## 3 Results and Discussion
### Creep Assessment
#### 3.3.2. Creep Response--Statistical Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Output Variable** & **Input Variable** & **Sum of Squares** & **Degrees of Freedom** & **F-Statistic** & \(p\)**-Value** \\ \hline Output Critical volume for dislocation nucleation & Input Creep duration (s) & 0.004 & 1 & 3.717 & 0.112 \\ Output Critical volume for dislocation nucleation & Input Loading Speed (mN/s) & 0.003 & 1 & 2.550 & 0.171 \\ Output Critical volume for dislocation nucleation & Input Preset Depth (nm) & 0.017 & 1 & 15.745 & 0.011 \\ Output Maximum shear stress (Gpa) & Input Creep duration (s) & 0.002 & 1 & 1.282 & 0.309 \\ Output Maximum shear stress (Gpa) & Input Loading Speed (mN/s) & 0.000 & 1 & 0.151 & 0.714 \\ Output Maximum shear stress (Gpa) & Input Preset Depth (nm) & 0.020 & 1 & 11.348 & 0.020 \\ Output Net Creep Depth (nm) & Input Creep duration (s) & 99.552 & 1 & 21.260 & 0.006 \\ Output Net Creep Depth (nm) & Input Loading Speed (mN/s) & 247.741 & 1 & 52.908 & 0.001 \\ Output Net Creep Depth (nm) & Input Preset Depth (nm) & 1.591 & 1 & 0.340 & 0.585 \\ Output Peak Hardness (Gpa) & Input Creep duration (s) & 0.060 & 1 & 1.291 & 0.307 \\ Output Peak Hardness (Gpa) & Input Loading Speed (mN/s) & 0.007 & 1 & 0.150 & 0.714 \\ Output Peak Hardness (Gpa) & Input Preset Depth (nm) & 0.527 & 1 & 11.307 & 0.020 \\ Output Strain Rate Sensitivity Factor & Input Creep duration (s) & 0.000 & 1 & 0.012 & 0.917 \\ Output Strain Rate Sensitivity Factor & Input Loading Speed (mN/s) & 0.001 & 1 & 0.127 & 0.736 \\ Output Strain Rate Sensitivity Factor & Input Preset Depth (nm) & 0.007 & 1 & 1.447 & 0.283 \\ Output Strain rate Exponent & Input Creep duration (s) & 475.580 & 1 & 3.479 & 0.121 \\ Output Strain rate Exponent & Input Loading Speed (mN/s) & 499.093 & 1 & 3.651 & 0.114 \\ Output Strain rate Exponent & Input Preset Depth (nm) & 1853.284 & 1 & 13.557 & 0.014 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ANOVA results. \"Maximum Shear Stress (Gpa)\" with the Input \"Preset Depth (nm)\" showing an F-statistic of 11.35 and a \(p\)-value of 0.019919. These results underscore that the \"Input Loading Speed (mN/s)\" is paramount in its correlation with \"Output Net Creep Depth (nm)\", closely followed by the correlation between \"Input Creep duration (s)\" and \"Output Net Creep Depth (nm)\". Additionally, the analysis reveals that \"Input Preset Depth (nm)\" is significantly correlated with various outputs, highlighting the substantial influence of certain input variables on specific outputs. This analytical approach facilitates the identification of the most influential input variables for each output, guiding the direction for subsequent investigations or optimizations. **Method 2: Random Forest Regression Analysis**  
The Random Forest Regression analysis depicted in Figure 15 provides a visual representation of feature importances for various output variables. Feature importance in the context of a Random Forest model is an indication of the utility of each input variable in the construction of the model and its effectiveness in predicting the output variable. This utility is assessed based on the contribution of each feature to the reduction in impurity within the trees that make up the forest. In constructing the ensemble of trees that constitute a Random Forest, each tree is generated from a sample drawn with replacement (a bootstrap sample) from the training dataset. A key aspect of this process is the consideration of a random subset of features for determining the best split at each node within a tree. The cumulative measure of a feature's contribution to decreasing node impurity across all trees provides the basis for determining feature importance. The analysis yields several observations regarding the significance of input variables for predicting different output variables. For the output variable Peak Hardness (Gpa), the input variable Preset Depth (nm) is identified as the most crucial, with Loading Speed (mN/s) and Creep duration (s) also contributing, albeit to a lesser extent.