loess predict with new x values

Question

I am attempting to understand how the predict.loess function is able to compute new predicted values (y_hat) at points x that do not exist

Answer 1

To better understand what is happening in a loess fit try running the loess.demo function from the TeachingDemos package. This lets you interactively click on the plot (even between points) and it then shows the set of points and their weights used in the prediction and the predicted line/curve for that point.

Note also that the default for loess is to do a second smoothing/interpolating on the loess fit, so what you see in the fitted object is probably not the true loess fitting information, but the secondary smoothing.