# Regression Approach to a Novel Lateral Flatness Leveling System for Smart Manufacturing
## 4 Results and Discussion  
After carrying out the experiment through machine learning using the multiple regression method, the results from the machine operator and the machine learning output are compared in this section. The experiment was carried out using the same input condition for both the machine operator's method and the machine learning method. The sensor fed the sample data into the machine learning section to train and predict the backup roll set parameters for the corresponding scenario. On the other hand, the experienced machine operator also put down the recommended parameters based on years of experience. Each of the backup sets from 1 to 5 was simulated with the MLR method as shown in Tables 2-6. Each of the regression models was simulated with the related independent variables. The independent variables were mostly sheet metal coil-related properties marked with line speed and flatness readings from the laser sensor in the system. In addition, it can be seen that the line speed of the production line had a lower coefficient than the other independent variables, as the line speed did not have much impact on how to level a coil sheet. On the other hand, the coil thickness and flatness readings had the  
Figure 5: Methodology flowchart used for leveling with the proposed machine learning method. strongest impact on the regression model, as they both had higher coefficients than the other independent variables. As shown from the results, all of the independent variables had \(p\)-values less than 0.05, and the null hypothesis could be rejected. This \(p\)-value was used in statistical testing to determine the probability of extreme results or inform a statistically significant relationship. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Backup Set 3** & **Coefficient** & **Standard Error** & \(p\)**-Value** \\ \hline Constant & 19.48 & 2.54 & \(5.3\times 10^{-13}\) \\ Coll thickness & \(-19.45\) & 2.85 & \(1.4\times 10^{-11}\) \\ Coll width & 3.56 & 0.68 & \(1.8\times 10^{-14}\) \\ Coil tensile strength & 6.53 & 0.62 & \(1.9\times 10^{-13}\) \\ Coil yield strength & 5.92 & 0.23 & \(1.8\times 10^{-16}\) \\ Coil outer diameter & 2.67 & 0.17 & \(2.7\times 10^{-13}\) \\ Coil inner diameter & 3.5 & 0.42 & \(1.8\times 10^{-13}\) \\ Line speed & 0.278 & 0.17 & \(6.8\times 10^{-14}\) \\ Flatness reading & 30.51 & 2.54 & \(2.1\times 10^{-13}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Multiple linear regression model for backup set 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Backup Set 1** & **Coefficient** & **Standard Error** & \(p\)**-Value** \\ \hline Constant & 20.52 & 6.2 & \(3.5\times 10^{-16}\) \\ Coil thickness & \(-19.63\) & 2.15 & \(2.1\times 10^{-15}\) \\ Coil width & 2.69 & 0.25 & \(4.5\times 10^{-13}\) \\ Coil tensile strength & 7.32 & 0.86 & \(5.9\times 10^{-13}\) \\ Coil yield strength & 6.27 & 0.18 & \(7.8\times 10^{-15}\) \\ Coil outer diameter & 1.64 & 0.11 & \(6.0\times 10^{-13}\) \\ Coil inner diameter & 3.52 & 0.42 & \(7.5\times 10^{-16}\) \\ Line speed & 0.24 & 0.12 & \(8.7\times 10^{-13}\) \\ Flatness reading & 21.53 & 1.58 & \(3.6\times 10^{-14}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Multiple linear regression model for backup set 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Backup Set 1** & **Coefficient** & **Standard Error** & \(p\)**-Value** \\ \hline Constant & 16.55 & 5.73 & \(1.8\times 10^{-10}\) \\ Coil thickness & \(-19.87\) & 2.74 & \(1.5\times 10^{-14}\) \\ Coil width & 3.74 & 0.78 & \(3.6\times 10^{-11}\) \\ Coil tensile strength & 5.43 & 0.82 & \(5.2\times 10^{-7}\) \\ Coil yield strength & 5.27 & 0.74 & \(3.4\times 10^{-13}\) \\ Coil outer diameter & 2.85 & 0.19 & \(2.5\times 10^{-12}\) \\ Coil inner diameter & 3.47 & 0.23 & \(1.5\times 10^{-12}\) \\ Line speed & 0.18 & 0.02 & \(2.8\times 10^{-14}\) \\ Flatness reading & 26.45 & 2.15 & \(7.8\times 10^{-12}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Multiple linear regression model for backup set 4.