# Nanomaterials' Influence on the Performance of Thermal Insulating Mortars--A Statistical Analysis
## 3 Results and Discussion
### Uni and Bivariate Analysis
#### 3.1.3 Discussion of the Uni and Bivariate Analysis  
From Table 5, it is seen that the average value of \(f\!c\) is \(\sim\) 1.33 MPa and of \(fu\) is \(\sim\) 0.16 MPa, with both properties presenting a higher concentration of formulations (positive asymmetry) on lower values. This indicates the influence that a small number of mortars with higher values can present. It is also possible to see that, as already known [25, 69], these mortars tend to present lower mechanical performance than current cement-based mortars, which seems associated with the inclusion of the nanomaterial silica aerogel [99]. Something that is also noted is the need for an increased \(w\!p\) ratio when compared to conventional cement-based mortars [100], which can also influence their physical and mechanical performance due to an increased porosity. For the physical characteristics (\(\lambda_{10^{\circ}C,dry}\), \(W\) and \(\Lambda\)) it was found, as shown in Table 5, that the average values are of 0.122 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\); 0.479 kg\(\cdot\)m\({}^{-2}\cdot\)min\({}^{-0.5}\) and 2.0 \(\times\) 10\({}^{-11}\) kg\(\cdot\)m\({}^{-2}\cdot\)s\({}^{-1}\cdot\)Pa\({}^{-1}\). These are results with lower \(\lambda_{10^{\circ}C,dry}\) and \(\Lambda\) than conventional cement-based mortars, but with higher \(W\)[101, 102]. \begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow{2}{*}{**Variable**} & \multicolumn{10}{c|}{**Correlations in Bold are Considered Significant: \(p\)-_Value_ **\textless{} 0.05**} \\ \cline{2-13}  & **Bar** & **Cons** & **BDs** & **w/p** & **AC** & **fu** & **BDs** & **Ed** & **fc** & **ft** & **W** & **A**\({}_{10^{\circ}C,dry}\)** & **A**\({}_{10^{\circ}C,dry}\)** & **TK** & \(\Lambda\) \\ \hline
**Bar** & 1.00 & 0.06 & 0.91 & \(-\)0.62 & \(-\)0.31 & 0.21 & 0.85 & 0.57 & 0.52 & 0.71 & \(-\)0.28 & 0.72 & 0.68 & \(-\)0.48 & 0.22 \\ \hline
**Cons** & 1.00 & 0.03 & 0.15 & \(-\)0.07 & \(-\)0.25 & 0.13 & 0.10 & \(-\)0.02 & \(-\)0.06 & 0.03 & 0.18 & 0.15 & 0.06 & 0.01 \\ \hline
**BDr** & & 1.00 & \(-\)0.62 & \(-\)0.26 & 0.24 & 0.90 & 0.68 & 0.65 & 0.78 & \(-\)0.36 & 0.81 & 0.74 & \(-\)0.47 & 0.29 \\ \hline
**w/p** & & & 1.00 & 0.30 & \(-\)0.64 & \(-\)0.65 & \(-\)0.53 & \(-\)0.64 & \(-\)0.68 & 0.53 & \(-\)0.52 & \(-\)0.48 & 0.56 & \(-\)0.11 \\ \hline
**AC** & & & 1.00 & \(-\)0.09 & \(-\)0.27 & \(-\)0.45 & \(-\)0.30 & \(-\)0.29 & 0.20 & \(-\)0.45 & \(-\)0.44 & 0.18 & 0.09 \\ \hline
**fu** & & & & 1.00 & 0.24 & 0.18 & 0.50 & 0.42 & \(-\)0.35 & 0.17 & 0.07 & \(-\)0.44 & \(-\)0.00 \\ \hline
**BDu** & & & & & 1.00 & 0.64 & 0.59 & 0.80 & \(-\)0.45 & 0.85 & 0.82 & \(-\)0.53 & 0.26 \\ \hline
**Ed** & & & & & & 1.00 & 0.84 & 0.73 & \(-\)0.45 & 0.83 & 0.75 & \(-\)0.17 & 0.24 \\ \hline
**fc** & & & & & & 1.00 & 0.82 & \(-\)0.44 & 0.72 & 0.61 & \(-\)0.22 & 0.26 \\ \hline
**ft** & & & & & & 1.00 & \(-\)0.42 & 0.80 & 0.76 & \(-\)0.39 & 0.24 \\ \hline
**W** & & & & & & & 1.00 & \(-\)0.40 & \(-\)0.32 & 0.32 & \(-\)0.19 \\ \hline
**A**\({}_{10^{\circ}C,dry}\) & & & & & & & & 1.00 & 0.96 & \(-\)0.41 & 0.22 \\ \hline
**A**\({}_{10^{\circ}C,dry}\) & & & & & & & & & 1.00 & \(-\)0.43 & 0.24 \\ \hline
**TA** & & & & & & & & & & 1.00 & 0.18 \\ \hline \end{tabular} Note to Table 6: bold—significant correlations; cells with thick lines – highest positive correlations; cells with dashed lines—highest negative correlation.  
\end{table} 
Table 6: Matrix with the linear correlation coefficients between pairs of variables. Figure 1: Example of the scatterplot matrix. Both \(\lambda_{10^{\circ}C,dry}\) and \(\Lambda\) present interesting performance, but \(W\) can be further improved. All these characteristics present positive asymmetries, but, due to the high degree of magnitudes, the higher values influence the average performance.