# Speed-Flow-Geometric Relationship for Urban Roads Network
## 3 Methodology
### Model Development Using Multilinear Regression Analysis (MRA)  
As aforementioned, the speed-flow-geometric relationship models between the independent variable (ATS) and dependent variables (TV, TCSD, AccessD, IntersD, and RTD) for seven surveyed urban road groups were developed using the multilinear regression analysis. Four multilinear regression analysis steps were used to select the final model. First, multilinear regression analysis dealt with the model estimation where all possible independent variables were included in the regression analysis to develop the first estimation model. Herein, all independent variables were evaluated and tabulated. In the first model estimation, the statistical regression results included the F-test, R\({}^{2}\), _t_-test, and standard errors. The significant models were estimated using the F-test value [45; 53; 54]. When the _p_-value of the F-test was below 0.05 (the confidence level is 95% for the entire model development), it was declared as statistically significant. Second, multilinear regression analysis involved the model elimination wherein the backward elimination was performed for all independent variables listed in the previous step. This elimination was carried out using the _t_-test of each variable wherein any variable with _p_-value above or equal to 0.05 (\(\geq\)0.05) for the _t_-test was removed from the regression. This process was repeated until all the independent variables confirmed that they have a significant impact on average travel speed (ATS) based on their _t_-test (_p_-value \(<\) 0.05). Third, multilinear regression analysis entailed with the model verification wherein the assumption rules for the residuals of the regression as well as the multi-collinearity condition between the independent variables was applied. In this step, the residual satisfied the assumptions test, such as linearity,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group No.** & **Cross-Sectional Parameters Condition of the Surveyed Urban Roads (SUR)** & **Number of** & **Road’s Group Proportion** \\  & **Groups (Group Symbol)** & **SUR in Group** & **(\%)** \\ \hline
1 & No Median, One Lane Number, Low Side Friction [M0, NL1, SF0] & 37 & 18.78 \\ \hline
2 & No Median, One Lane Number, High Side Friction [M0, NL1, SF1] & 22 & 11.17 \\ \hline
3 & No Median, Two Lane Number, Low Side Friction [M0, NL2, SF0] & 17 & 8.63 \\ \hline
4 & No Median, Two Lane Number, High Side Friction [M0, NL2, SF1] & 25 & 12.69 \\ \hline
5 & Have Median, Two Lane Number, Low Side Friction [M1, NL2, SF0] & 36 & 18.27 \\ \hline
6 & Have Median, Two Lane Number, High Side Friction [M1, NL2, SF1] & 37 & 18.78 \\ \hline
7 & Have Median, Three Lane Number, Low Side Friction [M1, NL3, SF0] & 21 & 10.66 \\ \hline
8 & Have Median, Three Lane Number, High Side Friction [M1, NL3, SF1] & 2 & 1.02 \\ \hline
9 & No Median, Three Lane Number, Low Side Friction [M0, NL3, SF0] & 0 & 0 \\ \hline
10 & No Median, Three Lane Number, High Side Friction [M0, NL3, SF1] & 0 & 0 \\ \hline
11 & Have Median, One Lane Number, Low Side Friction [M1, NL1, SF0] & 0 & 0 \\ \hline
12 & Have Median, One Lane Number, High Side Friction [M1, NL1, SF1] & 0 & 0 \\ \hline  & & 197 & 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Grouping the surveyed urban roads based on the cross-sectional parameters.  
homoscedasticity and independence. Furthermore, the model verified the multicollinearity value between the independent variables using the VIF index. Some literature reports revealed that VIF must be below 10 (between any two independent variables) [45; 54; 55]. Fourth, multilinear regression analysis dealt with the model validation that was conducted by comparing the calculated average travel speed (ATS) from the developed models with the estimated average travel speed (ATS) from the moving observer method (MOM) for the new selected urban roads segment. This comparative evaluation was performed using the t-paired test between the mean values of each average travel speed (ATS) group.