## 4 Results and Discussion
### Estimation and Verification Results of Inverted Linear Model
There is no basis for rejecting the hypothesis that brake pad wear depends on at least one of the variables \(\mathrm{X_{i}}=\{\mathrm{X_{2}},\mathrm{X_{3}}\}\). For each coefficient of the regression model \(\alpha_{i}\), we test the hypothesis of its significance. We verify it with a statistic with a Student's t-distribution with 26 degrees of freedom. The empirical values of the t-Student's statistic and the corresponding values of the critical \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{R^{2}}\) & \(\widetilde{\mathbf{R^{2}}}\) & **Std Error** & **Observation** & \\ \hline
**0.972** & **0.961** & **3.897 \(\times\) 10\({}^{-7}\)** & **29** & \\ \hline  & **Coefficients** & **Std Error** & \(t\)**Stat** & \(p\)**Value** \\ \hline Intercept & \(1.02\times 10^{-5}\) & \(2.14\times 10^{-6}\) & 4.780 & \(1.14\times 10^{-4}\) \\ \(\mathrm{X_{1}}\) & \(7.12\times 10^{-5}\) & \(4.61\times 10^{-5}\) & 1.546 & \(0.137\) \\ \(\mathrm{X_{2}}\) & \(8.18\times 10^{-4}\) & \(1.43\times 10^{-4}\) & 5.740 & \(1.29\times 10^{-5}\) \\ \(\mathrm{X_{3}}\) & \(-1.96\times 10^{-4}\) & \(6.20\times 10^{-5}\) & \(-3.162\) & \(0.005\) \\ \(\mathrm{X_{4}}\) & \(-8.79\times 10^{-7}\) & \(1.29\times 10^{-6}\) & \(-0.683\) & \(0.502\) \\ \(\mathrm{X_{5}}\) & \(3.00\times 10^{-4}\) & \(3.36\times 10^{-4}\) & 0.894 & \(0.381\) \\ \(\mathrm{X_{6}}\) & \(-7.08\times 10^{-6}\) & \(2.63\times 10^{-5}\) & \(-0.269\) & \(0.791\) \\ \(\mathrm{X_{7}}\) & \(5.37\times 10^{-6}\) & \(7.24\times 10^{-6}\) & 0.742 & \(0.466\) \\ \(\mathrm{X_{8}}\) & \(1.72\times 10^{-5}\) & \(5.73\times 10^{-5}\) & 0.300 & \(0.767\) \\ \hline ANOVA & df & SS & MS & F & Significance F \\ \hline Regression & 8 & \(1.05\times 10^{-10}\) & \(1.32\times 10^{-11}\) & 86.598 & \(8.01\times 10^{-14}\) \\ Residual & 20 & \(3.04\times 10^{-12}\) & \(1.52\times 10^{-13}\) & & \\ Total & 28 & \(1.08\times 10^{-10}\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Multiple regression results for the inverted linear model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{R^{2}}\) & \(\widetilde{\mathbf{R^{2}}}\) & **Std Error** & **Observation** & \\ \hline
**0.965** & **0.962** & **3.830 \(\times\) 10\({}^{-7}\)** & **29** & \\ \hline  & **Coefficients** & **Std Error** & \(t\)**Stat** & \(p\)**Value** \\ \hline Intercept & \(1.22\times 10^{-5}\) & \(4.41\times 10^{-7}\) & 27.598 & \(8.69\times 10^{-21}\) \\ \(\mathrm{X_{2}}\) & \(1.02\times 10^{-3}\) & \(8.22\times 10^{-5}\) & 12.463 & \(1.80\times 10^{-12}\) \\ \(\mathrm{X_{3}}\) & \(-2.34\times 10^{-4}\) & \(3.47\times 10^{-5}\) & \(-6.734\) & \(3.81\times 10^{-7}\) \\ \hline ANOVA & df & SS & MS & F & Significance F \\ \hline Regression & 2 & \(1.04\times 10^{-10}\) & \(5.22\times 10^{-11}\) & 355.962 & \(1.29\times 10^{-19}\) \\ Residual & 26 & \(3.82\times 10^{-12}\) & \(1.47\times 10^{-13}\) & & \\ Total & 28 & \(1.08\times 10^{-10}\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Multiple regression results for the new inverted linear model. level of significance (\(p\)-value) are shown in Table 7. All the coefficients of the model are significantly different from zero (the values of the critical level of significance are less than the accepted level of significance \(\alpha\) = 0.05). There is no basis for rejecting the hypothesis that all model coefficients are significantly different from zero. The current structure of the inverse linear model is correct and is represented by the relation (22) and geometric interpretation in Figure 3:  
\[\hat{\gamma}_{2}=\frac{\mathrm{x}_{2}\mathrm{x}_{3}}{1.22\times 10^{-5}( \mathrm{x}_{2}\mathrm{x}_{3})-2.34\times 10^{-4}(\mathrm{x}_{2})+1.02\times 10^{-3}( \mathrm{x}_{3})} \tag{22}\]