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Learning about linear regression, I was teached that when a linear regression is calculated for a set of points, I can only make predictions with this linear model on the interval setted by the first and last points.

However, if a non-linear (or linear) model is adjusted and we are looking for forecasting points after the last one, what is happening in difference of the first example? Or the first assumption is wrong?

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  • $\begingroup$ You would get a different answer depending on whether or not you take the Bayesian approach. I recommend the book Statistical Intervals: A Guide for Practitioners by Gerald J. Hahn and William Meeker. The second edition is coming out in April of 2017. $\endgroup$ – Michael Chernick Feb 11 '17 at 14:10
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The first assumption is wrong. Think about it this way: if the problem at hand requires extrapolation (i.e. predictions outside of that interval) for specific subject-domain reasons, should I just give up and go home?

No, instead you must accept that uncertainty is inevitable and that extrapolated predictions will be less reliable. In the usual "never extrapolate" example, a function looks linear in the sampled interval but isn't outside of it; yes, this means that your predictions will be wrong, but you may still need to make them. Simply accept that model uncertainty means that you can't be as sure of the model's properties outside of what you've actually observed.

The same is true for forecasting: you couldn't possibly tell people "forecasting is not allowed", they just need to understand the uncertainty involved.

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