## 3 System Model
### Traffic Data Preprocessing Model  
In order to reduce the computational burden caused by abundant variables, the model needs to filter the variables firstly. In accordance with the difference in effect, whether variables have a good impact to forecast traffic flow data, the model filters some useless parameters and retains some effective variables. We assume a matrix \(Q\) as the presentation of collected traffic flow data, which is denoted as follows:  
\[Q_{s\times z}= \begin{bmatrix}q_{11}&q_{12}&\dots&q_{1z}\\ q_{21}&q_{22}&\dots&q_{2z}\\ \vdots&\vdots&\ddots&\vdots\\ q_{s1}&q_{s2}&\dots&q_{sz}\end{bmatrix} . \tag{1}\]  
Here, the columns of \(Q\) denote characters of observed traffic flow data, e.g., the real-time speed, the number of lanes, etc. The number of collected characters is \(z-1\), and the last column records observed traffic flow values. The rows of \(Q\) denote the traffic flow data in different times slots. The number of traffic flow data collection time slots is \(s\). So as to find the conclusive variables, the paper chooses the Multiple Regression Analysis method [21] to analyze the numerous variables. Multiple regression analysis is the method to research the linear correlation between multiple independent variables and dependent variables. The formula of the multiple regression model is as follows:  
\[\widehat{Q_{z}}=\widehat{\beta_{0}}+\sum_{i=1}^{z}(\widehat{\beta_{i}} \widehat{Q_{i}})+\delta. \tag{2}\]  
Here, \(\widehat{Q_{z}}\) is the dependent variables traffic flow. \(\widehat{Q_{i}}\) is the total vectors corresponding to each variable, \(\widehat{\beta_{i}}\) is the regression coefficient, and \(\delta\) is the disturbance term. Since the dependent variable to be regressed is the continuous variable data, the Ordinary Least Squares (OLS) model [22] is suitable to evaluate the multiple regression model, whose representation is as follows:  
\[L=\sum_{i=1}^{z}(\widehat{Q_{i}}-\widehat{Q})^{2}, \tag{3}\]  
where \(\widehat{Q_{i}}\) is real traffic data, and \(\widehat{Q}\) is the result calculated by regression. The purpose of the OLS model is to minimize \(L\), making the regression formula match the real traffic data as much as possible. Based on multiple regression, we can obtain an equation for the minimum value tested by OLS model. The selected variables need to use the Joint Hypotheses Test [23] to test the significance of the overall regression equation. The test aims to evaluate whether the overall interpretation of the dependent variable by all independent variables is appropriate. The Joint Hypotheses test is used to analyze statistical models that use more than one parameter to determine whether all of the parameters in the model are suitable for estimating the parent variable. The statistical value of the F-test can be calculated to obtain the statistic value by  
\[F=\frac{MSR}{MST}=\frac{\frac{SSR}{DP_{R}}}{\frac{SST}{DP_{T}}}, \tag{4}\]  
where \(DF_{R}\) is the degrees of freedom for SSR (Regression Sum of Squares), and \(DF_{T}\) is the degrees of freedom for SST (Sum of Squares for Total). The calculated F-value can be obtained by checking the table for its corresponding \(P_{F}\). \(P_{F}<0.05\) means that the original hypothesis is rejected and not all coefficients are 0, so the regression is significant. Otherwise, it means that we do not reject the original hypothesis, i.e., all coefficients are 0 and the model is not reasonable. After satisfying the Joint Hypotheses test, the goodness of fit of the overall regression equation needs to be tested. It is judged on the basis of R-squared, which is denoted as follows:  
\[R^{2}=1-\frac{SSE}{SST}=1-\frac{\sum_{i=1}^{z}(Q_{i}-\widehat{Q})^{2}}{\sum_{ i=1}^{z}(Q_{i}-\overline{Q})^{2}}, \tag{5}\]  
where \(\overline{Q}\) is mean value of real traffic data. The model fits better with a larger \(R^{2}\) value. Due to the redundance of matrix \(Q\), the collected characters of traffic flow should be selected and filtered based on R-squared.