Can I use a "reach" variable as independent in a multiple linear regression? I'm trying to model sales and I want to use publicity reach as an independent variable.
The thing is, the reach from period A cannot be added to the reach of period B, $Reach(A\cup B) \ne Reach(A) + Reach(B)$.
I was told that I can't use reach because of this. What do you think?
 A: Reach can be used. Many variables that might be interesting to include in a model cannot meaningfully be added together. For example, average staff tenure, interest rates, total customers, etc. Also, categorical variables such as what month the sales are occurring in or what advertising agency you used can't really be added together but are valuable in models.
A: Adding up the values a variable takes over the different time periods has meaning only if this cumulative sum can have a meaningful interpretation. For example, it would be reasonable to try to explain a person's weight as years go by, by the person's age, among other things. Obviously adding the values of the time series for "age" has no meaning at all -but including the variable in such a regression makes sense. 
In your case too, adding, period's A reach to period's B reach is meaningless -so it cannot be used as a criterion as to whether to include the variable "reach" in the regression.  
A final note: under certain assumptions, the "percentage of target population that saw an ad", can be interpreted as an estimate of the probability that any given member of the population may see the ad.
