## 3 Results and Discussion
### Nanoindentation-Based Basic Mechanical Property Assessment
#### 3.2.2 Statistical Analysis
It is important to note that ANOVA helps in identifying the presence of significant differences but does not detail which groups differ or describe the nature of these differences, necessitating further analysis for a comprehensive understanding. **Method 4: Partial Dependence Plots** \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Output** & **Input Feature Category** & **F-Value** & \(p\)**-Value** & **Significant** \\ \hline
1 & Output Eit (GPa) & Loading Speed Category & 3.306 & 0.108 & No \\
2 & Output Eit (GPa) & Indentation Depth Category & 0.275 & 0.769 & No \\
3 & Output HV & Indentation Depth Category & 15.443 & 0.004 & Yes \\
4 & Output HV & Loading Speed Category & 0.048 & 0.953 & No \\
5 & Output nit (%) & Indentation Depth Category & 10.003 & 0.012 & Yes \\
6 & Output nit (%) & Loading Speed Category & 0.708 & 0.530 & No \\ \hline \end{tabular}
\end{table} 
Table 2: ANOVA analysis results. The Partial Dependence Plots (PDPs) displayed in Figure 6 visualize the impact of input features on output features within a fitted regressor model, arranged such that each row represents a different output feature, and two columns correspond to the PDPs for \"Input Initial Indentation Depth (nm)\" and \"Input Loading Speed (mN/s)\", respectively. From these plots, several relationships between input features and output features emerge. For the \"Input Initial Indentation Depth (nm)\", the plots reveal a decreasing trend in hardness value (HV) with increasing indentation depth, suggesting that deeper indentations may lead to lower hardness values. The elastic indentation (Eit) also shows a decreasing trend with increased indentation depth, implying a reduction in the material's elastic response with deeper indentations. Conversely, the strain rate sensitivity factor (nit %) exhibits a fluctuating yet overall increasing trend with increased indentation depth, indicating higher nit (%) at deeper indentations, possibly due to enhanced plastic deformation effects. Regarding the \"Input Loading Speed (mN/s)\", the dependence plots indicate a positive relationship between loading speed and hardness value (HV), where an increase in loading speed leads to an increase in HV. This relationship could stem from the material's rate-dependent deformation characteristics. Similarly, the elastic modulus (Eit) appears to increase with the loading speed, suggesting higher elastic modulus values at higher speeds, possibly due to rate-dependent elasticity. The nit (%) shows a less definitive, although  
Figure 6: The Partial Dependence Plots (PDPs) constructed in the present effort. slightly positive, trend with the increased loading speed, hinting at a subtle dependence of plastic deformation characteristics on the rate of loading. Summarizing the insights from PDPs, indentation depth significantly affects all three output parameters, highlighting that deeper indentations generally result in decreased hardness and elastic modulus, while nit (%) tends to increase. Loading speed also significantly impacts the outputs, with both hardness and elastic modulus increasing with higher loading speeds, although its effect on nit (%) is less pronounced but slightly positive. These observations underline a complex interaction between loading speed and indentation depth on the material's mechanical properties, including hardness, elastic modulus, and strain rate sensitivity. The PDPs provide a nuanced understanding of how variations in loading conditions and indentation depths influence the mechanical behavior of materials, reflecting the intricate dynamics between the rate of loading and depth of indentation on material properties. In synthesizing the insights from correlation analysis, Random Forest Feature Importance, ANOVA, and Partial Dependence Plots, a detailed examination of each input-output relationship helps to identify consensus or divergence across these analytical methods:  
1.