# A Predictive Method for Temperature Based on Ensemble EMD with Linear Regression
## 5 Experimental Procedures
### Assessment Standard  
Various assessment standards exist for assessing models, each of which is tailored to specific objectives. Common tasks include pairing, regression, dual clustering, ranking, classification, and clustering. To ensure the accurate and efficient evaluation of the proposed method, the MAE, R\({}^{2}\), and RMSE were chosen as assessment standards to measure prediction errors and evaluate the effectiveness of the model. The calculation formula for the mean absolute error (MAE), shown in Equation (36), represents the mean absolute error value. This metric provides a better reflection of the true state of predicted value inaccuracies. \[MAE\left(\widetilde{y}\!,\!y\right)=\frac{1}{m}\!\sum_{k=1}^{m}|y_{k}- \widetilde{y_{k}}| \tag{36}\]  
In Equation (36), the symbols \(\widetilde{y}\) and \(y\), respectively, denote the predicted and real values from the test dataset. Additionally, \(m\) indicates the length of the test data sequence. R square (R\({}^{2}\)) is a metric used to gauge a model's predictive ability, and is calculated as the ratio of the sum of squares for regression to the sum of squares for total deviation. A higher R\({}^{2}\) value indicates a more accurate and effective model, with 1 being the best score possible. Models with an R\({}^{2}\) value over 0.9 are generally considered superior, while negative values suggest very poor performance, indicating predictions worse than the average. The calculation formula for R\({}^{2}\) can be found in Equation (37). \[R^{2}\left(\widetilde{y}\!,\!y\right)=1-\frac{\sum_{k=1}^{m}|y_{k}-\widetilde{ y_{k}}|^{2}}{\sum_{k=1}^{m}|y_{k}-\overline{\overline{\overline{y}}_{k}}|^{2}} \tag{37}\]  
The symbols \(\widetilde{y}\), \(\overline{\overline{y_{k}}}\), and \(y\) in Equation (37) correspond to the predicted value, average value, and true value from the test dataset, respectively. Meanwhile, \(m\) denotes the length of the test data. The formula used to compute the mean value \(\overline{\overline{y_{k}}}\) is detailed in Equation (38). \[\overline{\overline{y_{k}}}=\frac{1}{m}\!\sum_{k=1}^{m}y_{k} \tag{38}\]The calculation formula for the widely used evaluation index, the root mean square error (RMSE), alternatively referred to as the standard error, is depicted in Equation (39). This metric is particularly responsive to exceptionally small or large errors within test datasets. \[RMSE\left(\widetilde{y},y\right)=\sqrt{\frac{1}{m}{\sum_{i=1}^{m}{\left({y_{i}- \widetilde{y_{i}}}\right)}^{2}}} \tag{39}\]  
In Equation (39), the symbols \(y\) and \(\widetilde{y}\) denote the sequences of real and predicted values for the test data, respectively. Additionally, \(y_{k}\) and \(\widetilde{y_{k}}\) depict the actual and forecasted values, respectively, for the \(i\)-th element within the test data sequence. The symbol \(m\) signifies the length of the test dataset sequence. Incorporating the reviewers' suggestions, we utilized four metrics--AIC, SBIC, HQIC, and AICc--to analyze the experimental results of the model. This approach allows for a better evaluation and selection of models, as well as a balanced consideration of the models' fit and complexity. Although these four criteria are commonly used to evaluate small sample regression models, they can also be applied here. A brief introduction to these four criteria is provided below. The AIC (Akaike information criterion), depicted in Equation (40), is a commonly used model selection criterion that is designed to balance a model's fit and complexity. By minimizing the AIC value, the best model can be chosen, with a smaller AIC typically indicating a better model. This criterion is particularly important when evaluating the fit of a model, especially in cases of small sample sizes. \[AIC=2*(k-ln(L)) \tag{40}\]  
In Equation (40) and the subsequent equations, Equations (41)-(43), \(k\) is the number of parameters of the model and \(L\) is the maximum likelihood estimation of the model.