## 4 Discussion  
To illustrate the performance of models in the _Out-of-Sample_ study, we employed _Linear Regression_, _XGBoost_, and _Spline Continued Fraction_ on the training set and plotted the predictions versus the actual temperatures for the entire dataset (in Figure 5). We were able to reproduce the results of the _Out-of-Sample_ test from [PERSON] [7] Figure 4(a), with an _RMSE_ of 17.7. The _Out-of-Sample_ models for _Spline Continued Fraction_ and _XGBoost_  
Figure 4: Runtime (in seconds) required for model building and prediction by the regressors for 100 runs of the _Out-of-Domain_ test, in which samples with the lowest 90% of critical temperatures were drawn as the training data and an equal number of samples drawn from the top 10% highest critical temperatures constituted the test data. Figure 3: Statistical comparison of the regressors for the _Out-of-Domain_ test: (**a**) heat map showing the significance levels of the \(p\)-values obtained by the Friedman post hoc test and (**b**) critical difference (CD) plot showing the statistical significance of the rankings achieved by the different regression methods. were used to predict the critical temperature for the entire dataset. Together, the figures show that Spln-CFR performed better in modelling _Out-of-Sample_ critical temperatures than _Linear Regression_, particularly for larger temperatures. Figure 6 shows the actual versus predicted critical temperature for the _Out-of-Domain_ test for the _Linear Regression_, _XGBoost_, and _Spline Continued Fraction_ models. Recall that in the _Out-of-Domain_ test settings we trained each of the models with the samples from the bottom 90% of the observed temperature, which is < 89 K, and measured the samples' test performance using the top 10% of the observed critical temperatures, with 2126 samples in the test set. Another set of our observed results are interesting for discussion and might be relevant for future research directions. In Table 2, we report the top twenty predicted versus actual (_y_) temperatures for all ten regression methods for a single run of the _Out-of-Domain_ test. The last row of the table shows the averages of the corresponding actual critical temperatures for the materials with the highest twenty predicted values by each of the models. Interestingly, _XGBoost_'s top twenty predictions of the critical temperature are all below 90 K (in the range of 87.48 to 89.64 K). Similarly, _Random Forest_'s top twenty predictions are in the range of 87.69 to 87.89 K. The top twenty predicted critical temperatures by the _Linear Regression_ are in the range of 81.83 to 91.59 K. In contrast, the top twenty predicted critical temperatures by _Spline Continued Fraction_ vary from 98.39 to 114.14 K, which by comparison represents the highest starting and ending values among all the regressors. We report the average temperature (_x_), average relative errors (_y_), and _RMSE_ score for the top twenty predictions. _XGBoost_ shows the lowest value for both \(y\) (0.036) and _RMSE_ (3.775) among the ten regressors. In terms of those scores, our proposed Spln-CFR is in the fourth position. However, looking at the average of the predictions, Spln-CFR has the highest average prediction temperatures for the top twenty predictions on the _Out-of-Domain_ test. Figure 5: _Out-of-Sample_ test results, showing the predicted vs. actual temperatures for the entire dataset with regression models trained on the training data: (**a**) _Linear Regression_ (replicating the outcome from Hamidieh), (**b**) _XGBoost_, and (**c**) _Spline Continued Fraction_. Figure 6: _Out-of-Domain_ test results, showing the predicted vs. actual temperatures of the samples for the highest 10% of critical temperatures, where the models were fitted using the samples with the lowest 90% critical temperatures. The _x_-axis values up to 145 K are shown, leaving one extreme value (185 K) outside of the visualized area.