Re: Pls help Curve ftting


Teresa wrote:
> Hi All,
>
> The equation x - [(2y+c)^3/2-c^3]/y is very helpful to me. I forgot
> I could just do the calculation in this way.><
> But when doing so, I found the fitting is unreasonable(the value of y
> is very large).

Do you mean the fitted values are very large, not at all
close to the experimental values?

> Is there any thing I should set besides the
> boundaries of coefficients?

Perhaps just a better initial guess. Do you have any idea
what it should be?

Note that y is very small (1e-8 to 1e-9). If c is much
larger than y, you may be getting some severe numerical
errors. Your equation may need some rethinking.

> Also,
> > Are the errors to be calculated in x or in y (or >something else
> altogether?). The above suggestion >calculates the errors in x.
>
> I dont understand the meaning of the above question. In my case, I
> want to find the parameter c with some experimental data x and y.

The question has to do with your "goodness of fit" criterion.
Consider any point with a nearby curve. How do you measure
how far that point is from the curve?

Usually least squares wants to minimize the vertical
distance between curve and data points, so a good fit will
fall close to the data points vertically.

This error function, when minimized, will mean that at
each value of y in your data, the HORIZONTAL distance
to the curve is small. Is that a reasonable thing
to minimize?

There's also something called "total least squares"
which tries to make sure the distance of each point
to the closest point on the curve is minimized. The
direction to the closest point could be horizontal,
vertical, or some other direction.

- Randy

.

Relevant Pages

  • Re: Average distance between points
    ... convert these distances (one distance for each of the points in your ... image) into a cumulative distribution function curve. ... wouldn't vary much as a function of how dense the dots are distributed ...
    (sci.image.processing)
  • Re: SRs velocity addition -- ANY Experimental Evidence?
    ... >Insisting that the light curve of binaries will be as cahotic ... >About half of all stars are binaries. ... >> The most important is observer distance. ... >while very few of them are, it means that the ballistic theory is wrong. ...
    (sci.physics)
  • Re: SRs velocity addition -- ANY Experimental Evidence?
    ... >Insisting that the light curve of binaries will be as cahotic ... >About half of all stars are binaries. ... >> The most important is observer distance. ... >while very few of them are, it means that the ballistic theory is wrong. ...
    (sci.physics.relativity)
  • Re: Quick and earnest question about MMX
    ... Distance is all the explanation needed, ... The curve gives a wealth of information, ... WHAT observed velocity curve? ... close observer should measure. ...
    (sci.physics.relativity)
  • Plotting the Curves of Coriolis, Einstein, and NoEinstein (is Copyrighted.)
    ... The experimentally measured distance of fall at ... his curve on the same graph will have ... increases as the square of the velocity at any point in time. ... And static weight doesn't change for objects ...
    (sci.physics)
Loading