## 4 Process and Result  
Relationship between Glass Weathering and Its Chemical Composition Based on an Improved Logistic Regression Model with Double Adaptive Elastic Net  
Based on the data in Table 1, we use Matlab and SPSS to conduct modeling and calculation of the Daen-Logistic Regression model. The dependent variable here is a dichotomous variable (i.e., weathered and unweathered states), and the content of various chemical components is set as the independent variable. The double adaptive elastic net model can determine the classification results of weathered or unweathered glass under different conditions for each independent variable, which can avoid the variability of the results when the independent variables are selected differently, make the classification more adaptive, and reduce the influence of strongly correlated variables on other variables. The calculation gives the following in Table 1:  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Regression Coefficient of** \\ **High Potassium Glass** \\ **Types \(\beta\)** \\ \end{tabular} & \begin{tabular}{c} **Significance \(p\)-Value of High** \\ **Potassium Glass type** \\ **(P \(>\) \(\|\)t\(\|\))** \\ \end{tabular} & \
\begin{tabular}{c} **Regression Coefficient of** \\ **Lead-Barium Glass Types \(\beta\)** \\ **(P \(>\) \(\|\)t\(\|\))** \\ \end{tabular} &
\begin{tabular}{c} **Significance \(p\)-Value of** \\ **Lead-Barium Glass Type** \\ **(P \(>\) \(\|\)t\(\|\))** \\ \end{tabular} \\ \hline \(\beta_{0}\) & 15.301 & P\({}_{0}\) & 0.000 & \(\beta_{0}\) & 31.077 & P\({}_{0}\) & 0.000 \\ \hline \(\beta_{1}\) & 2.718 & P\({}_{1}\) & 0.099 & \(\beta_{1}\) & 7.788 & P\({}_{1}\) & 0.005 \\ \hline \(\beta_{2}\) & 12.318 & P\({}_{2}\) & 0.000 & \(\beta_{2}\) & 1.016 & P\({}_{2}\) & 0.313 \\ \hline \(\beta_{3}\) & 5.410 & P\({}_{3}\) & 0.020 & \(\beta_{3}\) & 8.320 & P\({}_{3}\) & 0.004 \\ \hline \(\beta_{4}\) & 7.199 & P\({}_{4}\) & 0.007 & \(\beta_{4}\) & 0.039 & P\({}_{4}\) & 0.843 \\ \hline \(\beta_{5}\) & 7.051 & P\({}_{5}\) & 0.008 & \(\beta_{5}\) & 2.678 & P\({}_{5}\) & 0.102 \\ \hline \(\beta_{6}\) & 4.751 & P\({}_{6}\) & 0.029 & \(\beta_{6}\) & 0.222 & P\({}_{6}\) & 0.637 \\ \hline \(\beta_{7}\) & 1.072 & P\({}_{7}\) & 0.300 & \(\beta_{7}\) & 1.293 & P\({}_{7}\) & 0.255 \\ \hline \(\beta_{8}\) & 2.629 & P\({}_{8}\) & 0.101 & \(\beta_{8}\) & 25.165 & P\({}_{8}\) & 0.000 \\ \hline \(\beta_{9}\) & 1.792 & P\({}_{9}\) & 0.181 & \(\beta_{9}\) & 0.831 & P\({}_{9}\) & 0.362 \\ \hline \(\beta_{10}\) & 2.629 & P\({}_{10}\) & 0.105 & \(\beta_{10}\) & 13.764 & P\({}_{10}\) & 0.000 \\ \hline \(\beta_{11}\) & 3.142 & P\({}_{11}\) & 0.076 & \(\beta_{11}\) & 3.702 & P\({}_{11}\) & 0.054 \\ \hline \(\beta_{12}\) & 0.451 & P\({}_{12}\) & 0.502 & \(\beta_{12}\) & 0.161 & P\({}_{12}\) & 0.688 \\ \hline \(\beta_{13}\) & 1.490 & P\({}_{13}\) & 0.222 & \(\beta_{13}\) & 0.942 & P\({}_{13}\) & 0.332 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Return coefficients of chemical components in high potassium and lead-barium glasses \(\beta\) and significance \(p\)-value.  
Figure 2: Processing flow chart.  
From the table of high potassium glass type, it can be seen that the values of two chemical components, SiO\({}_{2}\) and K\({}_{2}\)O, are relatively large, and the values of the significance \(p\)-value are less than \(p=0.1\), so these two chemical components have the greatest influence on whether the surface of high potassium glass is weathered or not. From the table of lead-barium glass type, it can be seen that the values of three chemical components, SiO\({}_{2}\), PbO, and P\({}_{2}\)O\({}_{5}\), are relatively large, and the values of the significance \(p\)-value are less than \(p=0.1\), so these two chemical components have the greatest influence on whether the surface of high potassium glass is weathered or not.