A former colleague of mine who was one of those few econometricians who could make a non-econometrician understand what they are trying to say by focusing on the "spirit of the equations" (his words) had a very great way of putting how to approach stat/econometric models.
This is how he said it:
A model helps you grasp reality easily. It doesn't mean it is real. If it were real, then life would be a lot simpler that it really is. It also doesn't mean it is NOT real: it is an abstraction of what is real - i.e., lifted off what is really happening. The end goal of the abstraction is for us to be able to understand reality.
Think of it as the map of London Undeground:
If you really want to look at how the tubes are laid down in London, here is how it looks like:
The tubes are laid down complicated - but the schematic diagram of the tubes' stations makes it a lot easier to go around the City.
That's what equations and models are for: Guideposts. Schematic diagrams of complex phenomena. That one can then use with confidence to get from one point to another.
In the years that I have been working with statistical/econometric models, I have observed that there are three main categories of people - from clients to agencies to finance people - based on their responses to the models.
There are those who would look at the innards of a model, turn it upside down, question every probability value and statistic, and attempt to backtest/stress-test the model - until they are satisfied it works. After such satisfaction, the equation is the end-all/be-all of decisions and choices.
Then there are those who would look at the model - and turn up their noses towards it, with the belief that the equaiton cannot capture reality - that it is just a set of equations and numbers. That after all is said and done, it is the "human mind, wisdom, and experience that really count in making decisions". There's always the belief that "not everything can be captured by an equation - situations are far too complex to be simplified into one equation".
Then there are those who would look at the model, take an interest in its explanatory power, question its validity, backtest it, stress test it - and then look at the implications of the various parts of the model and how it could affect reality and decisions that they have to make into the future.
Thanks to Kottke.Org for the photos.