## 3 Results and Discussion
### Nanoindentation-Based Basic Mechanical Property Assessment
#### 3.2.2 Statistical Analysis  
In order to further examine the significance of the loading speed and the preset depth on the basic mechanical properties measured in the present effort, four different techniques were adopted to ascertain the strength of each input parameter and their impact on the resulting values. **Method 1: Correlation Matrix Analysis**  
The correlation matrix visualizes the linear correlation coefficients between various inputs and outputs. In the matrix, the color intensity and the sign of the values indicate the strength and direction of the linear relationship between variables. Red shades represent positive correlations, and blue shades represent negative correlations. The closer the value is to \(1\) or \(-1\), the stronger the positive or negative linear relationship, respectively. Graphical representation of the correlation matrix is shown in Figure 4.  
Figure 4: Graphical representation of the correlation matrix. Based on the image analysis, the most significant correlations identified are as follows: The correlation between the input initial indentation depth (nm) and the output hardness value (Hit) is marked by a correlation coefficient of \(-0.90\), indicating a strong negative correlation. This suggests that an increase in indentation depth leads to a significant decrease in the hardness value. Similarly, the initial indentation depth and the nit percentage show a strong negative correlation with a coefficient of \(-0.86\), meaning that a deeper indentation correlates with a lower nit percentage. Conversely, the input loading speed (mN/s) and the output modulus of elasticity (EIt, in GPa) have a positive correlation coefficient of 0.67, implying that higher loading speeds result in increased EIT values. There is also a strong positive correlation between the output hardness value (HV) and the nit percentage, with a correlation coefficient of 0.78, indicating that these outputs tend to increase or decrease in tandem. However, the correlation between output Elt (GPa) and output nIt (%) is moderately negative, with a coefficient of \(-0.50\), suggesting that an increase in Eli is associated with a decrease in nit, or vice versa. The matrix also displays weaker correlations, as denoted by coefficients closer to zero, highlighting less significant linear relationships. While these correlations offer insights into the dataset's linear relationships, it is crucial to remember that correlation does not equate to causation. Non-linear relationships might not be adequately represented by these coefficients. For a thorough understanding of the variables' inter-relations, further analyses, including causation analysis and non-linear modeling, might be required. Despite the need for cautious interpretation of correlation analysis outcomes, these results confirm earlier speculations regarding the impact of indentation depth on hardness values and the effect of loading speed on the modulus of elasticity. **Method 2: Random Forest Analysis**  
In the Random Forest analysis, Figure 5 showcases bar charts that depict the relative significance of each input feature toward predicting the output variables. Feature importance scores are assigned to indicate the utility and value of each feature within the model's construction. A higher score denotes greater importance, offering insights into the model's decision-making mechanisms. Observations from Figure 5 reveal that for the output variable HV (hardness value), the \"Input Initial Indentation Depth\" emerges as a crucial predictor, boasting a very high importance score. This underscores its primary role in determining the hardness value. On the other hand, the \"Input Loading Speed\" holds a considerably lower importance score, suggesting its subordinate influence on the hardness value compared to indentation depth. Regarding the output variable Eit (elastic indentation), a similar pattern is observed. The \"Input Initial Indentation Depth\" stands out as the most influential feature, asserting its significance in the model's predictions.