Hi Nick (=FellowExcellor??)

OK. A few more comments.

1. You are not very specific just what the "decomposition you are looking for" is. I made a suggestion - a common one with this sort of stuff, that it can be interpreted as the rate of change of the variable to be explained when one of the explanatory variables changes, the others being supposed hypothetically constant for the purposes of the exercise. This is usually done by partial differentiation. In my earlier post I gave the result for this, but if you mean something different by "decompose" you will need to explain it more clearly.

2. Another possibility (to interpret “decompose”, which may or may not coincide with the first, is to use a mathematical result called Taylor's Theorem. You are almost certainly using this implicitly when writing down your regression model in the first place, but since you say you are "not clued up on mathematical aspects" looking into it further is unlikely to be useful to you in the present context. If you wish you could implement it by writing your model as something like Y=a +b*X1 +c*X1^2 + etc. This would give you some of the curvature properties you seem to want.

3. A "multiplicative/non linear model" is more usually written in the form as Ln

=a + Ln(X1) + etc. This is typically easier to do regressions with, do subsequent mathematical, predictive etc. or other work with, has curvature properties which are often useful (almost certainly would be in your context), easier to interpret, etc. The way you write your model is not necessarily incorrect, just inconvenient for further use, and unless you have compelling reasons for supposing it is the most valid and reasonable form I think (especially with a limited mathematical background) you'd be better off using a more standard model formulation.

4. "diminishing returns etc." refers to a specific type of curvature property. However many nonlinear regression formulations can express this curvature property, and again I think you'd be better (again, unless you have compelling reasons otherwise) to stick to more standard formulations.

5. Using finite differences is also unlikely to be useful to you. George Boole (of Boolean repute say when you Dim excel variables as “boolean”) wrote a book on this back in the 1800’s and there’s been a fair bit of stuff done since. Basically, data for regression variables are usually collected at discrete time intervals (daily, weekly or whatever). The differentiation usually used to analyse “diminishing returns” or other curvature properties is logically not applicable to functions only defined at discrete intervals without putting considerable faith in “it’s a good enough approximation for my purposes” or similar, which at best constitute rather a leap of faith. Some good work has been done in recent years on getting results for data collected in continuous time (or very close to it) but most of this is pretty esoteric stuff .