       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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