## 5 Results
### Regression Analysis  
The analysis was carried out in three phases: (1) multivariate multiple regression analysis aiming to find the best set of predictor variables among the soundscape indicators included in the  
Figure 1: Perceived quality of urban and restaurant soundscape _types_ plotted in the _Pleasantness-Eventfulness_ circumplex. For details, see Methods section. 95% confidence ellipses are plotted, i.e., the ellipses have radii corresponding to 97.5% confidence intervals around means on \(x\) and \(y\) axes. The thickness of the ellipse circumference is proportional to the mean _loudness_ within the _type_. cross-correlation analysis above; (2) extending the multivariate model to include personality trait variables as predictors; (3) exploring the relationship between personality traits and soundscape indicator variables in separate univariate multiple regression models. Please note that in the context of a prediction, no distribution assumptions are required for statistics such as \(\beta\), \(sr^{2}\) (squared semipartial correlation), or \(R^{2}\) (total amount of variation explained); see [PERSON] ([49], p. 504) for a discussion. However, the probability values attached to these statistics do depend on distribution assumptions such as homoscedasticity, normality, and linearity. This point is important, and since our present data did not fulfil all required assumptions, the interpretation of significance levels and effect sizes of regression models will be tentative. An effect size statistic for sequential multiple regression is given by [PERSON] [50; 51]. In the first analysis phase, we conducted a process of forward stepwise multivariate linear regression analysis aiming to find the best set of independent variables for simultaneous prediction of _Pleasantness_ and _Eventfulness_ averaged across participants. We considered the five soundscape indicators that [PERSON] et al. [41] had reported (\(N_{10}\), \(L_{Aeq}\), \(N_{10}\)-\(N_{30}\), \(L_{10}\)-\(L_{90}\), and \(L_{A\text{-}C}\)) and the predetermined soundscape _type_ categorical variable. Not unexpectedly, _type_ explained the largest amount of variation. In Experiment 1, which had 12 cases, _type_ on its own explained 68.2% (multiple \(R^{2}\)) of the variation in mean ratings of _Pleasantness_ and _Eventfulness_. In Experiment 2, which had 15 cases, soundscape _type_ explained 51.8% of the variation in the two dependent variables. We then analysed if the predictive model could be improved by the addition of one or more of the acoustic variables. The difference between basic and extended models was tested using ANOVA. In Experiment 1, an extended model with _type_ and _loudness_ (\(N_{10}\)) as predictors explained 79.1% of the variation in the dependent variables. The increase over the basic model was significant (Pillai = 0.62, \(p\) = 0.05). In Experiment 2, the amount of variation explained by the extended model was raised to 64.0%, but in this case the increase was not significant (Pillai = 0.37, \(p\) = 0.12). Adding a third variable did not make any significant improvements and the process was stopped at this point. In the second phase, we investigated the influence of individual differences on soundscape evaluations and moved from using averaged responses to using all the available data. The personality trait variables have been described previously. Note that since the models in the previous phase predicted average responses, the amounts explained are quite high. Because a certain amount of error is attached to the measurement of individual participant traits, as well as error attached to their individual quality ratings, we expected the multiple \(R^{2}\) to be lower when all the data were included. In this situation, the model with soundscape _type_ and \(N_{10}\) as predictors explained 42.3% of the variation in _Pleasantness-Eventfulness_ in Experiment 1, and 20.4% in Experiment 2.