# 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
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & \(p\)**-Value** \\ \hline Model & 370.06 & 9 & 41.12 & 44.90 & <0.0001 ** \\ \(X_{1}\) & 12.13 & 1 & 12.13 & 13.24 & 0.0083 ** \\ \(X_{2}\) & 41.82 & 1 & 41.82 & 45.66 & 0.0003 ** \\ \(X_{3}\) & 21.71 & 1 & 21.71 & 23.71 & 0.0018 ** \\ \(X_{1}X_{2}\) & 12.64 & 1 & 12.64 & 13.80 & 0.0075 ** \\ \(X_{1}X_{3}\) & 21.44 & 1 & 21.44 & 23.41 & 0.0019 ** \\ \(X_{2}X_{3}\) & 12.39 & 1 & 12.39 & 13.53 & 0.0079 ** \\ \(X_{1}\)2  & 5.32 & 1 & 5.32 & 5.81 & 0.0468 * \\ \(X_{2}\)2  & 222.46 & 1 & 222.46 & 242.94 & \textless{}0.0001 ** \\ \(X_{3}\)2  & 9.11 & 1 & 9.11 & 9.95 & 0.0160 * \\ Residual & 6.41 & 7 & 0.9157 & & & \\ Lack of fit & 2.36 & 3 & 0.7880 & 0.7791 & 0.5640 \\ Pure error & 4.05 & 4 & 1.01 & & \\ Cor total & 376.47 & 16 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The regression and variance analysis of the size qualification rate of crushed film. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & \(p\)**-Value** \\ \hline Model & 272.09 & 9 & 30.23 & 135.41 & \textless{}0.0001 ** \\ \(X_{1}\) & 6.64 & 1 & 6.64 & 29.75 & 0.0010 ** \\ \(X_{2}\) & 8.04 & 1 & 8.04 & 36.01 & 0.0005 ** \\ \(X_{3}\) & 17.02 & 1 & 17.02 & 76.25 & \textless{}0.0001 ** \\ \(X_{1}X_{2}\) & 2.42 & 1 & 2.42 & 10.83 & 0.0133 * \\ \(X_{1}X_{3}\) & 5.38 & 1 & 5.38 & 24.11 & 0.0017 ** \\ \(X_{2}X_{3}\) & 3.59 & 1 & 3.59 & 16.08 & 0.0051 ** \\ \(X_{1}\)2  & 0.1684 & 1 & 0.1684 & 0.7543 & 0.4139 \\ \(X_{2}\)2  & 200.32 & 1 & 200.32 & 897.18 & \textless{}0.0001 ** \\ \(X_{3}\)2  & 20.84 & 1 & 20.84 & 93.36 & \textless{}0.0001 ** \\ Residual & 1.56 & 7 & 0.2233 & & \\ Lack of fit & 0.7059 & 3 & 0.2353 & 1.10 & 0.4468 \\ Pure error & 0.8570 & 4 & 0.2143 & & \\ Cor total & 273.66 & 16 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The regression and variance analysis of the impurity content of crushed film. Regarding the quadratic regression model for the impurity content of crushed film, 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 0.9869, and the predicted R\({}^{2}\) is 0.9538, with a difference of less than 0.2 between them. The coefficient of variation (CV) is 3.56%, indicating good reliability and stability of the model data. The signal-to-noise ratio is 29.3490, significantly greater than 4, indicating that the quadratic regression model is reliable and capable of accurately predicting the impurity content of crushed film. Finally, the non-significant variables, \(X_{1}\)\({}^{2}\), can be elminated. The model is shown in Equation (11). \[Y_{2}=9.07+0.91X_{1}+1.00X_{2}-1.46X_{3}+0.78X_{1}X_{2}-1.16X_{1}X_{3}+0.95X_{2 }X_{3}+6.90X_{2}^{2}+2.23X_{3}^{2} \tag{11}\]