st: Re: Stata command for parameter calculation with least square method?

["Michael Blasnik" <michael.blasnik@verizon.net>]

In addition to the -nl- suggestion, you could also take logs of x and y and 
use -regress- , adding the -noconstant- option for your first example.  It 
depends on how you think the error term is best represented since taking 
logs makes the error multiplicative (which often makes sense for equations 
of the sort you show).


Michael Blasnik

----- Original Message ----- 
From: "Tobias Pfaff" <tobiaspfaff@gmx.net>
To: <statalist@hsphsun2.harvard.edu>
Sent: Thursday, March 01, 2007 6:02 AM
Subject: st: Stata command for parameter calculation with least square 
method?



> Hi,
>
> for given data points I want to find out a parameter for a function such
> that the function fits best to the data points.
> The function would be: f(x)=x^alpha.
> The data points are:
>
> x_values y_values
> -------- --------
> 0,0000 0
> 0,0156 0,45
> 0,0313 0,52
> 0,0625 4,83
> 0,0938 11,66
> 0,1250 12,79
> 0,1875 21,5
> 0,2188 25,69
> 0,2344 27,89
> 0,2500 29,93
>
> I know how I could do that with the least square method and the Excel
> solver.
> Which Stata command would deliver the same result? Is _reg3_ the 
> appropriate
> command? How would the command line look like?
>
> Furthermore, I want to do the same with 2 unknown parameters, e.g. for the
> function f(x)=-k*(-x)^alpha. Which command would be appropriate for 2
> unknown parameters (here: k and alpha)?
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