*3.5. Statistical Indexes*

The performances of DTR, FFANN-BP and RFR are evaluated by using four commonly used statistics indices, which are the coefficient of determination (*R*2), root mean square error (RMSE), mean absolute error (MAE), and Mean Absolute Percentage Error (MAPE) between the predicted and observed air pollutant concentrations. The indices are defined as [34].

$$R^2 = \frac{\sum\_{i=1}^n (p\_i - \sigma)^2}{\sum\_{i=1}^n (o\_i - \sigma)^2} \tag{13}$$

$$RMSE = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} (o\_i - p\_i)^2} \,\tag{14}$$

$$MAE = \frac{1}{n} \sum\_{i=1}^{n} |o\_i - p\_i|\_{\prime} \tag{15}$$

$$MAPE = \frac{1}{n} \sum\_{i=1}^{n} |\frac{o\_i - p\_i}{o\_i}|\,\tag{16}$$

where *oi*, *pi*, *o*¯, *p*¯ and *n* are the observed, predicted and the mean of observed and predicted concentrations and the number of observations, respectively. The coefficient of determination indicates the closeness between the overall trend of the predicted value of the model and the observed value. The mean absolute error and root mean square error reflect the deviation of the observed value from the predicted value. The higher the value of *R*2, the better the model performance. Correspondingly, the lower the value of the RMSE, MAE and MAPE, the better the model acquired.
