## 3 Results and Discussion
### Nanoindentation-Based Basic Mechanical Property Assessment
#### 3.2.2 Statistical Analysis
For the relationship between Input Initial Indentation Depth and Output HV (hardness value), correlation analysis reveals a strong negative correlation of \(-0.90\), while Random Forest analysis assigns a high importance score to indentation depth. ANOVA underscores this with a statistically significant effect, and Partial Dependence Plots illustrate a decreasing trend in HV as indentation depth increases. The unified conclusion from all methods is that indentation depth significantly and negatively impacts hardness value, indicating lower hardness at greater indentation depths. 2. Regarding Input Initial Indentation Depth and Output nit (%), there is a strong negative correlation of \(-0.86\) from correlation analysis and a high importance score from Random Forest, slightly lower than that for HV. ANOVA shows a statistically significant effect, whereas Partial Dependence Plots suggest an increasing trend in nit (%) with deeper indentations. Despite the negative correlation, the increasing trend in nit (%) indicated by PDPs points to a potential increase in nit (%) with indentation depth, highlighting possible non-linear relationships not captured by the correlation coefficient. 3. In the case of Input Loading Speed and Output Elt (GPa), correlation analysis shows a moderate positive correlation of \(0.67\). Random Forest assigns a lower importance score to loading speed compared to indentation depth, and ANOVA does not find a statistically significant effect. However, Partial Dependence Plots depict an increasing trend in Elt with higher loading speeds. This suggests a generally positive effect of loading speed on Elt, although the lack of statistical significance in ANOVA indicates a potentially weaker or more complex relationship. 4. For the correlation between Output HV and Output nit (%), a strong positive correlation of \(0.78\) suggests that these outputs tend to increase or decrease in tandem, hinting at an underlying material property that influences both. Lastly, the moderate negative correlation of \(-0.50\) between Output Elt (GPa) and Output nit (%) suggests an inverse relationship, possibly reflecting different material responses under elastic and plastic deformations. In summary, indentation depth emerges as a pivotal factor influencing both HV and nit, corroborated by all analytical methods, with deeper indentations associated with lower hardness and possibly higher nit. The impact of loading speed on material properties like Elt and HV is less definitive; while PDPs and correlation analyses suggest a positive influence, ANOVA's lack of statistical significance and its reduced feature importance in Random Forest highlight a more nuanced effect. The observed discrepancies, particularly in the analysis of nit (%), underscore the presence of non-linear relationships that correlation coefficients alone cannot fully capture. Additionally, the inter-relations between different output variables suggest complex dependencies in material responses under varied conditions, emphasizing the intricate dynamics of mechanical behavior in materials science.