## 5 Results and Analysis Using Learning Analytics Techniques
### Regression Analysis and Correlations
This means that, if a student has a high _Mus_ dimension, it does not provide much information about their _Inter_ dimension. Finally, the _Mus_ dimension is the least correlated with the remaining seven dimensions with an average correlation of \(r\) = 0.36. On the other hand, Table 8 indicates that the SRLAS dimensions are also positively correlated. Notably, _Anx_ and _ExtMot_ are the least correlated with all the other dimensions; however, they possess a high correlation between them (\(r\) = 0.50, as discussed in Section 5.1). The average correlation for _Anx_ with the remaining variables is \(r\) = 0.19 and for _ExtMot_, it is \(r\) = 0.23. This means that _Anx_ and _ExtMot_ have a low linear association concerning the other dimensions. The SRLAS dimension that presents the higher correlation with the remaining seven dimensions is _SelfReg_, with an average correlation of \(r\) = 0.54. Consequently, it is found that the dimension that best represents the SRLAS construct as a whole is _SelfReg_. Individually, the highest correlation is found between _SelfReg_ and _IntMot_, with \(r\) = 0.75. In other words, on average, the more intrinsically motivated the students are, the more self-regulated they are and vice versa. The lowest correlation coefficient is found between _ExtMot_ and _IntProc_, with \(r\) = 0.019, which is an indicator of the level of independence between the students' information processing capacity and their extrinsic motivation. All \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & **Final Grade** & _Intra_ & _Inter_ & _Lin_ & _Spa_ & _LogMath_ & _Mus_ & _BodKin_ \\ \hline _Intra_ & 0.04 & & & & & & & \\ _Inter_ & 0.06 & 0.39 & & & & & & \\ _Lin_ & 0.01 & **0.68** & 0.52 & & & & & \\ _Spa_ & 0.00 & 0.38 & **0.64** & 0.43 & & & & \\ _LogMath_ & 0.17 & **0.74** & 0.50 & **0.72** & 0.49 & & & \\ _Mus_ & \(-\)0.08 & 0.40 & 0.15 & 0.43 & 0.27 & 0.41 & & \\ _BodKin_ & 0.07 & 0.55 & 0.44 & 0.54 & 0.46 & **0.61** & 0.49 & \\ _Nat_ & \(-\)0.04 & 0.57 & 0.28 & 0.45 & 0.33 & 0.53 & 0.37 & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Correlations table for MI dimensions. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & Final Grade & _IntMot_ & _ExtMot_ & _FitMood_ & _Anx_ & _SelfReg_ & _SocInt_ & _InfSearch_ \\ \hline _IntMot_ & 0.130 & & & & & & \\ _ExtMot_ & \(-\)0.182 & 0.108 & & & & & \\ _FitMood_ & 0.014 & **0.505** & 0.267 & & & & & \\ _Anx_ & \(-\)0.208 & 0.090 & **0.500** & 0.186 & & & & \\ _SelfReg_ & 0.096 & **0.751** & 0.247 & **0.627** & 0.181 & & & \\ _SocInt_ & \(-\)0.029 & **0.515** & 0.159 & 0.453 & 0.191 & **0.548** & & \\ _InfSearch_ & 0.025 & **0.604** & 0.284 & **0.525** & 0.130 & **0.720** & 0.445 & \\ _InfProc_ & 0.104 & **0.705** & 0.019 & 0.412 & 0.026 & **0.697** & **0.561** & **0.632** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Correlations table for SRLAS dimensions. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Final Grade** & _Lin_ & _LogMath_ & _Mus_ & _Nat_ \\ \hline _IntMot_ & 0.130 & 0.212 & 0.237 & 0.169 & 0.108 \\ _ExtMot_ & \(-\)0.182 & 0.038 & \(-\)0.014 & 0.226 & 0.188 \\ _Anx_ & \(-\)0.208 & \(-\)0.031 & \(-\)0.111 & 0.116 & 0.103 \\ _SelfReg_ & 0.096 & 0.264 & 0.250 & 0.255 & 0.205 \\ _SocInt_ & \(-\)0.029 & 0.165 & 0.184 & 0.162 & 0.154 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Correlations table for SRLAS versus MI dimensions. these findings agree reasonably well with the results obtained with the PCA presented in Section 5.1  
Finally, Table 9 presents the main cross-correlations between MI and SRLAS dimensions. In general, we observed low correlations, which can be interpreted as evidence of the level of independence between the MI and SRLAS constructs.