# Multi-Factor Highway Freight Volume Prediction Based on Backpropagation Neural Network
## 4 Case Analysis of Highway Freight Volume Forecasting Based on Neural Network
### Multicollinearity Test  
(1) Multicollinearity test  
Before any modeling work, a more thorough investigation should be conducted on the relationship between the input features and how they affect the output variance to avoid the selected variables being independent and having the same distribution, which may lead to wrong predictions due to problems such as multicollinearity or heteroscedasticity.  
The VIF (variance inflation factor) is an indicator used to measure the severity of multicollinearity between independent variables. When the VIF value is greater than 10, we usually think that there is a serious multicollinearity problem. Multicollinearity means that there is a high degree of correlation between independent variables, which may lead to inaccurate parameter estimation of the regression model, thus affecting the predictive ability and explanatory ability of the model.  
The variance inflation factor of the regression coefficient can be expressed as:  
\[\text{VIF}_{i}=1/1-R_{i}^{2} \tag{4}\]  
The square indicates the coefficient of determination obtained by fitting the regression equation with the first variable as the dependent variable and the remaining independent variables.  
The larger the VIF value, the stronger the correlation between the variable and the other independent variables.  
Tolerance and VIF are two important indicators in collinearity diagnosis, and they are reciprocal relationships. Tolerance greater than 0.1 is usually indicates no collinearity problem. Tolerance and VIF can be selected to judge collinearity in the study, but in general, describing the VIF value is more common because it is more intuitive, and when the VIF value is large, the tolerance value will be small and not easy to observe. They are generally used to calculate the correlation between the independent variables in the multiple linear regression model, so it is necessary to ensure the applicability and accuracy of the model.  
Using SPSS for linear regression analysis, the data can be obtained and are presented in Table 3.  
The purpose of multicollinearity regression analysis is to predict dependent variables through independent variables. From the table, we can see that except for the tolerance of road diesel consumption greater than 0.1 and VIF less than 10, other independent variables do not meet the requirements, and the collinearity between independent variables is more serious.  
The DW (Durbin-Watson) test is often used to detect whether the residual has autocorrelation. The D-W value is between 0-4, and the closer it is to 2, the greater the possibility that the observed values are independent of each other. Using SPSS for analysis, the following Table 4 can be obtained.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & \multicolumn{2}{c}{**Colinearity Statistics**} \\ \hline (constant) & allowance & VIF \\ Road diesel consumption & 0.704 & 1.42 \\ Population & 0.016 & 61.654 \\ Highway freight volume turnover & 0.03 & 32.914 \\ Gross domestic product & 0.003 & 369.396 \\ Highway mileage & 0.05 & 20.078 \\ Gross domestic product by road & 0.002 & 454.474 \\ Number of road operating trucks & 0.071 & 14.067 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Collinearity statistics.  
From the table, we can see that the value of DW is 1.762, which is very close to 2, and the observation values are more likely to be independent of each other.  
Reduction in multicollinearity  
By gradually excluding the factors with strong influence of multicollinearity, and then conducting multiple multicollinearity tests through SPSS, the collinearity Table 5 and independent test Table 6 can finally be obtained.  
Finally, we choose five independent variables: road diesel consumption, road mileage, road operating truck ownership, gross domestic product, and Chinese freight volume as the dependent variable.