This is a pure Julia loess implementation, based on the fast kd-tree based approximation described in the original Cleveland, et al papers[1,2,3], implemented in the netlib loess C/Fortran code, and used by many, including in R's loess function.

Loess exports two functions, loess and predict, that train and apply the model, respectively. The amount of smoothing is mainly controlled by the span keyword argument. E.g.:

using Loess, Plots

xs = 10 .* rand(100)
ys = sin.(xs) .+ 0.5 * rand(100)

model = loess(xs, ys, span=0.5)

us = range(extrema(xs)...; step = 0.1)
vs = predict(model, us)

scatter(xs, ys)
plot!(us, vs, legend=false)

There's also a shortcut in Gadfly to draw these plots:

plot(x=xs, y=ys, Geom.point, Geom.smooth, Guide.xlabel("x"), Guide.ylabel("y"))

Multivariate regression is not yet fully implemented, but most of the parts are already there, and wouldn't require too much additional work.

[1] Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. Journal of the American statistical association, 74(368), 829-836. DOI: 10.1080/01621459.1979.10481038

[2] Cleveland, W. S., & Devlin, S. J. (1988). Locally weighted regression: an approach to regression analysis by local fitting. Journal of the American statistical association, 83(403), 596-610. DOI: 10.1080/01621459.1988.10478639

[3] Cleveland, W. S., & Grosse, E. (1991). Computational methods for local regression. Statistics and computing, 1(1), 47-62. DOI: 10.1007/BF01890836