When we have a scatterplot between two variables Y, X we usually want to present a curve that relates the two variables. Firstly, because it allows us to see if the relationship is linear (or almost linear); secondly, because interpreting scatterplots is sometimes hard; and, finally, because we might want to have a simple model that can be used to predict Y in terms of X capturing all possible nonlinear patterns.
Locally Estimated Scatterplot Smoothing (LOESS) regression works by fitting lots of local models around each point. These local models are then averaged out. In particular, each model (fitted around a point X0,Y0) is fitted using weighted least squares (each point is weighted by how close the regressors are to the point X0). There is a parameter specified by the user, called the bandwidth, which specifies how much data is used in each one of these regressions...
