## 4 Data Analysis and Results  
### Correlation Between UCS and BTS  
Various types of curves, including linear (y = ax + b), power (y = axb), exponential (y = aex), and logarithmic (y = a + ln x), were fitted to the data. The degree of fitting data to a curve can be measured using the value of coefficient of correlation (r). This parameter is one of the most common and widely used statistical criteria to evaluate the accuracy of a regression equation established between two variables [58; 85]. For a correlation equation, the r is between 0 and 1, in which a higher r indicates better accuracy for predicting a dependent variable by an independent variable. In the present study, the value of r was used as a comparative measure to select the most appropriate regression curve. Based on which curve had the highest r, the corresponding correlation equation was chosen as the best empirical equation between the UCS and BTS. According to the r values, a linear correlation equation was obtained between UCS and BTS. As shown in Figure 4, there is a good r value equal to 0.81 for the correlation equation between the UCS and BTS as follows:  
\[\text{UCS }=\ 11.905\times\text{BTS}\qquad\qquad\text{r }=\ 0.81 \tag{2}\]  
Figure 3: Number of data of igneous stones types collected from the previous studies. \begin{table}
\begin{tabular}{c c c} \hline
**Stone Class** & **Stone Subclass** & **Stone Type** \\ \hline Igneous & Plutonic & Anorthosite, Aplite, Diorite, Dunite, Gabbro, \\  & Plutonic & Granite, Granitoid, Granoidorite, Monzogranite, \\  & & Monzonite, Norite, Peridotite, Svenite, \\  & & Syenogranite, Tonalite, Troctolite \\  & Subvolcanic & Diabase, Spilite \\  & Volcanic (flow) & Andesite, Basalt, Dacite, Rhyolite, Trachytte \\  & Pyroclastic & Ignimbrite, Tuff \\ \hline \end{tabular}
\end{table} 
Table 3: Stone types used in the present study. The correlation equation between UCS and BTS established in the present study was compared with those that were reported in the previous studies. According to the literature, there are many correlation equations to predict UCS of various rocks using their BTS. Some of these equations are presented in Table 4. [PERSON] and [PERSON] [46] developed a linear correlation between the UCS and BTS of igneous rocks with a good r equal to 0.96. Based on the results of [PERSON] et al. [58], there is a linear relationship with an r of 0.73 between UCS and BTS for the various rock classes. In another study, [PERSON] and [PERSON] [74] reported an excellent power correlation between UCS and BTS for various rock classes with an r of 0.95. [PERSON] and [PERSON] [77] proposed an excellent power equation (r = 0.95) to predict UCS various rock classes using their BTS. [PERSON] and [PERSON] [88] prepared a power correlation to predict UCS using BTS (r = 0.97) for sedimentary rocks. [PERSON] and [PERSON] [89] established a linear correlation between UCS and BTS (r of 0.81) for sedimentary rocks. According to a study by [PERSON] et al. [90], a linear equation between UCS and BTS with a moderate r equal to 0.67 was obtained for sedimentary rocks. In another study, [PERSON] et al. [91] offered a moderate linear correlation (r of 0.78) between UCS and BTS for igneous rocks. In a study by [PERSON] and [PERSON] [92] on igneous rocks, a power correlation with a good r of 0.89 was obtained between UCS and BTS. [PERSON] et al. [93] developed a linear correlation to predict UCS from BTS with a good r equal to 0.91 for sedimentary rocks. Based on their experimental test results on metamorphic rocks, [PERSON] [94] established a linear correlation to express the relationship between UCS and BTS with an excellent r of 0.96. [PERSON] et al. [95] determined the UCS and BTS of the sedimentary rocks and results showed a moderate linear correlation between these parameters (r of 0.79). For sedimentary rocks, a linear equation with a r of 0.73 between UCS and BTS was obtained by [PERSON] [96].