## 3 Results and Discussion
### Creep Assessment
#### 3.3.2. Creep Response--Statistical Analysis
However, the presence of sharp changes or non-linear trends in the plots may also reflect limitations in the data or the need for more sophisticated modeling approaches to fully elucidate the underlying patterns and interactions. **Method 4: Correlation analysis (Linear and very basic)**  
Figure 17 presents a correlation matrix that evaluates the linear relationships between various input factors and output variables, utilizing correlation coefficients that range from \(-1\) to \(1\). In this matrix, a coefficient of \(1\) signifies a perfect positive linear relationship, indicating that as one variable increases, so does the other. Conversely, a coefficient of \(-1\) denotes a perfect negative linear relationship, where an increase in one variable leads to a decrease in another. A coefficient of \(0\) means there is no linear relationship between the variables. The matrix visually represents these relationships via a color spectrum from blue (indicating negative correlation) to red (indicating positive correlation), with the intensity of the color corresponding to the strength of the relationship. From the analysis of the correlation matrix, several key observations emerge. The Input Preset Depth (nm) shows a strong negative correlation with both \"Output Peak Hardness (GPa)\" and \"Output Maximum Shear Stress (GPa)\", with coefficients of \(-0.79\), suggesting that an increase in the preset depth is associated with reductions in peak hardness and maximum shear stress. The Input Loading Speed (mN/s) has a moderately positive correlation with \"Output Net Creep Depth (nm)\", at a coefficient of \(0.63\), indicating that higher loading speeds may lead to an increase in net creep depth. Similarly, Input Creep duration (s) is strongly positively correlated with \"Output Net Creep Depth (nm)\" at a coefficient of \(0.68\), highlighting that longer durations of creep are linked to greater net creep depths. Furthermore, there is a nearly perfect correlation between the \"Output Strain Rate Exponent\" and \"Output Strain Rate Sensitivity Factor\", with a coefficient of \(0.99\), indicating these two outputs vary in almost identical manners with changes in input factors. Additionally, Output Critical Volume for Dislocation Nucleation is strongly negatively correlated with both \"Output Strain Rate Exponent\" and \"Output Strain Rate Sensitivity Factor\", with coefficients of \(-0.66\) and \(-0.23\), respectively. This suggests that as the critical volume for dislocation nucleation increases, there tends to be a decrease in the strain rate exponent and sensitivity factor. The correlation matrix thus offers a succinct overview of how each input might influence the outputs, which is pivotal for grasping the dynamics within the dataset. Leveraging these insights can aid in focusing efforts on factors that warrant further investigation, modeling, or process enhancement. Figure 16: Partial Dependence Plots (PDPs) for various output variables using an Artificial Neural Network (ANN) model. To synthesize the insights derived from various analytical methods, including ANOVA, Random Forest, Partial Dependence Plots (PDPs), and the correlation matrix, a comprehensive comparison of the findings related to key input variables is provided:  
1. Regarding Input Preset Depth (nm), ANOVA highlights its significant effect on both \"Output Peak Hardness (GPa)\" and \"Output Maximum Shear Stress (GPa)\". The Random Forest analysis identifies it as an important feature for several outputs, while PDPs suggest a positive impact on the outputs. However, the correlation matrix reveals a negative correlation between \"Output Peak Hardness (GPa)\" and \"Output Maximum Shear Stress (GPa)\". This consensus indicates that while ANOVA and Random Forest recognize the significance of this input, the negative correlation observed in the correlation matrix contrasts with the positive relationship indicated by PDPs and the significant effects noted in ANOVA, hinting at possible non-linear effects that may not be captured in linear analyses. 2.