Statistical Analysis of the United States Renewable Energy

Study Case Statistical Analysis of the United States Renewable Energy Mix 2015–2022 Michael Kurniawan (2018123456) University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States kurniaml@mail.uc.edu Abstract Based on data from the U.S. Energy Information Administration (EIA) and the U.S. Department of Energy (DOE), since 2015 the percentage of renewable energy in the United States has shown consistent growth. This is in line with the statement made by the President of the United States at the Conference of Parties (COP) 26 United Nations Framework Convention on Climate Change (UNFCCC) in Glasgow, UK, in November 2021, that the US is committed to contributing to global emission reductions and achieving net-zero emission targets. One of the strategic steps taken is the diversification of fossil fuels to renewable energy. This study analyzes the growth trend of renewable energy mix in the US for the period 2015–2022 using simple linear regression and piecewise linear regression models. The analysis is linked to the DOE's target that by 2025, the renewable energy mix can reach 23%. The estimation results show that the simple linear regression model predicts an achievement of 17.53%, while the piecewise linear regression models produce a prediction of 23.05%. Keywords: renewable energy mix, simple linear regression, piecewise linear regression, target, prediction MICHAEL KURNIAWAN 1 Study Case INTRODUCTION Climate change is a global challenge faced by all of humanity. One of the main causes is the dominance of fossil fuels, which produce large amounts of carbon emissions, thereby accelerating global warming [1]. Historical studies show that from 1750 to 2005, carbon emissions were a major factor in climate change [2]. Various initiatives, both at the national and international levels, have been undertaken to mitigate the impact of global warming. The 2018 Intergovernmental Panel on Climate Change (IPCC) report shows that global warming has increased the average surface temperature of the earth by about 1.5°C, which has a significant impact on health, food security, water availability, and energy supply. Therefore, the transition to renewable energy has become a global necessity. In addition, research also shows the positive impact of renewable energy on economic development, thereby strengthening the direction of sustainable development [3][4][5]. Each country pursues different strategies in implementing energy transition, depending on its renewable energy resource potential. The renewable energy mix is not only important for energy security, but also plays a role in fulfilling carbon emission reduction commitments [5]. The United States has great potential for energy diversification, including biofuels, biomass, geothermal energy, hydropower, wind, ocean wave, tidal, and solar energy. Since 2007, the US government, through the Energy Independence and Security Act, has established the National Renewable Energy Council to design national energy policies, including the development of renewable energy infrastructure. Since 2011, energy transition efforts have intensified with reduced dependence on fossil fuels and increased investment in renewable energy through collaboration between the Department of the Treasury and the DOE. According to EIA data, the renewable energy mix in the US increased from 4.9% in 2015 to 14.11% in 2022. The DOE is targeting 23% by 2025. This study aims to analyze trends in the US renewable energy mix for the period 2015–2022 and predict the 2025 target using simple linear regression and piecewise linear regression. The main question is whether both models are capable of producing estimates in line with the government's target. Several previous studies have analyzed the energy mix using various methods, such as descriptive statistics [1], policy analysis [3][6][7], panel quantile regression [8], and MICHAEL KURNIAWAN 2 Study Case multiple linear regression [9]. However, studies using simple linear regression and piecewise linear regression are still limited. METHOD The data used is the US renewable energy mix (%) for the period 2015–2022. Using a statistical approach, a renewable energy mix trend model was developed to predict achievements in 2025. Analysis steps: 1. Develop a simple linear regression model for data from 2015–2022. 2. Use the model to predict the energy mix for 2023–2025. 3. Develop a simple linear regression model for data from 2015 to the government's 2023 target. 4. Make predictions for 2023–2025. 5. Develop a simple linear regression model for data from 2015 to 2024. 6. Develop Piecewise Linear Regression Models (PLRM) for data from 2015 to 2024. 7. Use PLRM to predict the energy mix for 2023–2025. Simple Linear Regression Model (RLS) The general regression model is formulated in Equation (1): y=E(y)+ε where: • y = response variable • E(y) = deterministic component • ε = random error RLS model (Equation 2) y = β0 + β1x + ε where: • x = predictor variable • β0 = regression constant • β1 = regression coefficient Parameter estimation is obtained using the least squares method. MICHAEL KURNIAWAN 3 Study Case Model Accuracy Model accuracy was tested using Analysis of Variance (ANOVA) as shown in table 1. Hypothesis: • H0: the model does not fit the data • H1: the model fits the data Criteria: H0 is rejected if p < 0.05. The coefficient of determination (R2R^2) was used as an additional measure. Table 1. Simple Linear Regression ANOVA Test Results Regression Model Assumptions Regression model in Equation (4): yi = β0 + β1xi + εi,i = 1,2,…, n Assumptions: 1. εi∼N(0,σ2) with estimation : 2. εi is uncorrelated with εj. The parameter tests are shown in Table 2. MICHAEL KURNIAWAN 4 Study Case Table 2. Significance Test of Regression Coefficients Residual Check The accuracy of