I have a degree in statistics yet I've never thought about the relationship between linear models and business decisions in this way. You're absolutely right. This is the best comment I've read all month.
I don't follow - could you explain this with a couple of examples? What would a business proposal look like that is analogous to a nonlinear model vs. one that is analogous to a linear model?
I’m neither of the previous posters, so I may be off…
For simplicity, I’m going to assume each variable in the model is independent of every other variable.
We can interpret the coefficients in linear models. This relationship holds for the model for the range of values it is based on. This relationship is the same for the whole range of the model. (We can’t extrapolate outside of what’s been modeled.)
y = c1x1 + c2x2 +…+ cnxn (excuse the poor formatting)
The sign tells you the direction (+ means it will increase the value of y, - means it will decrease the value of y), the value of the coefficient tells you how much the y will change for a given 1-unit change in the x value.
Since this is linear, you get the same change to the output for the relevant increases no matter your starting point.
So, the regression model would say x1, x3, and x5 have positive coefficients and variables x2, x4 have negative coefficients. If you want y to increase, either start doing more of x1, x3, x5 or do less of x2, x4. Depending on what these are and your limited investment budget, for example, you may pick doing x3 if that is the largest positive coefficient.
Again, since this is linear, you can keep on putting resources into the largest coefficient and get the same increase up until your model is no longer valid.
For non-linear models, you can still interpret the coefficients, but the interpretation depends on your starting conditions and where you are on the graph.
There may be asymptotes in your non-linear model, so there is a point of diminishing returns where if you keep putting resources into a variable with a positive coefficient, this will not keep getting you commensurate results.
Sorry I don’t have any actual examples here and I don’t have time to go digging through my old textbooks to look for any.
How I understand the comment: a non-linear suggestion is that the budget for X should be 300k. The (supposedly linear) alternative is that the budget for X should increase.
What I think is the important part, is that it is better to ask decision makers for decisions on setting a continuous parameter, than to make binary yes/no or go/no-go decisions. When it's a decision by committee, I can see why that is.
