# Multivariate Regression Analysis for Identifying Key Drivers of Harmful Algal Bloom in Lake Erie
## 1 Introduction
Furthermore, higher chlorophyll-a concentrations do not always signify high toxin levels but may indicate a higher probability of exceeding certain thresholds [38]. Therefore, understanding the main drivers of HABs remains pivotal for accurate prediction and prevention efforts. Various prediction models have been developed to address HAB dynamics. Physical process-based models, such as the Environmental Fluid Dynamic Code (EFDC) [39], Water Quality Simulation 2000 (QUAL2K) [40], and Water Quality Analysis Simulation Program (WASP) [41], rely on detailed physical and biochemical processes but face challenges in handling spatial data and high costs [42; 43; 44; 45]. While these models have high prediction accuracy with complete data, constructing perfect data, particularly with spatial resolution, is costly and involves practical limitations. Statistical models that correlate physicochemical and meteorological variables often struggle with capturing nonlinear relationships [46; 47], limiting their predictive accuracy [48]. Both approaches contribute valuable insights but face limitations in predicting HAB dynamics under varied conditions [49]. To address these challenges, data-driven models have emerged as promising alternatives for predicting HABs. These models, increasingly applied in hydrology, water resources, and environmental management, can uncover complex relationships without the need for explicit mathematical modeling of unknown processes [50; 51]. Data-driven approaches [52; 53] offer a significant advantage in analyzing and predicting HAB occur rences, providing more accurate and reliable results, and support informed decisions for the public through visualization and communication systems [54; 55]. The objective of this study is to quantitatively identify the key physical, chemical, and biological drivers of HABs using multivariate regression analysis. Specifically, we aim to (1) assess the relative importance of explanatory variables, (2) identify the major drivers of HAB dynamics, and (3) quantify the relationship between water quality variables and HAB formation. Statistical methods such as correlation analysis, multivariate regression analysis, and the ANOVA F-test were applied to our dataset. In addition, multivariate regression analysis was also conducted for total suspended solids (TSS), which is an important indicator for monitoring water quality and measuring the degree of water pollution, to further demonstrate the robustness of our approach. The HAB analysis framework developed in this study is designed for broad application to lakes, rivers, and coastal areas. We anticipate that this framework will serve as a valuable tool for scientists and stakeholders, offering practical guidance for understanding and mitigating HAB risks globally. This paper is structured as follows: Section 2 describes the methodology, including data collection and correlation and multivariate regression analysis. Section 3 presents the results and discussion, highlighting the key drivers for HAB. Section 4 concludes with insights into the implications of the findings and suggestions for future research.