## 3 Results
However, absolute values close to 1 indicate that the points align, forming a line, increasing the dispersion of the points in relation to the line when the absolute value of \(r_{xy}\) decreases. In the present study, positive values close to 1 indicate a good alignment of the reference and estimated values, which is one of the requirements for the application of the developed method. 2. The root of normalized root mean square deviation nRMSD >= 0, defined as \[nRMSD=\frac{RMSD(v_{e},v_{r})}{\sigma_{r}},\] (16) where \[RMSD(v_{e},v_{r})=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(v_{e,i}-v_{r,i}\right) ^{2}}\] (17) is the root mean square deviation and \(\bar{v}_{r}\) is the mean of the reference values. The RMSD serves to aggregate the magnitudes of the differences between the estimated and reference values for several specimens in a single measurement. It is a widely used measurement to assess the accuracy of predictions, but it depends on the scale. For this reason, in this study, we used the version normalized by the mean value of the reference, which generally varies between 0 and 1 in different applications, although it can exceed 1 in cases with a very low correlation between the estimated and expected data. In our case, we require low values of \(nRMSD\), much lower than 1. The concomitant use with \(r_{xy}\) is due to the fact that although both measurements measure the distance between the estimated and reference values, they accomplish this differently: with bivariate \(r_{xy}\) and univariate \(nRMSD\) as they capture different characteristics of the compared data. 3. Finally, after correcting for systematic deviations, the estimated values must be proportional to the reference values and vice versa, and the proportionality coefficient must be close to 1. In other words, the coefficient of the proportional model \(v_{r}=a\ v_{e}\) must be close to 1. Applying minimum squares, the formula for \(a\) was obtained, such that \[a=\frac{\sum_{i=1}^{n}v_{e,i}v_{r,i}}{\sum_{i=1}^{n}\left(v_{e,i}\right)^{2}}.\] (18) Including the proportionality coefficient is strictly necessary, as neither \(r_{xy}\) or \(nRMSD\) are affected by the dependence slope or the displacement of the line that represents the relationship between the estimated and reference values. In other words, two linear dependence functions \(y=a_{1}x+b_{1}\) and \(y=a_{2}x+b_{2}\), with \(a1\
eq a2\) and \(b1\
eq b2\), can have the same \(r_{xy}\) and \(nRMSD\) correlation coefficients. This indicates that these two metrics do not carry information on the type of linear dependence that relates the two variables. In this case, the dependence between the reference values and the estimated values being proportional is a requirement to validate the developed method, which implies that considering the null intercept, \(b=0\), the linear coefficient of the regression is close to 1, \(a\to 1\). The calculated metrics are shown in Table 8, and in Figure 11 we plot the reference values on the vertical axis and the estimated values for the pore, gravel, and EVA contents on the horizontal axis, together with the proportional model obtained by regression in each case. Analyzing the component with the best of each of the metrics, it can be noted that the EVA estimates have the closest coefficient to 1 (\(a=1.0178\)), the porosity estimates have the highest correlation (\(r_{xy}=0.9099\)), while the gravel volume estimates have the lowest \(nMSD=0.1473\). Under these conditions, it is difficult to conclude which of the three compositional variables was the best estimated. Therefore, we introduce a quality metric of estimates, \(Q\in[0,1]\), which considers the three basic metrics in an integrated manner. The quality is defined according to the harmonic mean of the deviations from the optimal value of each metric, as follows:  
Table 7.0  
This metric varies between 0 and 1 and gives equal weight to all the integrated metrics, serving as an indicator to compare the performance of concrete characterization methods.