## 3 Results and Discussions
Variability is the amount of dispersion present in the data. Two data sets can differ in both location and variability; or they can be characterized by the same variability, but by a different measure of position; or again, they may have the same position measure, but differ considerably in terms of variability. One measure that considers how observations are distributed or concentrated around a central trend measure is the root mean square error. The mean squared error (MSE) of an estimator with respect to the estimated parameter is defined as follows [53]:  
\[MSE=\frac{1}{N}\ \sum_{i=1}^{N}(x_{i}-\hat{x}_{i})^{2} \tag{12}\]  
Here,  
* \(x_{i}\) is the real value. * \(\hat{x}_{i}\) is the predicted value. * \(N\) is the number of the observation. Another way to measure model performance is to use the correlation coefficient. Correlation is an index that measures the association between two variables, more specifically, it measures the degree to which two variables move together [54]. Regardless of the type of correlation index you intend to use, all indices have some common characteristics. The two sets of scores are associated with the same individuals or events, or with different subjects but associated with each other from a specific point of view. The value of the correlation index vary between \(-1\) and \(+1\); both extreme values represent perfect relationships between the variables, while \(0\) represents the absence of relationship. This at least if we consider linear relationships. A positive relationship means that individuals who get high values in one variable tend to get high values on the second variable. And vice versa is also true, that is, those who have low values on one variable tend to have low values on the second variable. A negative relationship indicates that low scores on one variable correspond to high scores on the other variable [55]. In Table 6 are shown the MSE and the correlation coefficient returned by the model. The values in Table 6 tell us that the errors made in the prediction of the reverberation time are very low; specifically, there is a slight increase in the error passing from the training set to the test set. Consistent with this result, the correlation coefficient presents values very close to unity indicating a strong correlation between the real values and those predicted by the model. Additionally, in this case there is a slight decrease in R passing from the training set to the test set. These results tell us that the procedure proposed in this work can return the values of the reverberation time of a room using simple sound recordings. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **MSE** & **R** \\ \hline Training & \(3.58\times 10^{-3}\) & \(9.94\times 10^{-1}\) \\ Validation & \(9.13\times 10^{-3}\) & \(9.87\times 10^{-1}\) \\ Test & \(9.01\times 10^{-3}\) & \(9.79\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: MSE and R for the regression model. Figure 7: Parameter changes during the training process. The term epoch refers to one cycle through the full training dataset. (**a**) Shows the variation of the gradient at each step performed by the algorithm for adjusting the weights of the connections, as described in Equation (7). (**b**) Shows how the scalar parameter \(\upmu\) was used to balance the two contributions of the algorithm Newton and gradient descent changes, as described in Equation (10).