## 4 Results
### Creation of a Model of the Dependence of the Magnitude of Deflection on Selected Parameters  
The aim of this extended research is to find a regression model that expresses the dependence of the magnitude of conveyor belt deflection on two independent input parameters: impactor weight and impact height. For both cases (the presence/absence of the support system), we started with the following model:  
\[Deflection=f(Weight,\ Height)+\varepsilon, \tag{2}\]  
where \(\varepsilon\) is a random error. The output variable _Deflection_ is a continuous variable that is determined by analyzing the video recording.  
The parameters of the model were obtained using the least squares method, which was sensitive to outlier values. For that reason, the input data were assessed for outliers and influential values, and values that were recorded under conditions of severe belt damage were excluded from the database.  
The best regression model without a support system (Model I) has a point estimate of the following form:  
\[Deflection=b_{0}+b_{1}Weight+b_{2}Height, \tag{3}\]  
Or, if a support system is present (Model II), then it is  
\[Deflection=b_{0}+b_{1}Weight*Height, \tag{4}\]  
where \(b_{0}\), \(b_{1}\), and \(b_{2}\) are point estimates of the model parameters. Point estimates of the parameters, their statistical significance, and the significance of the models are shown in Tables 4 and 5.  
The test results show that the Model I regression model is statistically significant (\(p\)-value = \(3\times 10^{-4}\) < \(\alpha\)), and both variables are considered statistically significant (\(p\)-value \(<\alpha\)). The coefficient of determination is equal to 0.911, which means that 91.1% of the variability of the Deflection variable can be explained using the proposed regression model.  
The test results show that the Model II regression model is also statistically significant (\(p\)-value = 1.2 \(\times\) 10\({}^{-25}\) < \(\alpha\)), and both variables are considered statistically significant (\(p\)-value \(<\alpha\) variable), which represents the interaction between weight and impact height. The coefficient of determination is equal to 0.831, which means that 83.1% of the variability of the Deflection variable can be explained by the proposed regression model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Estimate** & **Standard Error** & **t-Stat** & \(p\)**-Value** & \
\begin{tabular}{c} **95\%-Confidence Interval** \\ **Lower** \\ \end{tabular} &
\begin{tabular}{c} **Interval** \\ **Upper** \\ \end{tabular} \\ \hline Intercept & \(-\)14.624 & 3.939 & \(-\)3.712 & 0.0004 & \(-\)22.471 & \(-\)6.776 \\ Weight & \(-\)27.404 & 1.079 & \(-\)25.389 & \(<\)0.0001 & \(-\)29.554 & \(-\)25.254 \\ Height & \(-\)0.524 & 0.047 & \(-\)11.074 & \(<\)0.0001 & \(-\)0.618 & \(-\)0.429 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameter estimates—Model I (\(\alpha\) = 0.05).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Estimate** & **Standard Error** & **t-Stat** & \(p\)**-Value** & \
\begin{tabular}{c} **95\%-Confidence Interval** \\ **Lower** \\ \end{tabular} &
\begin{tabular}{c} **Interval** \\ **Upper** \\ \end{tabular} \\ \hline Intercept & \(-\)31.981 & 1.329 & \(-\)24.069 & \(<\)0.00001 & \(-\)34.637 & \(-\)29.325 \\ Weight*Height & \(-\)0.246 & 0.014 & \(-\)17.490 & \(<\)0.0001 & \(-\)0.274 & \(-\)0.218 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameter estimates—Model II (\(\alpha\) = 0.05).  
The empirical and theoretical (model) deflection values for the selected input parameters are shown in Figure 13.