## 2 Accuracy of Predictive Methods and What Is Required
### Cases Requiring Quantitative Predictions over the Data Range  
For a polymer, it can be important to predict the glass transition temperature Tg within a few degrees. Depending on the application, one is seeking polymer leading to a certain Tg. In Figure 2, we have displayed three correlations between experimental and modelled Tg values, with different methods providing different quality. Here we see that even R\({}^{2}\)=0.99 still does not yield Tg prediction  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Discipline** & **r Meaningful if** & **R\({}^{2}\) Meaningful if** \\ \hline Physics & r \(<-0.95\) or 0.95 \(<\) r & 0.9 \(<\) R\({}^{2}\) \\ \hline Chemistry & r \(<-0.9\) or 0.9 \(<\) r & 0.8 \(<\) R\({}^{2}\) \\ \hline Biology & r \(<-0.7\) or 0.7 \(<\) r & 0.5 \(<\) R\({}^{2}\) \\ \hline Social Sciences & r \(<-0.6\) or 0.6 \(<\) r & 0.35 \(<\) R\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Typical variability values for acceptable or good methods for various disciplines (these should be interpreted as typical values; the numbers in the table were taken from [[http://condor.depaul.edu/sjosst/it223/documents/correlation.htm](http://condor.depaul.edu/sjosst/it223/documents/correlation.htm)]([http://condor.depaul.edu/sjosst/it223/documents/correlation.htm](http://condor.depaul.edu/sjosst/it223/documents/correlation.htm))).  
that are all within a few degrees accuracy. In fact, one would need R\({}^{2}\) = 0.999 level to have sufficiently good predictions, something that might be difficult to achieve.  
A similar case is the prediction of a boiling point with the application of separation using distillation in mind. To predict whether two compounds can be separated, not only the relative order of the boiling points should be correct but also the reliability of the predicted difference in boiling points is crucial. The last requirement must be satisfied by any predictive method to be really useful.  
A further class of examples comprises the cases of chemical equilibria. These are the cases where it is important to know whether in the reaction  
\[\text{A}+\text{B}\rightarrow\text{C}+\text{D} \tag{3}\]  
the equilibrium lies clearly to the right (all reactants transform in products) or to the left or the equilibrium is in between, all species being present all the time. When there is 0% or 100% yield, we have a large positive or negative \(\Delta\)G and an accurate prediction is less important. For cases where \(\Delta\)G is close to zero we actually need a very accurate, at the level of 4 kJ/mole accuracy, prediction in order to assess whether we have 20% or 80% yield for instance as that may well determine the economic feasibility of a process. A specific example is the transaminase reaction  
\[\text{X-NH}_{2}+\text{YC}\text{=O}\rightarrow\text{XC}\text{=O}+\text{Y-NH} _{2} \tag{4}\]  
with the final amine as given target molecule, the initial ketone is known and the question is what is the right choice for the initial amine to have a successful transformation (equilibrium largely on the right-hand-side). Relatively simple quantum mechanical calculations have been shown to be a successful toll to predict whether the reaction is thermodynamically favourable [34]. The oval in Figure 3 shows the effect of a 4 kJ/mole difference on the conversion and the data displayed reveal a good correlation between experimental data and model to allow for adequate predictions in an industrial context. The data that are really outside the oval on the right-hand side are those for which from experiments it is known that enzyme inhibition is known likely to occur.  
Similar arguments and cases can be put forward for many other properties of interest to chemists and chemical engineers.  
Figure 2: Neural network based methods for the glass transition temperature Tg for a series of polymers. Different models were built leading to different quality with R\({}^{2}\) ranging from 0.80 to 0.99. It can be seen clearly that for R\({}^{2}\) < 0.99 the model does not describe all Tg values within a few degrees.