The case of studies chosen in the territory of Vernier, considered in 2011 as the denser commune of the Canton of Geneva and as one of the most vulnerable.
A research have developed an index helping to identity at small scale specific/critical neighborhood and environment which need green areas in priority, by taking into consideration the type of the vegetation and the proximity to green. Improvements still need to be done in order to include social aspects into the model.  
A global visualization of the situation in 2015 is takes as reference. The hypothesis developped is an inverse relation between the distance to the nature
Initial data  
A set of data including a population file, a group of two vegetation layers of the Geneva's region and a vector file highlighting  the limits of the municipality of Vernier were used to perform the analysis. 
Note that all the data were georeferenced using the same coordinate systems  CH1903+LV03.  

Methods

In order to evaluate the correlation between populaation repartition and the distance to the closest green area, initial data were loaded on QGIS first and secondly on the GeoDa software. At first,  on the base of the hectometric geometry of the population file, a regular grid surrounding the Vernier municipality, was created (resolution of 100*100). Combining different Qgis functions allowed to obtain for each cell the distance from the closest green area. The grid was then exported on GeoDa where all the principal statistic analysis, as well as maps, were computed. 
First, a linear regression was established to explore the relation between our variables: 
\(y_j=\beta_0+\beta_1x_{1j}+\epsilon_j\), where the variable \(y_j\), correspond to the total population and the variable \(x_j\) to the distance from the green region and \(\epsilon_j\) to the residus of each location j
Based on a stationarity hypothesis  of the observed spatial phenomenon, this statistical analysis doesn't seem realistic for the study. Poor results obtain from this hypothesis push to put in place a regression with dependent spatially weighted variable in order to obtain a regression line for each spatial unit:
 \(y_j=\beta_0+\beta_1x_{j1}+\rho w_iy_i+\ \epsilon_j\) , with  \(w_i\) the weight of the spatial unit i relative to the spatial unit j and \(\rho\) the spatial lag computed by taking the weighted average of the neighboring cells.