the model is also tested with a residual plot: The residual plot is evaluated against the predicted values (y^). If the assumptions are met, the distribution pattern of the residuals is random. Figure 1. Random residual plot against predicted values Piecewise Linear Regression Models (PLRM) If the regression gradient changes at a certain point (knot), PLRM is used. General form (Equation 8): where k = knot point value. Table 3. Change in Intercept and Slope in PLRM MICHAEL KURNIAWAN 5 Study Case Figure 2. Scatter plot of the relationship between yy and xx at the node point x=70x = 70 The accuracy of PLRM was tested using a procedure similar to that of a simple linear regression model. RESULTS AND DISCUSSION United States Renewable Energy Mix (BET) Data 2015–2022. The BET data for the 2015–2022 period is shown in Table 4. Table 4. US BET Data for 2015–2022 RLS Model (Data until 2022) From the data processing in Table 4, the following regression equation was obtained (Equation 9): with R2 = 98.38% and standard deviation s = 0.44. Parameter inference is shown in Table 5. MICHAEL KURNIAWAN 6 Study Case Table 5. Significance test of model parameters Equation (9) The p-value is < 0.05 for both parameters, meaning that both are significant. The ANOVA test results (Table 6) also show that the model fits the data (p-value < 0.05). Table 6. ANOVA results for model Equation (9) Predictions and 95% confidence intervals for 2023–2025 are shown in Table 7. Table 7. BET AS predictions for 2023–2025 based on the Equation (9) model The residual plot against the predicted values (Figure 3) shows a random pattern without outliers, so the regression model in Equation (9) is considered valid. Figure 3. Residual plot with BET predictions for 2015–2022 using the Equation (9) MICHAEL KURNIAWAN 7 Study Case Model prediction results: • 2023 = 14.95% (below DOE target = 17.9%) • 2025 = 17.53% (upper prediction interval = 19.09%, still below the 23% target) RLS model with data up to the government's 2023 target By adding the government's 2023 target of 17.9%, we obtain the model (Equation 10): With R^2 = 95.28% and s = 0.97. Parameter inference is presented in Table 8, while ANOVA is presented in Table 9. Table 8. Significance test of model parameters Equation (10) Table 9. ANOVA results of model Equation (10) Both tests show that the model is significant. Predictions for 2023–2025 are shown in Table 10. Table 10. 2023–2025 US BET predictions for Equation (10) model RLS model with data up to the 2024 government target By entering the 2023 target = 17.9% and the 2024 assumption = 19.5% (values within the prediction interval), we obtain the model (Equation 11): with R^2 = 95.85% and s = 1.06. MICHAEL KURNIAWAN 8 Study Case Table 11. Significance test of model parameters Equation (11) Table 12. ANOVA results of model Equation (11) Although the parameters are significant, the residual plot (Figure 4) shows a nonrandom pattern and the presence of outliers, indicating that the model is not appropriate. Figure 4. Residual plot with BET 2015–2024 predictions from Equation (11) The scatter plot (Figure 5) shows a change in gradient in 2022, prompting consideration of the Piecewise Linear Regression Model (PLRM). Figure 5. Scatter plot of US BET 2015–2024 MICHAEL KURNIAWAN 9 Study Case PLRM model with data up to 2024 PLRM is formulated in Equation (12): PLRM data is shown in Table 13, with the regression equation (Equation 13): with R^2 = 98.88 % and s = 0.59. Table 13. US BET data for 2015–2024 for PLRM Table 14. Significance test of model parameters Equation (13) MICHAEL KURNIAWAN 10 Study Case Table 15. ANOVA results for Equation (13) model The residual plot (Figure 6) shows a random pattern without outliers, indicating that the PLRM model is more accurate. Figure 6. Residual plot with BET predictions for 2015–2024 using Equation (13) model The PLRM prediction results for 2025 are given in Table 16. Table 16. BET US predictions for 2023–2025 using Equation (13) Results: with targets of 17.9% for 2023 and 19.5% for 2024, the BET prediction for 2025 reaches 23.05%. MICHAEL KURNIAWAN 11 Study Case DISCUSSION The US government, through the Energy Policy Act and National Renewable Energy Plan, has set a target of 23% renewable energy by 2025 and 31% by 2050 (U.S. DOE Performance Report 2022). The results of the study show that the PLRM model is most consistent with the data. The 2025 prediction is close to the DOE target, provided that the targets for 2023 and 2024 are achieved. Currently, the use of renewable energy in the US is still relatively low compared to fossil fuels, especially oil and gas. However, there is still potential for growth. The 2020– 2050 trend projection estimates that the increase will be slow if the transition is not accelerated [11]. Opportunities and challenges include: • The development of renewable power plants such as small hydroelectric plants . • The great potential of biofuels as a substitute for petroleum fuels [13]. • Local studies in various regions, such as collaboration between engineering universities and city planning departments to map the potential for renewable energy [14]. Given that energy is a key pillar of development and welfare [15], cross-sector collaboration is essential to ensure that targets are met. CONCLUSION From the statistical analysis of BET AS 2015–2022 data, the following conclusions were drawn: 1. The simple linear regression model predicts a renewable energy mix of 17.53% in 2025, with a 95% confidence interval of 15.96%–19.09%. 2. The piecewise linear regression model predicts a 2025 renewable energy mix of 23.05%, with a 95% confidence interval of 20.61%–25.49%. Thus, achieving the DOE target of 23% by 2025 is more realistic when using the PLRM approach. MICHAEL KURNIAWAN 12 Study Case REFERENCE MICHAEL KURNIAWAN 13 Study Case MICHAEL KURNIAWAN 14