cumulative correlation coefficient is 0.916.So the degree of tightness of the relationship between the dependent variable (GDP) and all explanatory variables (consumption of primary energy from RES and investments in the development of RES) taken together is strong.
The coefficient of determination is 0.839.This indicates that 83.9 % of the GDP variability is explained by the independent variables (consumption of primary energy from RES and investments in the development of RES) included in the model.
It is necessary to compare the observed value of the Fisher criterion and the critical value to check the significance of the equation as a whole.In our case, we found the observed value of the Fisher criterion using the "Regression" function in the "Data Analysis" MS Excel package.It is 44.146.We found the critical value of the Fisher criterion at α = 0.05 according to the Fisher distribution table.It is 3.59.As we can see, the observed value of the Fisher criterion is above the critical value.Consequently, with a reliability greater than 0.95 and the risk of error less than 0.05, we can say that business activity in Germany depends on factors of green energy development in the country.
The resulting equation of the multiple power function has the following form: (1) Interpretation of estimates of its parameters:  b 0 = 516.23 billion USD.Under the conditions of primary energy consumption from RES per 1 TWh and investments in the development of RES per 1 billion EUR, the value of the country's GDP on average will be increase by 516.23 billion USD per year. b 1 = 0.25 %.Germany's GDP will increase by an average of 0.25 % per year if renewable primary energy consumption increases by 1 %, all other things being equal. b 2 = 0.18 %.Germany's GDP will increase by an average of 0.18 % per year if the volume of investment in renewable energy increases by 1 %, all other things being equal.
A graphical interpretation of the dependence of business activity in Germany on factors of green energy development in the country (primary energy consumption from RES and investments in their development) is presented in Figure 1.As a result of the statistical analysis of the economic component of sustainable development in Germany and indicators of green energy development, as well as economicmathematical modeling of potential dependencies with the application of correlation and regression analysis, we can construct predictions for the development of business activity in Germany for future periods (Figure 1).

Discussion
The nature of the predictions made for the development of business activity in Germany taking into account the use of green energy for future periods was as follows:  Prediction 1 provides for preservation of annual growth rates of primary energy consumption from RES and investment in the development of RES at the level of 8.0 % and 5.1 %, respectively. Prediction 2 provides for maintaining the annual growth rate of primary energy consumption from RES at the level of 8.0 % without increasing the volume of investment in the development of RES. Prediction 3 provides for maintaining the annual growth rate of investment in the development of RES at 5.1 %, while maintaining the consumption of primary energy from RES at the level of 2021.Thus, we can expect the following annual increase in the economic component of sustainable development in Germany for the predicted periods:  in case of Prediction 1 (maintenance of annual growth rates of primary energy consumption from RES and investments in the development of RES at 8.0 % and 5.1 %, respectively) the increment will be 2.1 % by the end of 2024. in case of Prediction 2 (maintenance of the annual growth rate of primary energy consumption from RES at 8.0 % without an increase in investment in the development of RES) the increment will be -0.6 % by the end of 2024. in case of Prediction 3 (maintenance of annual growth rates of the value of investment in the development of RES at the level of 5.1 % while maintaining primary energy consumption from RES at the level of 2017) the increment will be -3.6 % by the end of 2024.

Conclusion
According to the results of the predictions of the economic component of Germany's sustainable development, we can state the following.The development of green energy and the implementation of green economy principles in the business activities of Germany leads to an increase in the economic potential of the country and the achievement of the Sustainable Development Goals.In addition, it can be reasonably assumed that the active development of renewable and alternative energy sources is able to gradually reduce the pressure of the COVID-19 pandemic on the world economy.This is especially true for the G7 countries, which include Germany.In order to do so, investments in economic recovery must not only ensure the previous level of economic development, but also help to mitigate potential environmental shocks.So the challenge for governments is to make decisions that will overcome both the economic downturn and the climate crisis as well as create more sustainable economies.The development of green energy must be a priority in this direction.A statistical study confirms that the development of renewable and alternative energy sources increases the economic component of Sustainable Development of country.

Fig. 1 .
Fig. 1.Dynamics of actual GDP in Germany from 2002 to 2021 and forecast until 2024, USD billion.

Table 2 .
Carl Pearson correlation coefficients of variables and dependent.

Table 3 .
Indicators of the significance of the obtained models.