Are there generally accepted thresholds (number of data points, length of extrapolation, etc.) of what is reasonable to extrapolate?
ex·tra·po·la·tion noun
the action of estimating or concluding something by assuming that existing trends will continue or a current method will remain applicable.
For example, if we are given the following dataset:
Jan 1
Feb 2
Mar 3
Apr 4
May 5
Jun 6
Jul 7
It is reasonable to project that Aug will be 8, Sep will be 9, and so on. However, it would not seem reasonable to come to that same conclusion if we were only provided with this data:
Jan
Feb 2
Mar
Apr 4
May
Jun
Jul
From this data, it would be just as reasonable to project that Jun = 8 and Aug = 16 (doubling every two months).
Obviously more data and less extrapolation will always be more accurate, but are there scientific or logical points at which there is reasonable confidence in the prediction?