## 3 Results
Furthermore, it was found that the absolute percentage difference between the reference percentages and those estimated for EVA, pore, and gravel, decreases with the increase in the content of additives (EVA + fiber), as shown in Figure 10. That is, the quality is superior when analyzing concretes with more content of light aggregates, which is the objective in civil construction practice: to add the largest quantity of light aggregates possible without compromising the mechanical strength characteristics of the structures. \begin{table}
\begin{tabular}{c c c c c} \hline
**Component** & **MAPD (\%)** & **a (\%/\%)** & **sd (\%)** & **r** \\ \hline GRAVEL & 11.27 & \(-\)0.475 & 6.200 & \(-\)0.492 \\ EVA & 30.97 & \(-\)2.842 & 28.00 & \(-\)0.585 \\ PORE & 24.49 & \(-\)1.053 & 15.50 & \(-\)0.490 \\ \hline \end{tabular}  
* ACA = Increase in Additive Content (EVA + fiber).  
\end{table} 
Table 7: Mean absolute percentage difference (MAPD, Equation (11)), rate of decrease of the relative difference with ACA (a), standard deviation of the relative differences with respect to its decreasing linear trend with ACA (sd), and the correlation coefficient between the relative difference and the content of EVA + fiber (r) for the estimates of pore volume, EVA, and gravel. The percentage decrease rates of the relative differences (coefficient a, in the linear model equation y = a*x + b) vary between \(a=-0.475\) for gravel content and \(a=-2.842\) for EVA volume. In other words, the relative difference between the reference values and those estimated for the volume of gravel decreases 0.475%, on average, for each 1% increase in the EVA + fiber content, decreasing 2.842%, on average, in the case of the EVA volume. These rates of decrease are statistically supported by the significant anti-correlation observed, with coefficients varying between \(r=-0.49\) for pore content and \(r=-0.585\) for EVA volume. The standard deviation of the differences in relation to the linear model was confined to the range of \(sd=6.2\%\) for gravel content to \(sd=28.0\%\) for EVA content. The values of the rates of decrease in the relative differences between the estimated and the reference values, as well as the correlation with the content of additives (EVA + fiber) and the standard deviation in relation to the adjusted linear model, are listed in Table 7. These results confirm that the relative difference between estimates and references decreases as the proportion of light aggregates increases. From a practical point of view, it is also very important that there is a good correlation between the estimated and reference values. To assess the degree of correlation between the reference volumes and the estimates of the lightweight concrete components in the nine specimens studied, we used three different metrics:  
1. The linear correlation coefficient \(r_{xy}\in[0,1]\), defined as: \[r_{xy}=\frac{s_{xy}}{s_{x}s_{y}},\] (12) where \[s_{x,y}=\frac{1}{n-1}\sum_{i=1}^{n}\left(v_{r,i}-\bar{v}_{r}\right)\left(v_{ e,i}-\bar{v}_{e}\right)\] (13) is the covariance of the data, and \(\bar{v}_{r}\) and \(\bar{v}_{e}\) are the means of the reference and estimated values, respectively; \[s_{x}=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}\left(v_{r,i}-\bar{v}_{r}\right)^{2}}\] (14) is the root of the standard deviation of the reference values; and \[s_{y}=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}\left(v_{e,i}-\bar{v}_{e}\right)^{2}}\] (15) is the root of the standard deviation of the estimated values. The coefficient \(r_{xy}\) varies between \(-1\) and \(1\) where the positive sign indicates that the independent variable \(y\) increases when the independent variable x increases and  
Figure 10: Linearly decreasing trend of the absolute percentage differences of pore, EVA, and gravel contents (vertical axis) with increasing EVA + fiber content (horizontal axis). vice versa for the negative sign.