I am currently working on a regression problem where I have one variable (
x) of the data in the form of "histogram bins". I.e. I could have value ranges 900-999, 1500-1599 etc. However the data does not tell you the specific value.
My question is: In this situation, should I treat this variable as real-valued (maybe take the median of each bin)? Or should I treat it as categorical data with each 100-wide bin representing a separate category? If I do treat it as categorical, what would be the best encoding (Label, 1-hot, etc.)?
My confusion comes from the fact that even though the data as presented is categorical, it is morally a real-valued variable. I also have prior knowledge that my target variable
y should have a positive correlation with
x. So if I just went with an arbitrary encoding, would it be able to capture this correlation?