MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: FindFit power law problem

  • To: mathgroup at
  • Subject: [mg117200] Re: FindFit power law problem
  • From: Bill Rowe <readnews at>
  • Date: Fri, 11 Mar 2011 04:34:01 -0500 (EST)

On 3/10/11 at 6:06 AM, gwardall at (Gary Wardall) wrote:

>I was wondering if you really meant to transform both the x and y

>Fit[Log[10, data], {1, x}, x]

>Does just that. Some software transforms just the y data when
>estimating the coefficients for the model y = a x^b.

>What happens is they transform just the y data and use the linear


>Finding the coefficients aa and bb and state the results as



>is equivalent to:


>in turn is equivalent to:


>which is also equivalent to:


>Note then that a=Exp[aa] and b=bb.

>I hope my Algebra is correct.

Your algebra looks right. However,...

You start you post by asking about transforming both x and y.
You have a model where you transform y then seem to be
suggesting to do:

FindFit[xformedData, a Log[x] + b, {a,b}, x]

This is exactly the same as doing

FindFit[Log[data], a + b x, {a,b},x]

That is setting up the model as a linear function of Log[x] is
exactly the same as transforming both x and y then using a
linear model to fit the transformed data.

Note also, the difference in fit parameters comes about by
transforming y. For real data, errors are almost always
additive. Any non-linear transformation of measured y data with
additive error creates a fundamentally different model. The
point is f[y+error] does not map to f[y] + f[error] unless f is
a linear function. If the range for you data isn't too large,
doing a non-linear fit to the data will give approximately the
same result as doing a linear fit to appropriately transformed
data. A sufficiently small range in this context means the
deviation from true linearity is small. Or said differently, any
non-linear function restricted to a sufficiently small range
looks linear.

  • Prev by Date: Re: How to kill slave kernel securely?
  • Next by Date: Re: determining boundary of a region in n-dimensional euclidean space
  • Previous by thread: Re: FindFit power law problem
  • Next by thread: Re: FindFit power law problem