Univariate interpolation: moving beyond moving averages

Here is an article I wrote a little while ago describing a clever way to fuse moving averages and simple linear regression to obtain a neat way of smoothly interpolating univariate data (see the left figure). The method is known as locally linear regression, which is a special case of kernel smoothing.

The method can be generalized to interpolate multivariate data, but the extra computational expense is usually prohibitive. In those cases I would use locally constant regression (as discussed in the article) instead.