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st: Interpreting Non-Linear Least Squares


From   Stefan Nijssen <stefannijssen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Interpreting Non-Linear Least Squares
Date   Sat, 23 Apr 2011 16:58:24 +0200

Dear Statalist users,

In interpreting my variables, I have come upon the point to let Stata's non-linear least squares function calculate the exponent best fitting my data. However, interpreting the results I am struggling a bit. To me, the function I am looking for will be one like:

Y = b0 + b1*(Var)^b2

Y being the dependent, Var the independent. Now it might very well be the case that the answer is right in front of me, however somehow to me it seems different.

The NL least squares provides the following output, stating the estimated function has the form:

Y = b0 + b1*b2^ebitda

      Source |       SS       df       MS
-------------+------------------------------                              Number of obs =       141
       Model |  409394.932     2       204697.466         R-squared     =    0.1496
    Residual |  2327596.39   138  16866.6405         Adj R-squared =    0.1373
-------------+------------------------------                              Root MSE      =  129.8716
       Total |  2736991.32   140   19549.938              Res. dev.     =  1769.474

3-parameter asymptotic regression, oas = b0 + b1*b2^ebitda
------------------------------------------------------------------------------
         oas |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         /b0 |  -336.6996   165.5611    -2.03   0.044    -664.0642   -9.335052
         /b1 |   688.8096   178.0674     3.87   0.000     336.7163    1040.903
         /b2 |   .9999999   3.13e-09   3.2e+08  0.000     .9999999    .9999999
------------------------------------------------------------------------------
  Parameter b0 taken as constant term in model & ANOVA table

I feel a little stupid asking this, but can anyone give me some clues on how to read this?

Thanks a lot,

Stefan Nijssen
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