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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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    $\begingroup$ Does this answer your question? What is the difference between estimation and prediction? $\endgroup$
    – Carl
    Dec 16, 2022 at 0:12
  • $\begingroup$ @Carl Thank you for the flag: identifying duplicates takes effort and is always useful. But that thread would be a duplicate only if extrapolation and estimation were the same thing, but they are not. $\endgroup$
    – whuber
    Dec 16, 2022 at 14:55

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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, 2016 at 12:11
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    $\begingroup$ There is no "vs". Extrapolation is prediction outside of the ranged covered by data, interpolation is prediction inside this range. $\endgroup$
    – Roland
    Apr 4, 2016 at 12:14
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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, 2016 at 12:23
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    $\begingroup$ It is not clear to me that all predictive models extrapolate. E.g., time series analysis models based on well-informed and empirically backed data-generating processes, and dynamic empirical modeling methods, such as simplex projection, would seem to be interpolation-based, not extrapolation based. $\endgroup$
    – Alexis
    Dec 13, 2022 at 20:43
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    $\begingroup$ To add to what @Alexis said, in spatial statistics interpolation and extrapolation are both considered to be prediction. They are often distinguished by whether the support of the prediction (the x-values) lies within the convex hull of the data or not, respectively. In one dimension that distinction comes down to whether the prediction is made for an x value within the data range or beyond it (in either direction). $\endgroup$
    – whuber
    Dec 13, 2022 at 20:55
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The explanation is excellent, however, the casual association of the term prediction to future events may have been too subtle. In other words, I don't know that the implied other part of that explanation was derived. Prediction = future event, estimation = not necessarily future, i.e. fitted value, can be inferential (established population).

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