## 3 Validation and Experimentation
### Empirical Validation
#### 3.2.2 Quantitative
To facilitate this calculation, an initial step involved constructing a matrix to explore correlations across all dimensions, allowing the identification of those with stronger connections (demonstrating a correlation coefficient threshold exceeding 70%). Subsequently, scatter plots were generated for the mean scores of the selected dimensions, facilitating comparison and computation of the linear correlation coefficient (R\({}^{2}\)). This coefficient ranges between 0 and 1, indicating a stronger linear relationship between dimensions as it approaches 1. \begin{table}
\begin{tabular}{c c c|c c c c c} \hline \hline \multirow{2}{*}{**Tasks**} & \multicolumn{5}{c}{**Task Success Rate**} & \multicolumn{5}{c}{**Task Completion Ratio**} \\ \cline{2-9}  & \multirow{2}{*}{**\%**} & \multirow{2}{*}{**SD**} & **Task Type\%** & **Main Activity\%** & **N\({}^{\circ}\) of** & **N\({}^{\circ}\) of** & **Completed** & **Completion** \\  & & & **(SD)** & **(SD)** & **Tasks** & **Tasks** & **Tasks** & **Rate (\%)** \\ \hline T1 & 99 & 6.4 & TT1. 99 (6.4) & & & 0 & 39 & 100 \\ T2 & 68.4 & 32.4 & & & & 3 & 36 & 92.3 \\ T3 & 65.8 & 309 & & & & 1 & 38 & 97.4 \\ T4 & 66.7 & 26.5 & & & & 1 & 38 & 97.4 \\ T5 & 59.8 & 29.8 & & & & 3 & 36 & 92.3 \\ T6 & 51.3 & 20.6 & & & & 1 & 38 & 97.4 \\ T7 & 53.2 & 19.2 & & & & 1 & 38 & 97.4 \\ T8 & 71.8 & 25.1 & & & & 0 & 39 & 100 \\ T9 & 71.8 & 23.6 & & & & 0 & 39 & 100 \\ T10 & 62.4 & 26.7 & & & & 2 & 37 & 94.9 \\ T11 & 47.1 & 34.8 & & & & 7 & 32 & 82.1 \\ T12 & 62.2 & 22.9 & & & & 0 & 39 & 100 \\ T13 & 63.6 & 33.7 & & & & 4 & 35 & 89.7 \\ T14 & 59.5 & 32.2 & & & & 7 & 32 & 82.1 \\ T15 & 47.7 & 31.7 & & & & 7 & 32 & 82.1 \\ T16 & 37.4 & 32.9 & & & & 7 & 32 & 82.1 \\ T17 & 52.8 & 34.5 & & & & 6 & 33 & 84.1 \\ T18 & 41.5 & 38.5 & & & & 13 & 26 & 66.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Success rate and task completion by experiment participants. The most substantial correlation uncovered emerged between the ease of use and ease of learning dimensions, registering a robust linear correlation coefficient of R\({}^{2}\) = 0.8669, denoting a positive correlation between these aspects (see Figure 13). This correlation implies that users experience heightened ease of use while utilizing RestRho, particularly when the tool offers increased accessibility in mastering its functions. Figure 14 showcases the second most notable correlation observed, between utility and ease of use, unveiling a compelling linear correlation coefficient of R\({}^{2}\) = 0.8118. This statistical observation underscores a noteworthy trend: as RestRho exhibits enhanced user-friendly attributes, users tend to perceive greater practicality in the tool. This correlation underscores the pivotal role of usability in bolstering the perceived value of RestRho among users, accentuating the significance of an intuitive and seamless user experience in maximizing the tool's overall utility. Figure 12: RestRho usability. Mean score for each dimension that is measured in values between 1 and 5, including error bars (\(\pm\sigma\)). Figure 13: Correlation between the dimensions ease of use and ease of learning.