## 3 Methodology
### Statistical and Machine Learning Methods
#### 3.2.4 Regression Models  
MLR  
MLR is a statistical technique that models the relationship between a dependent variable (e.g., air pollutant concentration) and multiple independent variables (e.g., WS, temperature, RH, RainF). The model assumes a linear relationship and is expressed as:  
\[\hat{Y}=\alpha+\beta_{1}WS+\beta_{2} TEMP+\beta_{3}RH+\beta_{4}RainF \tag{1}\]  
where \(\hat{Y}\) represents the dependent variable (air pollutant concentration), while the independent variables--WS, TEMP, RH, and RainF--denote WS, temperature, RH, and RainF, respectively. \(\alpha\) is the intercept, and the \(\beta\) coefficients represent the regression parameters of the model. MLR provides insights into the linear contribution of each meteorological parameter to pollutant levels, enabling a straightforward interpretation of results. However, it may struggle to capture complex non-linear interactions. Random Forest (RF) Regression  
The random forest (RF) algorithm, first introduced by [PERSON] [28], is an ensemble learning method that improves decision trees through bagging (bootstrap aggregation) and random feature selection. It constructs multiple decision trees from bootstrapped subsets of the data, where each tree is trained using a randomly selected subset of features at each split. For classification, predictions are determined by majority voting, while for regression, they are averaged. This approach reduces overfitting, enhances generalization, and is robust to high-dimensional data. However, RF can be computationally expensive and less interpretable than single decision trees. RF's strength lies in its ability to handle large datasets, noisy features, and missing values while maintaining high accuracy. It inherently performs feature selection by considering only a subset of features at each split, reducing bias from dominant variables. Despite its advantages, RF requires careful tuning of hyperparameters like the number of trees and maximum depth to balance performance and efficiency. Its parallelizable nature makes it scalable, though inference can be slower due to the ensemble structure. In addition, RF regression is a powerful machine learning algorithm that excels at capturing complex, non-linear relationships within datasets. Unlike traditional models such as MLR, RF does not assume a linear dependency between independent and dependent variables, making it particularly suited for environmental studies. These studies often involve intricate interactions between meteorological factors and air pollutant concentrations, which RF can model effectively. At its core, RF operates as an ensemble method, leveraging the combined outputs of multiple decision trees to produce accurate and reliable predictions. This process begins with the random selection of subsets from the dataset, a technique known as bagging,Each decision tree in the ensemble is trained on a different subset, ensuring diversity and robustness. Additionally, at each split within a tree, a random subset of features is selected to prevent over-reliance on specific variables, further enhancing the model's balance and generalizability [29]. Each decision tree is constructed by recursively splitting the data based on the feature that minimizes prediction error at each node. The trees are grown until a predefined stopping criterion, such as maximum depth or minimum node size, is met. Once all trees are built, their outputs are aggregated, typically by averaging in regression tasks, to generate final predictions. This ensemble approach reduces variance and improves the model's ability to generalize to new data, making it particularly effective for datasets with high variability and complex relationships. To address the common issue of overfitting, RF introduces randomness at multiple stages of its process. This, combined with its ensemble structure, significantly reduces the risk of overfitting, even when working with noisy or incomplete datasets. Another valuable feature of RF is its ability to evaluate the importance of input variables.