## 4 Results and Discussion
### Results of Estimation and Verification of the Power Model  
For the power (quasi-linear) model specified by Formula (14), the parameter values are shown in Table 8.  
We will verify the constructed model at the significance level \(\alpha\) = 0.05. The model's coefficient of determination is \(\overset{\sim}{\mathrm{R}^{2}}\) = 0.941 (coefficient of convergence \(\varphi^{2}\) = 4.1% \(\varphi^{2}\) = 4.2%). The model explains 94.1% of the variation of the studied trait, this is a good fit of the model  
Figure 3: Geometric interpretation of the inverse linear model (22). Y\({}_{2}\)—Period of exploitation of the brake pads [km]; X\({}_{2}\)—Number of brake applications in the range of 0.15–0.24 [MPa]; X\({}_{3}\)—Number of brake applications in the range of 0.25–0.40 [MPa]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{R^{2}}\) & \(\overset{\sim}{\mathbf{R}^{2}}\) & **Std Error** & **Observation** & \\ \hline
**0.958** & **0.941** & **0.033** & **29** & \\ \hline  & **Coefficients** & **Std Error** & **t Stat** & **\(p\) Value** \\ \hline Intercept & 8.929 & 0.987 & 9.050 & \(1.65\times 10^{-8}\) \\ X\({}_{1}\) & 0.025 & 0.027 & 0.911 & 0.373 \\ X\({}_{2}\) & 0.162 & 0.051 & 3.149 & 0.005 \\ X\({}_{3}\) & \(-0.062\) & 0.038 & \(-1.621\) & 0.121 \\ X\({}_{4}\) & \(-0.004\) & 0.011 & \(-0.349\) & 0.730 \\ X\({}_{5}\) & 0.299 & 0.174 & 1.721 & 0.101 \\ X\({}_{6}\) & 0.013 & 0.032 & 0.427 & 0.674 \\ X\({}_{7}\) & 0.009 & 0.013 & 0.738 & 0.469 \\ X\({}_{8}\) & \(-0.016\) & 0.026 & \(-0.643\) & 0.527 \\ \hline ANOVA & df & SS & MS & F & Significance F \\ \hline Regression & 8 & 0.494 & 0.062 & 56.656 & \(4.62\times 10^{-12}\) \\ Residual & 20 & 0.022 & 0.001 & \\ Total & 28 & 0.516 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Multivariate regression results for the power model. to the empirical data. The significance of the regression coefficients was checked. We put hypotheses as for previous models. The F statistic, with the null hypothesis being true, has an F Snedecor 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 = 56.656, and the corresponding critical level of significance F = 4.62 \(\times\) 10\({}^{-12}\). 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 X\({}_{i}\) = {X\({}_{1}\), X\({}_{2}\),...,X\({}_{8}\)}. For each coefficient of the regression model, we pose hypotheses as for previous models. The empirical values of the Student's \(t\)-statistic and the corresponding values of the critical level of significance (\(p\)-value) are shown in Table 8. There are no grounds for rejecting the hypothesis that the model constants a = {\(\alpha_{0}\),...,\(\alpha_{8}\)}{\(\{\alpha_{2}\}\) are insignificant, i.e., equal to zero (the values of the critical level of significance for these coefficients are greater than the accepted level of significance \(\alpha\) = 0.05). There are no grounds for rejecting the hypothesis that the variables X\({}_{i}\) = {X\({}_{1}\),...,X\({}_{8}\)}{\(\{\chi_{2}\}\)} are insignificant. The current model structure is incorrect. Determination of the New Power Model  
The new quasi-linear power model is described by Equation (23):  
\[\text{lnY}=\text{ln}\alpha_{0}+\alpha_{2}\text{lnX}_{2}+\epsilon \tag{23}\]  
Estimation of structural parameters for the presented model is provided in Table 9.  
We verify the fit of the model at a significance level of \(\alpha\) = 0.05. The coefficient of the model is R\({}^{2}\) = 0.901 (convergence rate \(\varphi^{2}\) = 9.6%). The model explains 90.1% of the variability of the studied trait. This indicates a good fit of the model to the empirical data. We hypothesize that the coefficients of the regression model are not significant.