## 4 Discussion
Results of the _Out-of-Domain_ test for: (**a**) _Linear Regression_, with an _RMSE_ of 41.3; (**b**) _XGBoost_, with an _RMSE_ of 36.3; and (**c**) _Spline Continued Fraction_, with an _RMSE_ of 34.8. Because all the actual critical temperatures of the test set in the _Out-of-Domain_ settings were \(\geq\) 89 K, it is relevant to evaluate for how many of these samples each regression method was able to predict above that value. Here, we consider the predicted value as **P** = _critical temperature value_\(\geq\) 89 K (denoted as 'P' for positive) and **N** = _critical temperature value_\(<\) 89 K (denoted as 'N' for negative). In Table 3, we report the number of samples for which each of the methods predicted a temperature value in the P and N categories for the whole testing set of the _Out-of-Domain_ test. It can be seen that only six regression methods predicted the critical temperature of \(\geq\) 89 K for at least one sample. Both _Linear Regression_ and _XGBoost_ predicted two sample temperatures with the critical temperature \(\geq\) 89 K. Kernel Ridge predicted only one sample value within that range, while MLP Regressor and Linear SVR predicted it for 21 and 34 samples, respectively. The proposed _Spline Continued Fraction_ predicted 108 sample values of \(\geq\) 89 K, the best among all regression methods used in our experiments. We examined the consensus between the regression methods in _Out-of-Domain_ predictions. Only five regressors, (Spln-CFR, xg-b, mlp, l-regr, l-svr, and krnl-r), were able to predict at least one positive value (critical temperature \(\geq\) 89 K). We computed pairwise inter-rater agreement statistics, [PERSON]'s kappa [23], for these five regression methods. We tabulated the value of Kappa (\(\kappa\)) ordered by highest to lowest; the level of agreement is outlined in Table 4. It can be seen that in most cases there is either no agreement (nine cases) none to slight (four cases) between the pairs of regressors. Such behaviour is seen in the agreement between the pairs formed with Spln-CFR and each of the other five methods. MLP Regressor and Linear SVR have fair agreement in their predictions. The highest value is \(\kappa=0.67\) for _Linear Regression_ and _Kernel Ridge_, yielding substantial agreement. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rater 1** & **Rater 2** & **Value of Kappa (\(\kappa\))** & **Level of Agreement** \\ \hline Spln-CFR & xg-b & \(-\)0.001851 & No Agreement \\ Spln-CFR & mlp & 0.030476 & None to Slight \\ Spln-CFR & l-regr & 0.016365 & None to Slight \\ Spln-CFR & l-svr & 0.104988 & None to Slight \\ Spln-CFR & krnl-r & \(-\)0.000933 & No Agreement \\ xg-b & mlp & \(-\)0.001721 & No Agreement \\ xg-b & l-regr & \(-\)0.000942 & No Agreement \\ xg-b & l-svr & \(-\)0.001780 & No Agreement \\ xg-b & krnl-r & \(-\)0.000628 & No Agreement \\ mlp & l-regr & \(-\)0.001721 & No Agreement \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Inter-rater agreement between the pairs of regressor methods where the resulting models were able to predict at least one positive temperature value (\(T_{c}\geq\) 89 K). \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Regressor**} & \multicolumn{3}{c}{**Out-of-Domain Predicted Critical Temperature, \(T_{c}\)**} \\ \cline{2-3}  & **P (\(T_{c}\geq\) 89 K)** & **N (\(T_{c}\) \(<\) 89 K)** \\ \hline Spln-CFR & 108 & 2018 \\ xg-b & 2 & 2124 \\ rf & 0 & 2126 \\ grad-b & 0 & 2126 \\ mlp & 21 & 2105 \\ l-regr & 2 & 2124 \\ l-svr & 34 & 2092 \\ krnl-r & 1 & 2125 \\ ada-b & 0 & 2126 \\ lasso-l & 0 & 2126 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of times the different methods predicted a critical temperature value \(T_{c}\geq\) 89 K (denoted as ‘P’ for positive) and \(T_{c}<\) 89 K (denoted as ‘N’ for Negative) on the Out-of-Domain test.