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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?

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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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