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I wish to forecast Y for year 2018 but I only have two data points of Y in years 2006 and 2012.

I already did multiple linear regression (since I have a lot of predictors) but multiple linear regression does not consider the time aspect so my predictions are limited.

I was advised to do causal forecasting instead, which will apparently give me a forecast for the next year. I researched about it but only found regression once again and a few others (econometric, input-output etc)

Is there an actual model in causal forecasting that can solve my problem?

Katherine
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    How exactly does your data look like? What do you want to forecast? From your description it sounds like it is a time-series forecasting problem and it is not clear why do you want to use casual forecasting... – Tim Mar 28 '17 at 10:40
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    I don't think any model can help you make a reasonable forecast based on just two data points. – CodeWarrior Mar 28 '17 at 10:53
  • @Tim I want to forecast poverty – Katherine Mar 28 '17 at 12:04

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If you only have two data points, one of the things that you can do (without any other information about what your model should look like) that may be sensible is fit a line through them. That means you will need to collapse your multiple predictors into one dimension using some function, that is likely to be domain-specific.

With only two data points, it will likely not be a very valuable prediction, however.

rinspy
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    In what sense is the linear extrapolation the "best" one can do? Yes, it is *something* one can do, and under certain assumptions it's *reasonable,* but a claim of "best" is stronger than that. – whuber Mar 28 '17 at 14:59
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    I was thinking it is a model that makes the fewest assumptions, but actually just taking the mean of both values may be even "better" in that sense. But let's say that we just have two data points and no context, further information, etc. - and we want to predict the third point, what would be the way to do it that makes the fewest assumptions? – rinspy Mar 28 '17 at 15:34
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    Good question. The answer might be debatable, but we can rule out some things. For instance, a model in which the response is an independent random value from some fixed (but unknown and arbitrary) distribution makes several assumptions, but a model that posits independent random deviations from a linear trend over time uses at least one additional (strong) assumption--namely, there is a linear trend--and therefore cannot possibly be one that makes the fewest assumptions. That rules out linear extrapolation (fitting a line) as "best" in the sense of "makes the fewest assumptions." – whuber Mar 28 '17 at 15:54
  • The physical properties of the measurement system determine what is, and is not, reasonable. For example, radioactive decay of a particular isotope would be linear all right, but only on a semi-log plot. – Carl Mar 29 '17 at 07:53
  • In other words, prior knowledge about the system we are trying to model. Which reduces this question to whether there is such a thing as an uninformative prior: http://stats.stackexchange.com/questions/20520/what-is-an-uninformative-prior-can-we-ever-have-one-with-truly-no-information – rinspy Mar 29 '17 at 09:37