Discussion
As indicated in the results section, both scatterplots in figures \ref{206631} and \ref{691511} show a negative autocorrelation between the housing assistance and the distances. This tends to confirm the original hypothesis stating that more vulnerable people are located closer to service stations and their related polluted areas. This class of people seems therefore more prone to pollution, as some buildings are located within a 75m radius from service stations, mentioned in the paper \citep{Morales_Terr_s_2010} as the region of direct pollution impact due to the stations' emissions.
This comes as an interesting result and adds up to the fact that this group of population usually resides closer to road networks. Aggravated health risk factors could then be considered. Nevertheless, this conclusion is to be tempered. Indeed, the determination coefficient (R2) is close to zero in both cases : 0.0533 and 0.0488. This indicates the regression line does not fit the data very well and high residuals are to be expected.
This bad fitting is emphasized by the vulnerability grids obtained when applying the non-spatially and spatially weighted regression. The results are presented in the figures \ref{856441} and \ref{146549}. Both figures present the same kind of results. It is worth noticing that the regression models have a hard time approximating the higher housing assistance values as mentioned above.