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# st: Interpreting Non-Linear Least Squares

 From Stefan Nijssen <[email protected]> To [email protected] 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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```