Let's say I have a dataset to which I have estimated a relationship using non-parametric regression, specifically Kernel (obviously in this hypothetical example it's probably overfit slightly). The dataset is from x = 0 to x = 4. How would I go about extrapolating, and finding the y-value for say x = 4.2?
Would I simply extend the last connecting line of the regression, as depicted below? Or is this incorrect?
The reason I want to do this, is because I want to calculate LOOCV - which involves omitting each data point in turn, and I'm unclear on what to do when I omit the first last or data point in a range.
(Please be aware this is just randomly generated data, for illustrative purposes).
Edit 1: Emphasis on reason for asking.