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MathGroup Archive 1995

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Re: Exponetial Fit

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1802] Re: Exponetial Fit
  • From: rjfrey at rentec.com (Robert J. Frey)
  • Date: Mon, 31 Jul 1995 23:07:42 -0400
  • Organization: Renaissance Technologies Corp.

John L. White (crunch at s-cwis.unomaha.edu) wrote:
: 	I have tried to do a exponetial fit to a list of data from a physics
: experiment, but Mathematica does a terrible job when I do the following 
: command:  

: Exp[Fit[Log(data),{1,t},t]] 

I assume this is Exp[Fit[Log[data], {1,t}, t]]
 
: Does anyone know of a better way?  Thanx in advance, John
: -- 
I assume data is a vector of observations:{{x1,y1}, {x2,y2}, ...}

In what follows a and b are parameters to be estimated, t is the 
independent variable and y the dependent variable.

Generally, if the term "exponential model" is used, the model one 
wants to fit is:
	
	y == a Exp[b t]

if you take the Log of both sides:

	Log[y] == Log[a] + b t

The data pairs {t, Log[y]} can then be subject to a linear regression,
yielding estimates for Log[a] and b.

This isn't what you did.

Now, there is the power model:

	y == a t^b

if you take the Log of both sides:

	Log[y] == Log[a] + b Log[t]

The data pairs {Log[t], Log[y]} can then be subject to a linear regression,
yielding estimates for Log[a] and b. 

This does appear to be what you did in the Fit, but the final Exp is
still wrong.
--

Regards,
Robert (rjfrey at rentec.com 


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