## 4 Results and Discussion
### Estimation and Verification Results of Inverted Linear Model  
For the inverted linear model, Formula (2) for \(\mathrm{X_{i}}=\{\mathrm{X_{1}},\ldots,\mathrm{X_{8}}\}\), the results of parameter estimation are presented in Table 6.  
The constructed linear inverse model was verified at the significance level \(\alpha=0.05\). The model's coefficient of determination is \(\widetilde{\mathrm{R}^{2}}=0.961\) (coefficient of convergence \(\varphi^{2}=2.8\%\)). The model explains 96.1% of the variation in the studied trait, this indicates a good fit of the model to the empirical data. The significance of the regression coefficients was tested, and we formulated hypotheses for a linear model. The F statistic, with the null hypothesis being true, has a Snedecor F distribution with 8 degrees of freedom of the numerator and 20 degrees of freedom of the denominator. The empirical value of the statistic is F = 86.598, and the corresponding critical level of significance F = 8.01 \(\times\) 10\({}^{-14}\). The level is less than the accepted significance level \(\alpha=0.05\). We reject hypothesis H\({}_{0}\) in favor of H\({}_{1}\). There is no basis for rejecting the hypothesis that brake pad wear depends on at least one of the variables \(\mathrm{X_{i}}=\{\mathrm{X_{1}},\mathrm{X_{2}},\ldots,\mathrm{X_{8}}\}\). For each coefficient of the regression model, we hypothesize as for a linear model. The empirical values of the t-Student's statistic and the corresponding values of the critical level of significance (\(p\)-value) are shown in Table 6. No basis for rejecting the hypothesis that the  
Figure 2: Geometric interpretation of the linear model (21). \(\mathrm{Y_{1}}\)—Period of exploitation of the brake pads [km]; \(\mathrm{X_{2}}\)—Number of brake applications in the range of 0.15–0.24 [MPa]; \(\mathrm{X_{5}}\)—Number of vehicle load range \(<\) 20% [km]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{R^{2}}\) & \(\widetilde{\mathbf{R^{2}}}\) & **Std Error** & **Observation** & \\ \hline
**0.932** & **0.927** & **2583.179** & **29** & \\ \hline  & **Coefficients** & **Std Error** & \(t\) **Stat** & \(p\) **Value** \\ \hline Intercept & 19,472.544 & 6607.045 & 2.947 & 0.007 \\ \(\mathrm{X_{2}}\) & 44.004 & 12.043 & 3.654 & \(1.14\times 10^{-3}\) \\ \(\mathrm{X_{5}}\) & 234.194 & 64.799 & 3.614 & 0.001 \\ \hline ANOVA & df & SS & MS & F & Significance F \\ \hline Regression & 2 & \(2.38\times 10^{9}\) & \(1.19\times 10^{9}\) & 178.177 & \(6.65\times 10^{-16}\) \\ Residual & 26 & 173,493,185.4 & 6,672,814.821 & \\ Total & 28 & \(2.55\times 10^{9}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Multivariate regression results for the new linear model. model constants \(\alpha=\{\alpha_{0},\ldots,\alpha_{\mathrm{g}}\}\backslash\{\alpha_{2},\alpha_{3}\}\) are insignificant, i.e., equal to zero; incorrect model structure. New Inverse Linear Model  
For the new inverted linear model, Formula (2) for \(\mathrm{X_{i}}=\{\mathrm{X_{2}},\mathrm{X_{3}}\}\), model fitting was carried out at a significance level of \(\alpha=0.05\). Based on the verified data, we determine the parameter values of the new inverted linear model (Table 7). The model fit was verified at a significance level of \(\alpha=0.05\). The coefficient of the model is \(\widetilde{\mathrm{R}^{2}}=0.962\) (coefficient of convergence \(\varphi^{2}=3.5\%\)). Conclusion: The model explains 96.2% of the variability of the studied trait. This shows a very good fit of the model to the empirical data. We hypothesize that the coefficients of the regression model are not significant. The F statistic, with the null hypothesis being true, has a Snedecor F distribution with 2 degrees of freedom of the numerator and 26 degrees of freedom of the denominator. The empirical value of the statistic is F = 355.962, and the corresponding critical significance level F = 1.92 \(\times\) 10\({}^{-19}\). The level is less than the accepted significance level \(\alpha=0.05\). We therefore reject hypothesis H\({}_{0}\) in favor of H\({}_{1}\).