I have a hypothetical setting I am trying to use to better understand Euclidean distance. So of course this example will only work for the purpose of understanding a concept, rather than actually being realistic. I want to find the impact of urban trees on the indoor air quality of nearby buildings. Of course, this would be the idea that by being nearby more trees, your building would have cleaner air inside. However, I need to prove this, which I want to do with regression, saying that yes, there is a statistically significant relationship between proximity to trees and indoor air quality. I am trying to figure out how to actually get this distance-to-trees consideration into a data layer, and I am thinking I should use Euclidean distance.
How would Euclidean distance in this situation be different than just distance? More specifically, would Euclidean distance mean just the distance from a building to the nearest tree and that's it, ignoring all other trees less nearby, but still somewhat nearby? To conceptualize, let's say building A is 25 feet away from the nearest tree and that is the only tree within a 100 foot radius, and building B is 50 feet away from the nearest tree, but there are multiple of these trees that are 50 feet away. How would all of these distances be weighted? If we are conceptualizing these trees as radiating clean air, then which building would be more affected by the trees in terms of Euclidean distance? Yes, building A is closer to a tree than building B, but building B has more trees still somewhat close to it. This is the confusion I am having over whether I should use Euclidean distance. Would Euclidean distance still be appropriate for this situation since I am interested in proximity?
The goal would be to use the Euclidean distance raster output layer as the explanatory variable in a geographically weighted regression, with indoor air quality for buildings as the dependent variable, all in QGIS.