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Notes:
      1.  (-m# option or -set memory-) 1.00 MB allocated to data
      2.  Command line editing disabled
      3.  Stata running in batch mode


running /home/bpp/bin/profile.do ...

. do eckerle4.do 

. /* NIST/ITL StRD
> Dataset Name:  Eckerle4          (Eckerle4.dat)
> 
> File Format:   ASCII
>                Starting Values   (lines 41 to 43)
>                Certified Values  (lines 41 to 48)
>                Data              (lines 61 to 95)
> 
> Procedure:     Nonlinear Least Squares Regression
> 
> Description:   These data are the result of a NIST study involving
>                circular interference transmittance.  The response
>                variable is transmittance, and the predictor variable
>                is wavelength.
> 
> 
> Reference:     Eckerle, K., NIST (197?).  
>                Circular Interference Transmittance Study.
> 
> 
> 
> 
> 
> 
> Data:          1 Response Variable  (y = transmittance)
>                1 Predictor Variable (x = wavelength)
>                35 Observations
>                Higher Level of Difficulty
>                Observed Data
> 
> Model:         Exponential Class
>                3 Parameters (b1 to b3)
> 
>                y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2]  +  e
> 
> 
> 
>           Starting values                  Certified Values
>  
>         Start 1     Start 2           Parameter     Standard Deviation
>   b1 =     1           1.5         1.5543827178E+00  1.5408051163E-02
>   b2 =    10           5           4.0888321754E+00  4.6803020753E-02
>   b3 =   500         450           4.5154121844E+02  4.6800518816E-02
> 
> Residual Sum of Squares:                    1.4635887487E-03
> Residual Standard Deviation:                6.7629245447E-03
> Degrees of Freedom:                                32
> Number of Observations:                            35
> */
. 
. clear

. 
. scalar N         = 35

. scalar df_r      = 32

. scalar df_m      = 3

. 
. scalar rss       = 1.4635887487E-03

. scalar rmse      = 6.7629245447E-03

. 
. scalar b1        = 1.5543827178E+00  

. scalar seb1      = 1.5408051163E-02

. scalar b2        = 4.0888321754E+00  

. scalar seb2      = 4.6803020753E-02

. scalar b3        = 4.5154121844E+02  

. scalar seb3      = 4.6800518816E-02

. 
. qui input double(y x)

. 
. /* The following starting values led to convergence problems:
> 
> nl ( y = ({b1}/{b2}) * exp(-0.5*((x-{b3})/{b2})^2) ), ///
>         init(b1 1 b2 10 b3 500) eps(1e-10)
>         
> */
. 
. nl ( y = ({b1}/{b2}) * exp(-0.5*((x-{b3})/{b2})^2) ), ///
>         init(b1 1.5 b2 5 b3 450) eps(1e-10)
(obs = 35)

Iteration 0:  residual SS =  .0566829
Iteration 1:  residual SS =  .0072256
Iteration 2:  residual SS =  .0015258
Iteration 3:  residual SS =  .0014637
Iteration 4:  residual SS =  .0014636
Iteration 5:  residual SS =  .0014636
Iteration 6:  residual SS =  .0014636
Iteration 7:  residual SS =  .0014636
Iteration 8:  residual SS =  .0014636
Iteration 9:  residual SS =  .0014636

      Source |       SS       df       MS            Number of obs =        35
-------------+------------------------------         F(  3,    32) =   5088.73
       Model |  .698232665     3  .232744222         Prob > F      =    0.0000
    Residual |  .001463589    32  .000045737         R-squared     =    0.9979
-------------+------------------------------         Adj R-squared =    0.9977
       Total |  .699696254    35  .019991322         Root MSE      =  .0067629
                                                     Res. dev.     = -253.5517

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          b1 |   1.554383   .0154081   100.88   0.000     1.522998    1.585768
          b2 |   4.088832    .046803    87.36   0.000     3.993498    4.184167
          b3 |   451.5412   .0468005  9648.21   0.000     451.4459    451.6365
------------------------------------------------------------------------------
 (SEs, P values, CIs, and correlations are asymptotic approximations)

. 
. assert N    == e(N)

. assert df_r == e(df_r)

. assert df_m == e(df_m)

. 
. lrecomp _b[b1] b1 _b[b2] b2 _b[b3] b3 () /*
> */ _se[b1] seb1 _se[b2] seb2 _se[b3] seb3 () /*
> */ e(rmse) rmse e(rss) rss

_b[b1]               8.6
_b[b2]               8.3
_b[b3]              11.0
-------------------------
min                  8.3

_se[b1]              7.0
_se[b2]              6.4
_se[b3]              8.2
-------------------------
min                  6.4

e(rmse)             11.3
e(rss)              10.7

. 
. 
end of do-file