## 5 Discussion  
It is not necessary to use all metrics when evaluating the accuracy of a prediction result. As a matter of fact, one or two accuracy metrics are sufficient for evaluation. To determine the best option, clarifying the correlations between different accuracy metrics is an important issue. Figure 10 shows the correlation matrix of the seven accuracy metrics. In the correlation matrix, the Pearson correlation coefficient values were calculated using all evaluation results of the accuracy metrics (refer to Tables 3-6). Figure 9: Evaluation results of different group datasets using percentage-dependent metrics. The evaluation results of group 1 are minimum, and the evaluation results of group 2 are maximum. As can be seen from the correlation matrix, the correlation coefficients of any two metrics were greater than 0.95. This indicates that the accuracy metrics have strong correlations with each other. In detail, the correlation coefficient of R and R\({}^{2}\) was 0.99, the correlation coefficient of the MSE and RMSE was 1, the correlation coefficient of the MSE and MAE was 0.99, and the correlation coefficient of the MAPE and SMAPE was 0.99. Comparing the sensitivity of metrics is helpful to determine a suitable accuracy metric. In this study, the sensitivity of accuracy metrics was defined using the coefficient of variation (CV). The CV is a statistical measure of the dispersion of data points around the mean value. Higher CV values highlight results more sensitive to the predictions. The CV is illustrated by Equation (11):  
\[\text{CV}=\frac{\text{s}}{\text{u}} \tag{11}\]  
where s is the standard deviation and u is the mean value. According to the evaluation results of each metric (refer to Tables 3-6), the CV of each metric was calculated as shown in Figure 11. The CV values of R, R\({}^{2}\), MSE, RMSE, MAE, MAPE and SMAPE were 0.02, 0.04, 0.31, 0.16, 0.19, 0.20 and 0.20, respectively. For correlation-based metrics, R\({}^{2}\) is more sensitive to the prediction results. For scale-dependent metrics, the MSE is more sensitive than RMSE and MAE. That is why the MSE is the default evaluation metric in many machine learning algorithms. For percentage-dependent metrics, the sensitivities of the MAPE and SMAPE are the same. Based on the findings of this study, the proposed novel selection method of an appropriate accuracy metric for evaluating prediction results is as shown in Figure 12. First of all, it should be clarified that the purpose of this work was to evaluate the accuracy of a prediction or to compare the accuracy of different predictions. Figure 10: Correlation matrix of accuracy metrics. The purple line is the correlation line between two metrics, the number is the Pearson correlation coefficient value (refer to Figure 2). To evaluate the accuracy of a prediction result, it is necessary to clarify whether the scale of original data is clear or not. When the scale of original data is clear, both scale-dependent metrics and percentage-dependent metrics are options under the circumstances of results being without zero values in the actual values. Of these, the MAE is recommended from the scale-dependent metrics because the unit of the MAE is the same as the original data and easy to understand. The SMAPE is recommended as the appropriate metric of the percentage-dependent metrics. In comparison with the MAPE, the SMAPE places same penalty on both positive error and negative error. When the actual values are close to the true values, the MAE is recommended as the average value of the MAE. Figure 11: Coefficient of variations of each metric. Figure 12: Schematic diagram of the novel selection method for accuracy metrics (the \(\blacklozenge\) refers to the recommended metric for this case). values include zero values, only the scale-dependent metrics are available, and the MAE is therefore recommended. When the scale of original data is not clear, the percentage-dependent metrics are appropriate for evaluation.