## 2 ML Methodologies
### Supervised Learning
#### 2.1.2 Regression  
Regression belongs to the field of supervised ML and is primarily used for predicting continuous numerical values [75]. It is a statistical method that aims to understand the relationship between independent variables, denoted as X (input variables), and dependent variables, denoted as Y (continuous output). Regression plays a crucial role in developing prediction models within ML. In regression, the model is trained using a set of labeled data known as the training data. The training process involves finding the best-fitting line or curve that represents the relationship between the input variables and the continuous output. Once the model is trained, it can be used to make predictions on new, unlabeled data called the test data [15]. The model utilizes the learned patterns from the training data to estimate the output values for the test data. There are various regression methods available, each suited for different scenarios. However, regression can generally be classified into two main categories: simple linear regression and multiple regression [76]. **Simple linear regression** involves establishing a linear relationship between a single input variable and the output variable. The goal is to find a straight line that best fits the data points, minimizing the overall error or the vertical distance between the observed and predicted values [76]. **Multiple regression** involves predicting a dependent variable based on two or more independent variables. It assumes a linear relationship between the variables, meaning that the change in the dependent variable is assumed to be proportional to the change in the independent variables [76]. **Nonlinear regression** is used when the relationship between the dependent and independent variables is not linear. It models relationships that may follow curves, exponential growth, or other nonlinear patterns [77]. Regression analysis provides valuable insights into the relationships between variables and helps in making predictions or estimating values for new observations. Downward, Table 5 provides a concise overview of diverse linear regression algorithms. These methods are fundamental tools for modeling linear relationships between variables, making them valuable in numerous statistical and machine learning applications. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Algorithm** & **Description** & **Applications** & **Ref.** \\ \hline \multirow{6}{*}{Hydrological modeling} & Support vector machines (SVMs) & SVM-based modeling for classification. & Flood risk assessment based on historical data. & [66] \\ \cline{2-5}  & Decision trees & Tree-based models for classification. & Predicting river flow patterns in watersheds. & [67] \\ \cline{2-5}  & Random forest & Ensemble of decision trees for improved accuracy. & Forest cover classification for water conservation. & [68] \\ \cline{2-5}  & Gradient boosting & Ensemble method for boosted decision trees. & Estimating groundwater contamination sources. & [69] \\ \hline \multirow{6}{*}{Water quality analysis} & K-nearest neighbor (KNN) & Classify data based on neighboring points. & Water quality monitoring using sensor networks. & [70] \\ \cline{2-5}  & Neural networks & Deep learning models with multiple layers. & River pollution detection from satellite imagery. & [71] \\ \cline{2-5}  & Gaussian naïve Bayes & Probabilistic classifier based on Bayes’ theorem. & Forecasting of lake water quality and algal bloom prediction in reservoirs. & [72] \\ \cline{2-5}  & Kernel methods & Nonlinear classification with kernel functions. & Soil moisture prediction for agricultural planning. & [73] \\ \hline Data-driven analysis & Bayesian networks & Probabilistic graphical models for classification. & Hydrological risk assessment in watersheds. & [74] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Nonlinear classification algorithms for water resources management. In Table 6, we correlate various water management methodologies with distinct linear regression techniques.