## 4 Results
### Multiple Linear Regression
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factor** & **Estimate** & **SE 1** & **DF 2** & **T Value** & **_p Value_** & **R2 Value 3** \\ \hline AFE-based valence & \(1.755\) & \(0.365\) & \(129\) & \(4.810\) & \(<\)0.001 * & \(0.152\) \\ EDA Z-Score & \(0.114\) & \(0.056\) & \(129\) & \(2.020\) & \(0.046\) & \(0.019\) \\ Phasic & \(0.154\) & \(0.064\) & \(127\) & \(2.420\) & \(0.017\) & \(0.028\) \\ Slope & \(-310.810\) & \(92.645\) & \(144\) & \(-3.350\) & \(0.001\) * & \(0.060\) \\ Entropy & \(-0.240\) & \(0.157\) & \(144\) & \(-1.530\) & \(0.129\) & \(0.012\) \\ Centroid & \(0.000\) & \(0.000\) & \(144\) & \(-1.410\) & \(0.160\) & \(0.009\) \\ Spread & \(0.000\) & \(0.000\) & \(144\) & \(-2.940\) & \(0.004\) * & \(0.044\) \\ PPE 5 & \(0.000\) & \(0.000\) & \(144\) & \(-1.880\) & \(0.062\) & \(0.014\) \\ F0 Standard Deviation & \(0.017\) & \(0.006\) & \(144\) & \(2.610\) & \(0.010\) & \(0.032\) \\ F0 mean & \(0.001\) & \(0.004\) & \(144\) & \(0.260\) & \(0.799\) & \(<\)0.001 \\ Log energy & \(0.073\) & \(0.022\) & \(144\) & \(3.360\) & \(0.001\) * & \(0.079\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Regression results of Arousal dimension. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Factor** & **Estimate** & **SE 1** & **DF 2** & **T Value** & **_p Value_** & **R2 Value 3** \\ \hline AFE-based valence & \(-0.400\) & \(0.530\) & \(129\) & \(-0.75\) & \(0.452\) & \(0.005\) \\ EDA Z-Score & \(-0.133\) & \(0.082\) & \(129\) & \(-1.61\) & \(0.109\) & \(0.016\) \\ Phasic & \(-0.108\) & \(0.095\) & \(127\) & \(-1.14\) & \(0.255\) & \(0.008\) \\ Slope & \(367.030\) & \(136.200\) & \(144\) & \(2.69\) & \(0.008\) & \(0.049\) \\ Entropy & \(0.425\) & \(0.229\) & \(144\) & \(1.86\) & \(0.065\) & \(0.023\) \\ Centroid & \(0.000\) & \(0.000\) & \(144\) & \(1.53\) & \(0.129\) & \(0.014\) \\ Spread & \(0.000\) & \(0.000\) & \(144\) & \(2.07\) & \(0.040\) & \(0.029\) \\ PPE 4 & \(0.000\) & \(0.000\) & \(144\) & \(0.3\) & \(0.764\) & \(<\)0.001 \\ F0 Standard Deviation & \(-0.004\) & \(0.010\) & \(144\) & \(-0.41\) & \(0.681\) & \(0.001\) \\ F0 mean & \(-0.002\) & \(0.006\) & \(144\) & \(-0.38\) & \(0.702\) & \(0.001\) \\ Log energy & \(-0.049\) & \(0.032\) & \(144\) & \(-1.57\) & \(0.120\) & \between the evaluated dimension of arousal and EDA features, EDA z-score and phasic EDA, with respective \(p\)-values of 0.046 and 0.017, both were deemed insignificant following the Bonferroni correction (see Table 6). Within the context of this study, the amplitude of the extracted EDA features was not indicative of a user's arousal during voice user interface interactions. Thus, H2a is not supported. Multiple linear regressions between AFE-based valence and ground-truth dimension of valence revealed a relationship between the feature and the emotional intensity of users during voice user interface interactions. Indeed, the multiple linear regression revealed a significant relationship between the evaluated dimension of valence and AFE-based valence (\(p<0.0001\)). This fact remained valid following the Bonferroni correction. The R-squared value associated with AFE-based valence was of 0.402. Statistically speaking, approximately 40% of the dimension variable is explained by AFE-based valence (see Table 5). In other words, the amplitude of the extracted AFE-based valence feature is explicative of a user's valence during voice user interface interactions. Hence, H2b is supported.