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Running /home/krg/bin/profile.do ...
Compile number 170082

. 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 =  .0072256
Iteration 1:  residual SS =  .0015258
Iteration 2:  residual SS =  .0014637
Iteration 3:  residual SS =  .0014636
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
       Model |  .69823267          3  .232744222    R-squared     =     0.9979
    Residual |  .00146359         32  .000045737    Adj R-squared =     0.9977
-------------+----------------------------------    Root MSE      =   .0067629
       Total |  .69969625         35  .019991322    Res. dev.     =  -253.5517

------------------------------------------------------------------------------
           y | Coefficient  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
------------------------------------------------------------------------------

. 
. assert N    == e(N)

. assert df_r == e(df_r)

. assert df_m == e(df_m)

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

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

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

e(rmse)             11.3
e(rss)              10.7

. 
. 
end of do-file