# Water Quality Evaluation and Analysis by Integrating Statistical and Machine Learning Approaches
## 1 Introduction
Concurrently, machine learning revolutionizes environmental monitoring by enabling more effective enforcement of regulations. For instance, a data-driven approach to target high-risk facilities for water-pollution inspections can dramatically increase the detection of violations [10]. The study from [13] introduces the Synth Ridge Framework (SRF), a composite machine learning model combining feature engineering and an ensemble of gradient-boosting decision trees (XGBoost, LightBoost, CatBoost) to improve the accuracy of chlorophyll-a (Chla) concentration retrieval in optically complex water bodies. By enhancing input features and leveraging ensemble learning, SRF significantly outperforms baseline models in both accuracy and robustness, showing strong generalization across datasets from different satellite sensors. This study introduces a novel integration of a diagnostic statistical technique with a hybrid machine learning framework comprising Decision Tree Regression (DTR), Autoregressive Integrated Moving Average (ARIMA), and Random Forest (RF). While these models have individually been applied in previous water quality research, their combined use in a unified framework to address both temporal forecasting and categorical classification while maintaining model interpretability is relatively underexplored. In particular, ARIMA is not utilized as a general predictor but as a tool to model the temporal structure of individual water parameters, while DTR and RF provide explainability and classification capability. The methodological novelty lies in the comprehensive evaluation pipeline, which includes residual analysis, diagnostic and assumption testing, feature importance analysis, learning curve analysis, and principal component analysis (PCA). This integrative approach bridges the gap between statistical rigor and practical machine learning deployment, offering a more robust and interpretable framework for real-time environmental monitoring. Based on this innovation, the study aims to do the following:  
1. Develop and evaluate a hybrid machine learning framework that integrates statistical diagnostics for enhanced WQI prediction and classification. 2. Identify and quantify the most influential water quality parameters affecting WQI using feature importance analysis. 3. Assess model reliability and generalization through residual analysis, diagnostic testing, and learning curve analysis. 4. Reduce data dimensionality while preserving variance using PCA for computational efficiency and pattern discovery. The research is structured into five sections. Section 1 provides an introduction to the study. Section 2 outlines the theoretical background on statistical and machine learning approaches. Section 3 describes the methodology for identifying the data collection area and details the procedural steps for each statistical analysis, including feature importance, assumption and diagnostic tests, learning curve analysis, and PCA. Section 4 presents the results and discussion. Finally, Section 5 concludes the study and offers suggestions for future work.