## 3 Materials and Methods
### Methods  
In this study, three different models--linear regression [33], random forest [34], and XGBoost [35]--were comparatively analyzed.  
In linear regression, a regression equation is modeled using a linear prediction function, and parameters are estimated through data, which is referred to as a regression equation. Therefore, if the ultimate goal is to predict the value, a predictive model can be constructed using linearity.  
Random forest is a non-linear regression model that is an ensemble technique based on decision trees. Multiple instances of training were performed by extracting a certain number of samples of training data with bootstrap sampling, a method of extracting data a given number of times. Prediction values are then derived for each model, and the final prediction value is determined based on the average value of all derived prediction values. Random forest is easy to use and was selected as a candidate model, as it is proficient in dealing with multiple independent variables.  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline Independent variables & Day, season, city/province code, highest temperature, average cloudiness, precipitation level, sulfurous acid gas level, carbon monoxide level, ozone level, nitrogen dioxide level, and micro dust level \\ \hline \hline Dependent variables & Number of acute bronchitis patients Number of common cold patients Number of rhinitis and tonsillitis patients Number of inner ear inflammation patients Number of chronic bronchitis patients Number of intestinal inflammation patients Number of influenza and pneumonia patients Number of eczema and dermatitis patients Number of chicken pox patients Number of conjunctivitis patients Number of brain disease patients \\ \hline \hline Older adults (aged 65 years and over) & Number of acute bronchitis patients Number of eczema and dermatitis patients Number of chronic bronchitis patients Number of rhinitis and tonsillitis patients Number of brain disease patients \\ \hline \hline \end{tabular}
\end{table}
Table 2: Independent and dependent variables for children and older adults.  
XGBoost is one of the machine-learning techniques used for predicting various diseases in recent years [36] and has the advantage of being able to perform both non-linear and linear regression. XGBoost is a model that improves the performance and speed of gradient boosting by applying the boosting technique to the decision tree model. The boosting technique combines weak predictive models to create a strong predictive model. After data are predicted with a weak predictive model, the error from this process is trained on another weak predictive model. This process is repeated to reduce error and is applied sequentially. Hence, model t is determined by the error from model t-1. Ultimately, the model is trained by finding the weight that minimizes the loss between the actual value and the predicted value.  
Hyperparameters refer to values set by the user. However, there is a limit to repeated testing due to the user changing the values continuously, and it is difficult to intuitively observe the best value. GridSearchCV allows the user to determine the optimal hyperparameter. If the user inputs values that can be input into the hyperparameter, GridSearchCV determines the best parameter through the combination of parameters.