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


From   "Michael Blasnik" <michael.blasnik@verizon.net>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: Stata command for parameter calculation with least square method?
Date   Thu, 01 Mar 2007 07:06:20 -0500

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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