## 5 Discussion and Conclusions  
In this paper, we proposed a gasoline order prediction model for gas stations using a linear regression model to understand the trend of gasoline consumption in the road-based transportation system in South Korea. When training with a limited number of data samples, a model's accuracy tends to decrease due to the challenge of understanding the structures or patterns within the data samples. Additionally, it is difficult to determine the model's generalized performance due to over-reliance on a limited number of training sets. Accordingly, we performed data augmentation on our model using the Variational Auto-Encoder (VAE) with K-means clustering to implement a model with high accuracy and generalized performance. With the proposed methods, we could mainly solve two problems: the lack of data samples and class imbalance. First, to better reflect the characteristics of the data samples for augmentation, we grouped the datasets into clusters using K-means clustering. And then we augmented each cluster's datasets with VAE. When performing data augmentation without clustering, the dataset displays a limitation in reflecting its overall characteristics. We thus determined the optimal number of clusters and augmented datasets through experiments. By evenly augmenting the datasets in each group, the overall performance increased and solved the class imbalance issue. Out of the 167 variables of the augmented data, the Variance Inflation Factor (VIF) was used to explore the significant variables. By repeatedly removing the variable with the highest VIF, 11 significant variables were obtained from the 167 variables. Gasoline orders were influenced by the cooling degree day, Dubai crude oil prices, FFR, PPI fluctuation rate, NSI, USDX, international gasoline (95 RON) price, GPR, gasoline inventory at the gas station, S&P 500, and fuel tax. With 11 independent variables, we evaluated the linear, Ridge, Lasso, Elastic-Net, AdaBoost, Extra Trees, Random Forest, and XGBoost (Extreme Gradient Boosting) regression models. Among these models, linear regression showed the highest performance. To confirm the significance of the proposed model, we evaluated the reliability of the regression equation derived from linear regression using the \(p\)-value. Our gasoline order prediction model will be helpful to both gas station owners and the government. Gas station owners could adjust gasoline orders by observing the fluctuations in the independent variables. The government could understand the trend of gasoline consumption by monitoring the fluctuations in the independent variables and gasoline orders. Our model could also be used as a reference for adjusting fuel policies. Figure 5: The results of the linear regression for gasoline orders at gas stations in South Korea. However, there are limitations to the data samples used in the proposed method. Through interviews with gas station owners, we found that gasoline is ordered on average three times a week at gas stations. Gasoline is a product with a short price adjustment cycle, so gas stations adjust the quantities of orders immediately according to gasoline price fluctuations. This cannot be explained using monthly datasets. Collecting gasoline orders and related independence variables on a daily or weekly basis and analyzing their changes would enable more accurate predictions. With daily or weekly datasets, sensitive fluctuations in the real world can be clearly observed. In future research, we aim to automatically collect various news datasets using web crawling [35] and then analyze political, economic, and societal issues that cause outliers using a deep-learning-based text summarization method [36; 37]. In so doing, it is expected that the gasoline order prediction model can be more clearly understood and improved, thereby becoming a robust model. Conceptualization, S.Y. and M.P. ; data curation, S.Y. ; formal analysis, S.Y. ; funding acquisition, M.P. ; methodology, S.Y. and M.P. ; supervision, M.P. ; validation, S.Y. ; visualization, S.Y.