# Survivability Prediction of Open Source Software with Polynomial Regression
## 1 Introduction  
OSS (Open Source Software) has become a crucial part of modern software development, being applied in various fields, ranging from simple tools to complex operating systems [1]. While the adoption of OSS has greatly enhanced development convenience, it has also introduced various risks, such as project dependency issues [2]. The project dependency mainly refers to the possibility of the main project encountering issues due to bugs in open source components. These risks primarily arise from the collaborative nature of OSS development, where individuals and groups with diverse backgrounds participate autonomously, rather than being tied to a single organization. This characteristic may not guarantee the ongoing involvement of OSS contributors, which can impact its maintenance [3]. Decreased contributions can hinder bug-fixing efforts, leading to increased maintenance costs and efforts [4]. In fact, there have been cases where issues in OSS, such as the Shellshock incident [5], which affected several commercial software products, orchanges in DNS resolver code in the GNUC library, resulted in the disruption of some applications when making network requests [6]. To mitigate these risks, it is important to utilize OSS that is maintained in the long term, ensuring high survivability into the future, and preemptively replace OSS that does not meet this criterion [7]. However, evaluating survivability criteria is not always clear, making it difficult for users to assess and take action. Therefore, it is necessary to evaluate the maintainability of OSS based on factors such as repository characteristics and current status and make informed choices. Previous studies have attempted to estimate OSS survivability by predicting the repository activity or estimating decreases in contributor numbers [8; 9; 10]. However, these studies focused on overall development activities, including project dependencies, which limited their ability to accurately assess the remaining risks related to bugs. In this paper, we propose predicting the survivability of OSS using polynomial regression. We predict the trend of bug-fixing activities based on popularity, the number of contributors, and the code complexity of OSS. A higher value indicates a lower likelihood of survival. To address this, we formulated the two following RQs (research questions):  
1. Can the survivability of OSS be predicted through polynomial regression? 2. Can the survivability of OSS be modeled through polynomial regression? RQ1 concerns the ability of polynomial regression to accurately reflect the survivability of OSS based on the predicted target. RQ2 explores the feasibility of using polynomial regression to predict the target with the given features. To achieve this, we conduct three main steps: data collection and extraction, regression model setup and testing, and evaluation. Firstly, we collect information such as star counts and code complexity from project repositories using GitHub API and static analysis tools, and then the extract trend of OSS values representing the bug-fixing activity from the collected data. In the second step, we perform K-fold cross-validation for various degree values and select the degree showing the best performance to create the model. In the final step, we predict the survivability of OSS using the generated model. To demonstrate the model's performance, we compare the predicted results with the current state and features of the actual OSS. Additionally, the accuracy and fitness of the model are verified using RMSE (Root Mean Squared Error) and RSE (Residual Standard Error). These two metrics are employed to validate whether the model has been adequately trained and to ascertain the accuracy of the predictions made by the trained model. We conduct experiments targeting the OSS used in KakaoTalk commercial messenger app to validate our proposed method. We select these OSS components for evaluation to assess their viability in actual commercial applications.