[time-nuts] exponential+linear fit

[Jim Lux]

On 10/7/13 6:03 AM, Tim Shoppa wrote:
> Proposing a random fitting with various curves without an underlying
> physical (e.g. Eureqa) model seems... odd. That's more voodoo
> engineering/science than anything real. It doesn't surprise me that
> computer scientists would propose that as an approach to data, making it
> even more inappropriate.
>
> Having well-versed engineers and physical scientists looking at curves and
> striving to understand the various features with underlying well-understood
> and used physical models (including abnormalities in measurements), that
> seems appropriate.
>
> The originally proposed model of long term linear drift trend plus
> exponential decay of initial thermal conditions is very well understood and
> accepted.
>
>


however, sometimes, looking to see what else fits might lead to insight 
into what is going on "inside the box", when you don't have any information.


In general, though, I agree with you.  Every year at the International 
Science and Engineering Fair (and at the local and regional fairs before 
it), I see people fitting a straight line to data that is fundamentally 
not linear (e.g. RF signal strength vs distance, or aerodynamic drag vs 
velocity, or speed of sound vs temperature)

I can sort of forgive trying to use a polynomial fit for something for 
which the underlying physics says something different; especially if 
there's no other choice. Square roots are a particular problem and pop 
up surprisingly often: vterminal = sqrt(2*accel*distance), and are not 
modeled well by a polynomial.

However, the Excel plot with the linear regression, giving coefficients 
out to 5 digits and R^2 the same, is just inappropriate; particularly at 
the ISEF level.