# Multivariate Regression Analysis for Identifying Key Drivers of Harmful Algal Bloom in Lake Erie
## 3 Results and Discussions
### Discussions  
This study highlights the critical role of particulate organic nitrogen (PON), turbidity, and particulate organic carbon (POC) in driving Harmful Algal Bloom (HAB) dynamics in Lake Erie. The multivariate regression models developed to predict chlorophyll-a (Chl-a) and total suspended solids (TSS) demonstrated strong predictive performance (R\({}^{2}\) = 0.973 \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Unstandardized Coefficients** & **Standard Error (SE)** & **t** & _p_**-Value** \\ \hline \hline
**Model 1** & & & & \\ \hline Constant & 0.004 & 0.000 & 7.906 & \(<\)0.0001 \\ Turb & 0.113 & 0.038 & 2.963 & 0.0032 \\ TP & \(-\)0.035 & 0.012 & \(-\)2.837 & 0.0048 \\ POC & \(-\)3.453 & 0.076 & \(-\)45.688 & \(<\)0.0001 \\ PON & 4.115 & 0.091 & 45.380 & \(<\)0.0001 \\ TSS & \(-\)0.030 & 0.023 & \(-\)1.319 & 0.1879 \\ \hline \hline
**Model 2** & & & & \\ \hline Constant & 0.007 & 0.001 & 6.583 & \(<\)0.0001 \\ Turb & 1.477 & 0.037 & 40.445 & \(<\)0.0001 \\ TP & 0.196 & 0.023 & 8.392 & \(<\)0.0001 \\ POC & 2.125 & 0.350 & 6.077 & \(<\)0.0001 \\ PON & \(-\)2.705 & 0.415 & \(-\)6.521 & \(<\)0.0001 \\ Chl-a & \(-\)0.126 & 0.095 & \(-\)1.319 & 0.1879 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Estimates of coefficients for multivariate regression models. for Chl-a and 0.958 for TSS), indicating that these environmental variables account for most of the variance in bloom-related water quality parameters. However, caution must be taken in interpreting these relationships as causal. While several predictors showed strong statistical associations with the response variables, high correlation does not imply direct causation. Variables such as turbidity, PON, and POC likely act as recording indicators, reflecting an already developing bloom with increased organic matter and microplankton biomass. This interpretation is consistent with the current ecological literature on bloom progression and detection [69, 70]. Total phosphorus (TP), on the other hand, can be regarded as a causal driver, as it is a well-known trigger for cyanobacterial growth [71, 72] and can be actively managed through watershed-scale interventions (e.g., improved wastewater treatment, erosion control). We recommend prioritizing TP reduction in long-term nutrient management strategies [73]. Conversely, real-time increases in turbidity, PON, and POC should be used as triggers for short-term response actions, such as beach closures, public health notifications, or intensified field monitoring. Given the temporal resolution of the data and the nature of the predictors, the developed models are best suited for short-term forecasting, typically within a 1-2 week horizon. This aligns with the early warning needs of local environmental agencies and allows for targeted intervention during bloom initiation. Despite these promising results, it is important to acknowledge certain limitations. First, multicollinearity was present among some predictors (e.g., PON, POC, Turbidity), as indicated by high variance inflation factor (VIF) values. These variables were retained based on their ecological relevance and predictive performance. While multicollinearity may inflate coefficient variance, it does not necessarily compromise predictive validity in applied environmental modeling [62, 63, 64]. Second, the spatial scope of the data was limited to NOAA stations in the western basin. While the model may be transferable to other eutrophic lakes, regional hydrological differences--such as depth, stratification, or flow--may affect its generalizability and require local calibration. For instance, the shallow morphology and high sediment resuspension of western Lake Erie may amplify the effects of turbidity compared to deeper lakes [74, 75]. Third, key hydrometeorological factors, such as wind speed, precipitation, precipitation, and temperature anomalies, are known to influence nutrient resuspension and bloom dynamics [76]. These variables were not included here due to limited integration with in situ water quality datasets.