Is there a regression method (machine learning or otherwise) that gives ranges of expected values as opposed to one forecast? say you are looking at a time period and you want get a max value that the function is expected to take on in the time frame along with the min value, or perhaps an even more detailed look at different percentiles of expected values (I say expected values because it would be even better if you knew the probability associated with each value), does such a regression exist that can accommodate this
Would this all be done with a regression model such as linear regression then further analysis conducted using variance or std?
I am a complete self taught novice at statistics, but am more than willing to read up on any links provided, and do not need to be spoon fed.
Thanks in advance
 A: You are looking for prediction intervals (not to be confused with confidence intervals, which are about unobservable parameters, whereas prediction intervals are about quantities that will be observable in the future). As the linked Wikipedia article makes clear, these are common in "standard" regression, AKA Ordinary Least Squares.
If you are specifically interested in time series forecasting, you may want to look for the term interval forecast, as in (very roughly speaking) "there is an 80% chance that next year's inflation rate will be between 1% and 3%". These are often visualized using fan charts. Interval forecasts can be derived from more general density forecasts (cf. probabilistic forecasting), where you don't forecast a single value (a so-called "point forecast"), but output a full "predictive density", i.e., you try to forecast the full future distribution of your observable. You can obviously derive interval forecasts with any given coverage probability from a predictive density.
I hope this gives you enough terms to google ;-)
A: Something like quantile regression, perhaps?
In general though, wouldn't just bootstrap be used for these questions?
