# Design and Optimization of a Toothed-Plate Single-Roller Crushing Device for Waste Plastic Film
## 5 Analysis and Verification of Crushing Test Results
### Significance Test and Regression Model Construction  
ANOVA and regression analyses were conducted on the data from Table 3, and multivariate regression models were established. (1) Significance analysis of the size qualification rate of crushed film  
The regression and variance analysis of the size qualification rate of crushed film is shown in Table 4. All variables have a significant impact on the model. Specifically, the \(p\)-values for \(X_{1}\), \(X_{2}\), \(X_{3}\), \(X_{1}X_{2}\), \(X_{1}X_{3}\), \(X_{2}X_{3}\), \(X_{1}{}^{2}\), and \(X_{3}{}^{2}\) are less than 0.01, indicating extremely significant effects on the model. The \(p\)-value for \(X_{1}{}^{2}\) falls in the range of 0.01 to 0.05, indicating a significant effect on the model. The ranking of variables based on their significance in influencing the model, from highest to lowest, is as follows: \(X_{2}{}^{2}>X_{2}>X_{3}>X_{1}X_{3}>X_{1}X_{2}>X_{2}X_{3}>X_{1}>X_{3}{}^{2}>X_{ 1}{}^{2}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Levels** & **Feeding Speed** & **Number of Cutter** & **Crushing Roller Rotation** \\  & \(X_{1}\) **(m/s)** & **Toothed Plates \(X_{2}\)** & **Speed \(X_{3}\) (r/min)** \\ \hline \(-1\) & 0.250 & 6 & 600 \\
0 & 0.325 & 12 & 750 \\
1 & 0.400 & 18 & 900 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test factors and levels. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & \(X_{1}\) **(m/s)** & \(X_{2}\) & \(X_{3}\) **(r/min)** & \(Y_{1}\) **(\%)** & \(Y_{2}\) **(\%)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 3: Test schemes and results. The quadratic regression model for the size qualification rate of crushed film is shown in Equation (10). The model has a \(p\)-value of <0.0001, indicating its extreme significance. The lack of fit has a \(p\)-value > 0.1, indicating a good fit for this quadratic regression model. The adjusted R\({}^{2}\) for the model is 0.9611, and the predicted R\({}^{2}\) is 0.8829, with a difference of less than 0.2 between them. The coefficient of variation (CV) is 1.16%, indicating good reliability and stability of the model data. The signal-to-noise ratio is 18.8351, significantly greater than 4, indicating that the quadratic regression model is reliable and capable of accurately predicting the size qualification rate of crushed film. \[Y_{1}=87.46+1.23X_{1}-2.29X_{2}+1.65X_{3}-1.78X_{1}X_{2}-2.31X_{1}X_{3}+1.76X_{2 }X_{3}-1.12X_{1}^{2}-7.27X_{2}^{2}-1.47X_{3}^{2} \tag{10}\]  
(2) Significance analysis of the impurity content of crushed film  
The regression and variance analysis of the impurity content of crushed film is shown in Table 5. The \(p\)-values for \(X_{1}\), \(X_{2}\), \(X_{3}\), \(X_{1}X_{3}\), \(X_{2}X_{3}\), \(X_{2}\)2, and \(X_{3}\)2 are less than 0.01, indicating extremely significant effects on the model. The \(p\)-value for \(X_{1}X_{2}\) falls in the range of 0.01 to 0.05, indicating a significant effect on the model. The \(p\)-value for \(X_{1}\)2 is greater than 0.05, indicating that its influence on the model is not significant. The ranking of variables based on their significance in influencing the model, from highest to lowest, is as follows: \(X_{2}\)2 \(>X_{3}\)2 \(>X_{3}\) \(>X_{2}\) \(>X_{1}\) \(>X_{1}\)\(X_{3}\) \(>X_{2}\)\(>X_{3}\) \(>X_{1}\)2.