## 3 Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimens** & \begin{tabular}{c} **Average Value of** \\ **Compressive Strength (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Average Value** \\ **of UPV (km/s)** \\ \end{tabular} & \begin{tabular}{c} **Calculated Compressive** \\ **Strength (MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Absolute Error** \\ **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **Relative Error** \\ **(\%)** \\ \end{tabular} \\ \hline
1(A-B-C) & 19.23 & 3.79 & 21.33 & 2.11 & 10.96 \\
2(A-B-C) & 28.58 & 3.94 & 27.01 & 1.56 & 5.48 \\
3(A-B-C) & 28.34 & 3.94 & 27.01 & 1.33 & 4.70 \\
4(A-B-C) & 27.46 & 3.95 & 27.15 & 0.31 & 1.13 \\
5(A-B-C) & 43.05 & 4.20 & 40.40 & 2.65 & 6.16 \\
6(A-B-C) & 41.47 & 4.18 & 39.48 & 1.99 & 4.80 \\
7(A-B-C) & 39.64 & 4.17 & 38.58 & 1.06 & 2.67 \\
8(A-B-C) & 40.67 & 4.18 & 39.03 & 1.64 & 4.04 \\
9(A-B-C) & 40.59 & 4.08 & 33.37 & 7.23 & 17.81 \\
10(A-B-C) & 29.73 & 4.04 & 31.44 & 1.71 & 5.75 \\
11(A-B-C) & 31.21 & 4.10 & 34.68 & 3.47 & 11.12 \\
12(A-B-C) & 39.77 & 4.24 & 43.34 & 3.57 & 8.98 \\
13(A-B-C) & 38.56 & 4.26 & 44.12 & 5.56 & 14.42 \\
14(A-B-C) & 41.87 & 4.23 & 42.08 & 0.21 & 0.51 \\
15(A-B-C) & 36.59 & 4.15 & 37.50 & 0.91 & 2.48 \\
16(A-B-C) & 57.06 & 4.40 & 55.74 & 1.31 & 2.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results obtained for the statistical analysis of exponential regression. Figure 2: Presentation of the results of the compressive strength test concerning the calculated ultrasonic pulse velocity. The blue line represents the exponential trend of the values, and the red dashed lines represent the limits set with 95% confidence. The upper and lower reliability limits with a 95% confidence level were:  
\[\text{Upper limit}=0.0804\times e^{1.5246\times UPV} \tag{9}\]  
\[\text{Lower limit}=0.003\times e^{2.2424\times UPV} \tag{10}\]  
The graphic representation of these results is shown in Figure 3.  
In this estimation, if we were to obtain a UPV of 4.15 km/s, we would know with 95% confidence that the compressive strength value was between 33.39-44.97 MPa. The absolute and relative errors ranged from 0.20 to 1.6 and from 0.47 to 6.98%, respectively. For this second exponential regression, a higher R\({}^{2}\) was obtained, which means that the regression is better adjusted to the real data. In addition, both absolute and relative errors were lower than those obtained in the first regression. This may be because the samples were composed of natural materials from the same deposit that have a similar chemical composition. However, the size of the samples, which was smaller than in the previous case, can affect the trend. The same procedure followed for the exponential regression was repeated to study the possible linear trend of the results. The equation determined from the statistical analysis of exponential regression of the results, with a determination coefficient (R\({}^{2}\)) of 0.873, is as follows:  
\[\text{Compressive strength}=53.93\times UPV-185.55 \tag{11}\]  
The upper and lower reliability limits with a 95% confidence level were:  
\[\text{Upper limit}=53.939\times UPV-181.65 \tag{12}\]  
\[\text{Lower limit}=53.939\times UPV-189.45 \tag{13}\]  
The graphic representation of these results is shown in Figure 4.  
Figure 3: Presentation of the results of the compressive strength test concerning the calculated ultrasonic pulse velocity of the natural mordenite. The blue line represents the exponential trend of the values, and the red dashed lines represent the limits set with 95% confidence. In this estimation, if we were to obtain a UPV of 4.15 km/s, we would know with 95% confidence that the compressive strength value was between 34.27-42.32 MPa. Table 4 shows the results of the estimated compressive strength calculated by Equation (11) for the UPV values obtained. In addition, the relative and absolute errors between the real and calculated values were obtained. The absolute and relative errors of the results obtained by lineal regression vary from 0.09 to 6.17 and from 0.34 to 15.21%, respectively.