## 3 Results
### Inertia Estimation
#### 3.4.2 Stepwise Regression  
In addition to manual definition, stepwise regression is an algorithmic approach for defining approximation formulae. Starting from a basic model that contains variables and interactions up to a certain degree, variables that do not contribute significantly to the accuracy of the description are removed. For the considerations of a model that contains  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**All Vehicles**} \\ \hline
**Parameter** & **Control Variables** & **Correlation Coefficient** & \(p\)**-Value** \\ \hline Wheel base: 1 & Track width: t & 0.75 & \textless{}0.001 \\ Track width: t & Wheel base: 1 & \(-0.25\) & 0.136 \\ Empty mass: \(\text{m}_{\text{e}}\) & Driver mass: \(\text{m}_{\text{d}}\) & 0.69 & \textless{}0.001 \\ Driver mass: \(\text{m}_{\text{d}}\) & Empty mass: \(\text{m}_{\text{empty}}\) & 0.42 & 0.009 \\ COG-Position: \(\text{l}_{\text{r}}\) & Wheel base: 1 & \(-0.22\) & 0.195 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Partial correlation coefficients and \(p\)-values.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Approximation** & **Source** & **Comments** \\ \hline \(J_{2}=0.25 ml^{2}\) & [24] & \\ \(J_{2}=ml_{\text{r}}l_{\text{r}}\) & [24] & \\ \(J_{2}=0.1478 mLL\) & [11] & Passenger cars with front wheel drive \\ \(J_{2}=0.4622 mtl\) & [11] & SUV \\ \(J_{2}=0.1525 mL\) & [11] & Vans \\ \(J_{2}=0.95\ ml^{2}/4\) & [9] & Can be determined from the diagram of yaw inertia. \\ \hline \hline \end{tabular}
\end{table}
Table 7: Formulae for estimating the yaw moments of inertia of passenger cars.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**All Vehicles**} & \multicolumn{3}{c}{**Trikes**} & \multicolumn{3}{c}{**Velombiles**} \\  & & **[_in = 39_]** & & **[_in = 9_]** & **[_in = 30 (27)_]** \\ \hline
**Nr.** & **Model** & **Adj. R2** & **RMSE** & **Adj. R2** & **RMSE** & **Adj. R2** & **RMSE** \\ \hline
1 & \(J_{2}=c_{1}(m_{e}+m_{d})l^{2}\) & 0.74 & 3.64 & 0.72 & 2.01 & 0.63 (0.73) & 3.36 (3.04) \\
2 & \(J_{2}=c_{1}(m_{e}+m_{d})l^{2}\) & 0.75 & 3.60 & 0.87 & 1.36 & 0.71 (0.76) & 2.97 (2.85) \\
3 & \(J_{2}=c_{1}(m_{e}+m_{d})lL\) & 0.88 & 2.49 & 0.86 & 1.38 & 0.76 (0.75) & 2.75 (2.88) \\
4 & \(J_{2}=c_{1}(m_{e}+m_{d})l_{\text{r}}\) & 0.66 & 4.19 & 0.68 & 2.14 & 0.67 (0.68) & 3.18 (3.28) \\
5 & \(J_{2}=c_{1}m_{e}l^{2}+c_{2}m_{d}\) & 0.77 & 3.42 & 0.90 & 1.16 & 0.83 (0.86) & 2.28 (2.20) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Yaw inertia approximation models and results. Values in parentheses apply to the velombiles without the four-wheeled vehicle.  
all variables, their powers up to the third degree and interactions up to the third degree (e.g., \(\chi_{1}\), \(\chi_{1}\), \(\chi_{1}\), \(\chi_{1}\), \(\chi_{1}\), \(\chi_{1}\), \(\chi_{2}\), \(\chi_{2}\), \(\chi_{1}\), \(\chi_{2}\), \(\chi_{3}\),...) are used. The value of the adjusted R\({}^{2}\) serves as a quality criterion. Based on the algorithm, an interaction of two variables is only included in the model if these two parameters are also present in linear form in the model [34]. For the models, a physically meaningful description does not necessarily result on the basis of the stepwise regression. Thus, the formulae describe the observations, but do not fundamentally imply physical relationships or causalities. Table 10 shows the results of the stepwise regression for the group of all vehicles for different numbers of parameters and with and without interception terms.  
Stepwise regression thus also led to equations that essentially provided a good approximation of the observed values. Compared with the manually created models, however, there existed the disadvantage that the syntax was less flexible and interactions were only taken into account if the basic variables were also part of the approximation. Furthermore, parameter results partly contradicted the physical background. In order to achieve comparably good approximations such as the manually created formulae, considerably more parameters were necessary here.