I was hoping someone knows the solution or has an alternative form of approach. tried this out over on /r/askmath with little response.
Ok I will attempt to be as clear and as simple as possible. I have an item whose value can range across a large scale. Lets say this scale is 10-200 for now. This item has some ideal fixed value when the two conditions are fixed and constant (call them conditions A and B.) I need to create a constant for each that describes the affects of the changes in A or B on the value of the item. For now lets say A and B can range between 0-100 and have different ideal fixed values.
We initially approached this using the percent change formula since the real world effects of condition A are already looked at this way. The problem with this is that we get a different result if the change in condition A or B is 10 units if those 10 units of change occur at the low end of the scale or the high end. We believe the effect they have should be the same (lets just assume this for both conditions for now). In other words moving from a value of 10-20 in A should cause the same amount of change in the value of the item as moving from a value of 80-90 in A (one unit of A or B affects the value of the item one unit say, this should yield a 1 to 1 effect.)
We believe we have a solution to this involving adjusting the percent change to a standard value of A or B and then calculating the constant from that, but I am unclear as to whether we are just artificially fixing the problem or if it really represents the solution. I am not fantastic with LaTeX but will try to post our proposed solution if its requested. I also have a follow up question involving the fact A and B are affected by each other I would like to get answered if things get solved with this first part.
Also can any one point me to papers or books that discuss this type of data analysis?
Thanks so much for any help
Edit: It has been pointed out the the percent change formula assumes that the relationship of the change is not one to one, but a percent of one to one of the other. This is understood and part of the reason I am asking the question. That being as it may and with the possibility that it should a percent change, I still need to create a constant that is remains the same wether the change is in a low part of the scale or a high part.
It appears that value$=10+0.95A+0.95B$ seems to satisfy what you are looking for. An increment of $10$ in $A$ or $B$ increases the value by $9.5$ and value will range from $10$ to $200$ as $A$ and $B$ range over $0$ to $100$