## 3 Results
### Rules for Explaining the Results
However, at a higher casting speed of 7.5 mm/s with the same silicon content, the yield strength increases, reaching values near 320 MPa. The data density shading shows that our most reliable predictions for yield strength are in the middle region where the shading is darkest. The edges, especially the top right corners of the graphs, show lighter shading, indicating lower data density. This means predictions in these areas are based on fewer data points and are less certain. Elongation Based on Figure 3: Now, looking back at the earlier provided elongation graph with similar axes, we could analyze the elongation trend in relation to yield strength. Typically, as yield strength increases, elongation decreases because the material gets harder and less ductile. The exact relationship between these two properties would depend on the specific contour lines of the elongation graph; however, the general trend is such that regions of high yield strength on the graph may correspond to regions of lower elongation on the elongation graph, and vice versa. Interpreting the Relationship: If we were to look for an optimal region that provides a balance between high yield strength and acceptable elongation, we would aim for an area where both graphs indicate favorable values. However, it's important to keep data density in mind, as a high yield strength prediction is only as good as the amount of data backing it. We should be cautious about regions with high yield strength but low data density because the prediction might not be reliable. In a practical scenario, if we aim for a casting process that prioritizes yield strength without completely sacrificing ductility (elongation), we would look for an area with: High yield strength (higher values on the graph), Lower standard deviation (indicating consistency in the data), Acceptable levels of elongation (based on the previous elongation graph), and High data density (darker areas on the graphs). The exact values and trade-offs would depend on the material requirements and the specific application for which the material is being cast. We examined and attempted to explain the mutual influences for two input parameters in the preceding graphs using ChatGPT and the provided results. This indicates that a two-parametric analysis was conducted, averaging the general influence of the remaining input parameters. By maintaining the two most significant input parameters as the primary parameters (whose affects are graphically displayed), we can enhance our understanding of the phenomenon by including the remaining input parameters whose influence we are interested in as parameters with fixed values. Figure 5 illustrates the outcome, with yield strength plotted as a function of casting speed and Si content at a constant ram speed which amounts to 15.405 mm/s. An automated explanation of the results in Figure 5 was produced. The explanation also refers to the comparison of the results in Figure 5 with Figure 4:  
_Example Interpretation:_  
_Let's consider a hypothetical point at a silicon content of 0.95 wt.% and a casting speed of 7.3 mm/s._  
_From the graph (Figure 5a), we might determine the standard deviation at this point is approximately 19.1 MPa, indicating a moderate level of confidence in the yield strength pre-diction._  
_Looking at the graph (Figure 5b), the same point falls on a contour line labeled \"320.0\", suggesting the predicted yield strength at these parameters is 320 MPa._  
_This means that, while keeping the ram speed constant at 15.405 mm/s, a combination of 0.95 wt.% Si and a casting speed of 7.3 mm/s is predicted to result in a yield strength of 320 MPa, with a standard deviation of 19.1 MPa. This deviation should be considered when evaluating the precision and reliability of the predicted yield strength._  
_The two graphs you have presented now include the yield strength as the predicted value with the ram speed fixed at 15.405 mm/s.