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Re: st: Interpreting Non-Linear Least Squares


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpreting Non-Linear Least Squares
Date   Sat, 23 Apr 2011 17:01:00 +0100

You don't give the -nl- syntax you use, but

1. It is not clear that your first equation and your -nl- output line up.

2. The model you fitted is not obviously a success as -b2- has such an
implausibly high t value and the R-sq is mediocre. I suspect some
pathology.

3. You could reasonably post your data unless you are otherwise
reluctant to do so. You should certainly give the -nl- syntax.

4. Plot the data and the fit to see what is going on!

5. You should signal whether this is some theoretical equation that
evokes respect in your field or you are just interested in a good
curve fit.

Nick

On Sat, Apr 23, 2011 at 3:58 PM, Stefan Nijssen <stefannijssen@gmail.com> wrote:
> 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?
>

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