# Multi-Factor Highway Freight Volume Prediction Based on Backpropagation Neural Network
## 4 Case Analysis of Highway Freight Volume Forecasting Based on Neural Network
### Analysis of Output Results  
* The training set prediction results are compared with the test set prediction results, as shown in Figure 8.  
The comparison of the prediction results of the training set is as follows: RMSE = 78,755.4264. The comparison of the prediction results of the test set is as follows: RMSE = 35,812.9792. We can see that the difference between the two is large. The data show that the model performs better in the training set and performs relatively poorly in the test set.  
The analysis and comparison of training set and prediction set fitting graph is as shown in Figure 9.  
From the figure, we can see that in the predicted value image of the training set and the prediction set, in the fitting relationship between the scatter points of the predicted value and the real value of the training set, and the prediction set and the linear fitting line, we can compare and observe that the fitting effect of the training set and the test set is very significant and the scatter points are in or very close to the linear fitting line, which indicates that the model is very accurate in the prediction results of the training set.  
Output analysis of the prediction results of the training set and test set. The prediction results of the training set and the test set are shown in Table 8.  
Figure 8: Comparison of training set prediction results and test set prediction results.  
Figure 9: Comparison diagram of training set and prediction set fitting.  
The training set R\({}^{2}\) is 0.99424, and the test set R\({}^{2}\) is 0.99776, which are very close to 1, indicating that the model fits well in training. The MAE of the training set is 52,617.2825, and the MAE of the test set is 32,936.508. The MAE of the test set is lower, indicating that the average absolute value of the prediction error is smaller and the prediction is more accurate. The MBE of the training set is \(-\)20,266.4305, indicating that the average predicted value of the model on the training set is smaller than the true value. The MBE of the test set is 2942.7318, indicating that the average predicted value of the model on the test set is larger than the true value. The RMSE of the training set is 78,755.4264, and the RMSE of the test set is 35,812.9792. The RMSE of the test set is much smaller than that of the training set, which again indicates that the model has better prediction performance on the test set. Based on the above analysis, the following conclusions can be drawn: the model performs well on the training set but performs better on the test set.  
Analysis and forecast of freight volume in 2019-2021. The forecast results of China's freight volume in 2019-2021 are shown in Table 9.  
We use the data from 1997 to 2013 as the training set, and select the data from 2014 to 2018 as the test set to predict the freight volume in China from 2019 to 2021. It is predicted that the freight volume of China's highways in 2019 will be 38,378.47547 million tons. In 2020, the freight volume of China's highways will be 3,968,614.472 million tons. The actual freight volume of China's highways will be 3,435,480 million tons in 2019. In 2020, China's road freight volume will be 3,426,413 million tons, and in 2021, China's freight volume will be 3,913,889 million tons. It can be seen from the comparison that the predicted Chinese road freight volume from 2019 to 2021 is higher than the actual Chinese road freight volume.