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Interpolation typically means modeling the values of some curve inside the given data, and extrapolation — outside the given data. For example, if I know the temperature on Monday and Wednesday, and ask for what it was on Tuesday — this is interpolation. If I ask for what it was on Sunday before or Thursday after, it is extrapolation.

I am looking for a word that would encompass both. I thought of modeling, but is there perhaps something better?

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Would 'estimation' work for you? To mean, 'modeling' refers to whatever process you use to arrive at the interpolation, extrapolation or estimation? – Michael Owen Sartin Jan 14 '14 at 17:23
.....predicting – Edwin Ashworth Jan 14 '14 at 17:28
@EdwinAshworth prediction has a connotation of dealing with the future -- this is trying to produce past data of reasonable shape – gt6989b Jan 14 '14 at 19:16
@MichaelOwenSartin estimation has a close connection to what I want. the connotation is usually estimating a single quantity, -- I am working with an entire curve. I would upvote if you wrote it as an answer... – gt6989b Jan 14 '14 at 19:17
No (to the statement in your second clause) – it's predicting further points (representing ordered pairs) on a curve on the basis of data already to hand. Interpolation and extrapolation constitute informed guesswork based on trends deduced from data. You can't 'produce' data except by experimentation / observation. If I guess that my curve goes through (43, 126) say, that ordered pair is certainly not part of my data. – Edwin Ashworth Jan 14 '14 at 22:57
up vote 1 down vote accepted

"data fitting" or "curve fitting" - depending on the context.

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+1, closest one so far. I thought there was a direct connector of the two words, i guess not... – gt6989b Jan 14 '14 at 19:21

In either case, you're approximating the temperature, and are thus performing an approximation.

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Interesting alternative, but seems to miss a strong connotation from both words. Both inter- and extrapolation have a connotation of producing something unknown from something known, approximation does not necessarily. I did upvote, but it doesn't sound right in my context... – gt6989b Jan 14 '14 at 19:21
You may be thinking of approximation in too narrow a sense. Note how approximate is used to describe both interpolation and extrapolation in this article. – Gnawme Jan 14 '14 at 20:50

Estimation is defined at Wikipedia thus:

Estimation is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available.

It was my first choice for an answer because it is used in science and engineering.

My second choice was Approximation but after reading the Wikipedia section it seems to focus on the use of a simpler model as a substitute for a more complex model. I believe that amounts to the same thing as estimation.

Now, under the heading Numerical analysis, Wikipedia states

The field of numerical analysis includes many sub-disciplines. Some of the major ones are ... Interpolation, extrapolation, and regression

So perhaps numerical analysis is the best hypernym, even though it doesn't "sound" much like interpolation and extrapolation. On the other hand both estimation and approximation do "sound" right, both as headings or as actions.

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How about modeled, calculated, or predicted?

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To leave a helpful answer, you should explain why you believe these words would be appropriate, with links to appropriate references. If you are new to the Stack Exchange model, I encourage you to visit the Help Center for additional guidance. – choster Jan 14 '14 at 20:59

"Projecting" could work for both.

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For a single hypernym, I recommend regression.

See Wikipedia article for more.

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Ended up using the word fitting, which fits (pun intended) in both a point value sense and in a curve handling sense as well.

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If that is the one that works for you, you should really "accept" Yiorgos' answer, and maybe transfer this answer to there as a comment. And maybe vote for my explanatory answer, too :-) – Martin F Jan 17 '14 at 1:33

"Numerical Analysis" is probably the parent concept and therefore the best fit.

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Doesn't fit well for me. Perhaps you can say one numerically analyzes a curve, but it is not commonly used except to indicate the general field to which such questions belong, not an action... – gt6989b Jan 14 '14 at 19:19

Tough one. Perhaps "inference" ...

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Welcome to EL&U. Answers are best when they are explained, and accompanied by appropriate examples and/or reference citations. We want the poster to understand why you think inference would be appropriate. The Help Center will have additional guidance on how to use this site. – choster Jan 14 '14 at 18:51
Inference has strong links to statistics. – Martin F Jan 17 '14 at 1:25

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