# Evaluation of Turkey's Road-Based Greenhouse Gas Inventory and Future Projections
## 2 Materials and Methods
### Future Predictions  
In this study, polynomial regression was employed to model the nonlinear growth trend in the number of registered vehicles in Turkey. The accuracy of predicting future vehicle counts using the polynomial regression method is contingent on the breadth of the past information set. Moreover, more information is needed to estimate the number of vehicles traveling on state roads in the study area, which is used for emission calculations. Therefore, TurkStat's data on the number of vehicles registered for traffic in Turkey from 1966 to 2021 were used in the estimation study.  
A second-degree polynomial model was selected for its ability to capture the long-term curvature in the data without introducing excessive model complexity. The model was implemented using Python 3.7 (Python Software Foundation, Beaverton, Oregon, ABD) and the scikit-learn 1.4.2 library (Machine learning in Python Version 1.4.2). The model pipeline included PolynomialFeatures and LinearRegression, and the regression coefficients were estimated using the least squares method. The model achieved a coefficient of determination (R\({}^{2}\)) of 0.96, indicating a strong fit between the observed and predicted values. Additional performance metrics such as Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) and the high R\({}^{2}\) value indicate that the model provides sufficient accuracy for projection purposes. To minimize the risk of overfitting, higher-degree polynomial models were not considered, as they tend to increase model variance and reduce generalizability.  
The number of automobiles from 1966 to 2021 was analyzed to project the trend for the years up to 2050. This projection enabled the calculation of future emissions based on average per-vehicle emissions and emission factors defined in the EMEP/EEA air pollutant emissions inventory guide. For future emission predictions, GHG emissions were calculated based on the number of vehicles using state roads, and the average emissions per vehicle (Equation (2)) were calculated considering the total number of vehicles. Then, emissions were estimated using average emission amounts per vehicle and the number of vehicles projected for the future.  
\[MVE=\frac{\sum_{t=n}^{p}\ Em_{t}}{\sum_{t=n}^{p}\ Veh_{t}} \tag{2}\]  
where MVE is the mean vehicle emissions (kg emission/per vehicle), n is the first year used in the calculation, p is the final year used in the calculation, Em is the calculated emission value (kg), and Veh is the number of vehicles.  
Figure 2: Classification of registered vehicles in Turkey based on fuel type [29].  
This method provides a solid framework for forecasting future emissions and analyzing long-term trends. Using this and comparable predictive models may be valuable for forecasting.  
In the study, the Relative Standard Error (RSE) values were calculated to determine the uncertainty (Equation (3)). The Relative Standard Error (RSE) offers a dimensionless, percentage-based indicator of the uncertainty, thereby allowing for better comparability across datasets or studies.  
\[RSE=\frac{SE}{\overline{x}}\times 100 \tag{3}\]  
where SE represents the Standard Error, and \(\overline{x}\) is the arithmetic mean of the data [35].  
The Standard Error (SE) quantifies the uncertainty in how accurately a sample mean estimates the population mean. A smaller SE indicates greater reliability of the estimate and is calculated according to Equation (4) [36; 37].  
\[SE=\frac{\sigma}{\sqrt{n}} \tag{4}\]  
where \(\sigma\) is the standard deviation, and n refers to the sample size  
According to the Australian Bureau of Statistics (ABS), RSE values between 0-25% are considered reliable and suitable for publication and interpretation. RSEs between 25-50% indicate a high sampling error and should be interpreted with caution, while RSEs exceeding 50% reflect excessive uncertainty, rendering the estimates unreliable and unsuitable for publication [38].