Re: [Help-gsl] exponential fitting

[John D Lamb]

James Bergstra wrote:
> On Sat, Jul 08, 2006 at 08:43:54AM +0200, Petr Ent wrote:
>   
>> hi,
>> i am pretty new user of gsl, so please sory for this question...
>> what  is the easiest\fastest way to fit few points with an exponential 
>> function? i found example of non-linear least squares fitting, but it seems 
>> bit slow and difficult way to me. could this fitting be done with linear 
>> fitting?
>>     
>
> Maybe naive... but... take the log of your points and do a linear fit?
>
> James
>   
This may be a better approach. Roughly if you have points (x_1,
y_1),..., (x_n,y_n) and do a least squares fit on (x_1,log(y_1)),...,
(x_n,...,log(y_n)) to get coefficients a and b giving

log( y ) = ax + b,

Then the exponential fit is given by

y = A exp( bx )

where A = exp( a ) (a constant). This does depend on the usual linear
regression assumptions. You'd usually check these with a statistical
package such as R or SPSS. In particular, you probably want to check for
homoskedasticity.

-- 
JDL