fitting a quadratic function

fitting a quadratic function

Post by Hugo Coolen » Fri, 06 Dec 2002 21:04:57



I'm trying to fit a set of data tot the following  function:
d*(1 - x/e)**2

this does not give the expected result
However fitting first to a*x**2 + b*x + c and then deduce the
coefficients of the first equation from:

e = -2c/b or e =sqrt(c)/a
d = c

gives an acceptable result

Isn't it possible however to give a best fit directly to the first
equation?

regards,
hugo

 
 
 

fitting a quadratic function

Post by Hans-Bernhard Broeke » Sat, 07 Dec 2002 01:23:42


[...]

Quote:> d*(1 - x/e)**2
[...]
> Isn't it possible however to give a best fit directly to the first
> equation?

It is, but it's considerably harder.  The problem is that the
dependence of this functions on its parameters is quite non-linear,
and the parameters are strongly anti-correlated.

This means you'll probably need startup values for the parameters, and
that they will have to be at least vaguely in the right size, or the
fit will refuse to converge, or kick either of the parameters all the
way off to Alpha Centauri.

On top of all that, the function you compared that fit to:

Quote:> However fitting first to a*x**2 + b*x + c

has *three* parameters, whereas the one above has only two, so it's
less flexible by design.  This makes your comparison rather
unrealistic.
--

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