## 4 Result
### Result of ML Techniques  
#### 4.2.1 Regression Analysis (Regression Model)  
In monitoring the influence of input variables (height of fall H, weight of falling hammer W, type of impact I and strength of the conveyor belt S) on the output variable \(F\). We will start from a general model for each type of conveyor belt in the form of  
\[F=f(H,W,I,S), \tag{5}\]  
The best regression model for both output variables, regardless of the strength of the conveyor belt, is in the form  
\[F=\beta_{0}+\beta_{1}H+\beta_{2}W+\beta_{3}I+\beta_{4}S+\varepsilon, \tag{6}\]  
where \(\beta_{0}\), \(\beta_{i}\), \(i=1,\ 2,\ 3,\ 4\) are the parameters of the models, W is the weight of the falling hammer, H is the impact height, I is the type of the impactor of the hammer, S is the strength of the conveyor belt and \(\varepsilon\) is the random error. The variable I (impactor) is a dichotomous variable that takes the values I = 0 in the case of a spherical impactor and I = 1 in the case of a pyramidal impactor. Point estimates of model parameters are determined by the least squares method. The model was created using a training group of samples, which consisted of 70% of the samples (260 samples). Point estimates of the parameters of the regression model, standardized model parameters together with the statistical significance of the parameters (\(p\)-value) are in Table 3. The statistical significance of the overall model is tested through the F-test. The level of dependence of variable Y on the effect of \(k\) independent variables is expressed using the multiple coefficient of determination \(R^{2}\). The coefficient takes values from the interval \(\langle 0;1\rangle\). The closer the value is to 1, the tighter the dependency. The tables determine the values of the multiple coefficient of determination \(R^{2}\) and the statistical significance of the model (\(p\)-value). It turns out that input variables significantly affect the impact force in each type of conveyor belt. The strength of the dependence of the relationship is expressed through a multiple coefficient of determination \(R^{2}\) and the coefficient of determination is equal to the value 0.936. This means that 93.6% of the variability of the variable Impact Force can be explained by the proposed regression model. The Variance Inflation Factor (VIF) was used to check the multicollinearity of the variables. By multicollinearity we mean a strong correlation between independent variables. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Coefficients** & **Standardized Coefficients Beta** & **t Stat** & **VIF** & \(p\)**-Value** \\ \hline Model: Impact Force (\(p\)-value \(<10^{-16}\)), R\({}^{2}\) = 0.936 & & & & \\ Intercept & \(-16.21\) & \(1.5\times 10^{-17}\) & \(-21.447\) & & \(<\)10\({}^{-16}\) \\ H & 9.533 & 0.910 & 56.586 & 1.03 & \(<\)10\({}^{-16}\) \\ W & 0.254 & 0.496 & 29.723 & 1.11 & \(<\)10\({}^{-16}\) \\ I & 0.908 & 0.057 & 3.464 & 1.09 & 0.0006 \\ S & 0.0018 & 0.131 & 8.282 & 1.00 & \(<\)10\({}^{-16}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Regression Model—Impact Force (\(\alpha\) = 0.05). Strong multicollinearity reduces the accuracy of estimation of the regression coefficients, and the estimates obtained from the model are not reliable. If VIF = 1, then there is no correlation between one independent variable and the other independent variables. The generally accepted rule is that the problem of multicollinearity arises if any VIF coefficient is greater than 10. The values of the VIF coefficient are approximately equal to 1, which means that there is almost no multicollinearity (dependence) between a given input variable and the other input variables. We can assume that the model is stable and the parameters of the model are reliably estimated. Because the variables in the regression analysis are expressed in different units, standardized regression coefficients were used to compare the relative significance of individual input variables \(\beta_{i}^{*}\), \(i=1,\ldots,k\).