Local smoothing is a smoothing or generalization technique to further enhance the visual representation of a relationship between two variables. In Stata this is achieved with the lpoly (local polynomial smoothing) command. This is especially useful when you’re not getting satisfactory results with for example lfit or qfit. For instance:
sysuse nlsw88, clear
lpoly wage grade, nosc
Note the nosc option, which is short for no scatter. The bandwitdth is set to 1.35 and is a best guess by Stata, but can be se explicity by use of the bw option, like so:
lpoly wage grade, nosc bw(1)
A lower bandwith value gives a more pointy curve whereas a higher value gives a more rounder look. (From a purely visual perspective i think the default in this case as set by Stata was sensible enough).