Apologies if the question is too trivial but what exactly sets these two apart?

Let's say that I have a set of data for a hundred points (the independent variable may not be uniformly spaced) as:

{{1, 7}, {2, 8},...,{100, 5}}

Now, I can apply any of the extrapolation techniques (Newton's, Lagrange's or even Curve Fitting for that matter) and get a y = f(x). Now if I put in any x, in or out from my original data set, I can get the corresponding y. This way I predicted a y value which wasn't originally in my data set.

How is Prediction different from this?


Extrapolation is estimation of dependent values outside the range covered by the (independent) data the model has been fit to: https://en.wikipedia.org/wiki/Extrapolation. It's not the same as interpolation, which is estimation between original data points. Prediction usually refers to future events, but in your context you could say (regarding the estimates) prediction is a hypernym of fitted values + interpolation + extrapolation.

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    $\begingroup$ I understand the difference between extra/interpolation but that's not my question. Can you elaborate more upon Extrapolation vs Prediction? Your current answer (last statement) isn't satisfactory enough. $\endgroup$ – Hyperbola Apr 4 '16 at 12:11
  • $\begingroup$ There is no "vs". Extrapolation is prediction outside of the ranged covered by data, interpolation is prediction inside this range. $\endgroup$ – Roland Apr 4 '16 at 12:14
  • $\begingroup$ So prediction is just a term for saying extrapolation & interpolation. In other words, every prediction is either an extrapolation or an interpolation? $\endgroup$ – Hyperbola Apr 4 '16 at 12:16
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    $\begingroup$ Basically. Although prediction refers to, well, prediction of future observations (which is important for estimation of uncertainties) whereas that's not necessarily the case for extrapolation and interpolation. $\endgroup$ – Roland Apr 4 '16 at 12:23

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