## 4 Results
### Spatial Regression  
Finally, in our analysis we integrate geographic information generated by social media's users into AuGI concerning topography, transport infrastructure, cultural heritage sites, and socio-economic features. The spatial relationships and the explanatory factors behind observed spatial patterns were modeled using a spatial regression [34]. For each census tract, a measure of the set of independent variables was calculated. Preliminary results suggested excluding some explanatory variables from the model, because they did not comply with the Variance inflation factor (VIF) test. The VIF test provides a measure of the size of the multicollinearity generated by the inclusion of an explanatory variable in a ordinary-least-squares regression model. We assume that a variable should excluded from the set of the explanatory variables if the VIF is greater or equal to 10. [35]. The results of the statistical tests for measuring redundancy suggested that the following candidate's variables are included, normalized by the total area of the census tract:  
1. number of historical buildings in the TLS' census tract (variable \"N_hist_buildings\" in Table 2);
2. number of restaurants and facilities in the TLS' census tract (variable \"N_restaurants\" in Table 2);
3. hectares of natural protected areas in the TLS' census tract (variable \"H_natural_areas\" in Table 2);
4. distance from the airport (variable \"Distance_airport\" in Table 2);
5. proximity to the historic center of the municipality (variable \"Proxy_historic_center\" in Table 2);
6. distance from the municipality's beach (variable \"Distance_beach\" in Table 2). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Coefficient** & **Std. error** & **z-value** & **_p-value_** \\ \hline TPDI\_lag [19] & 0.0663 & 0.0307 & 2.1621 & 0.0306 \\ Constant & 0.0031 & 0.0102 & 0.3012 & 0.7633 \\ N\_restaurants & \(-\)0.0390 & 0.0300 & \(-\)1.3013 & 0.1932 \\ Proxy\_historic\_center & 0.4748 & 0.0585 & 8.1146 & 0.0000 \\ N\_hist\_buildings & \(-\)0.0273 & 0.0313 & \(-\)0.8724 & 0.3830 \\ H\_natural\_areas & 0.0027 & 0.0096 & 0.2834 & 0.0777 \\ Distance\_airport & 0.7661 & 0.0340 & 22.5511 & 0.0000 \\ Distance\_beach & 0.5470 & 0.0383 & 14.2922 & 0.0000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the spatial regression model: influence of each explanatory variable on dependent variable (tourist’s preference). The assumption was that if the value of the normalized TPPI is similar to the values that it takes in the closest spatial units, the variable is characterized by spatial autocorrelation. A spatially-lagged explanatory variable is added to control for spatial autocorrelation of the dependent variable [36]. We introduce, among the covariates of the spatial regression, a spatially-lagged dependent variable (variable TPPI-lag in Table 2) which controls for the spatial autocorrelation of the dependent variable TPPI. We follow the methodology proposed by [PERSON] [37], and implemented by [PERSON] and [PERSON] [38]. The presence of spatial autocorrelation related to positive preference, whose value is the normalized TPPI, is detected through the Moran's test [37, 39]. The result of the local Moran's index is quite significant at the second order of queen contiguity in respect of results obtained using a 2500 m spatial autocorrelation distance: adjusted R-squared is less than 40%, the \(p\)-value of the coefficient of the dependent variable is very significant (\(1.0\times 10^{-8}\)) and the value of the Moran's index is 0.024. The very low \(p\)-value indicates that local spatial autocorrelation of the dependent variable is highly significant. The results concerning the goodness of fit of the spatial regression shown in Table 2 are significant: R-squared is as high as 86%, which indicates that variables in the model explain about 86% of the variance of the positive tourists' preferences.