___  ____  ____  ____  ____ ©
 /__    /   ____/   /   ____/      17.0
___/   /   /___/   /   /___/       SE—Standard Edition

 Statistics and Data Science       Copyright 1985-2021 StataCorp LLC
                                   StataCorp
                                   4905 Lakeway Drive
                                   College Station, Texas 77845 USA
                                   800-STATA-PC        https://www.stata.com
                                   979-696-4600        stata@stata.com

Stata license: 10-user network perpetual
Serial number: 1
  Licensed to: Stata Developer
               StataCorp LLC

Notes:
      1. Stata is running in batch mode.
      2. Unicode is supported; see help unicode_advice.
      3. Maximum number of variables is set to 5,000; see help set_maxvar.


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

. do misra1a.do 

. /* NIST/ITL StRD
> 
> Nonlinear Regression
> 
> Difficulty=Lower  Exponential  k=2  N=14  Observed
> 
> Dataset Name:  Misra1a           (Misra1a.dat)
> 
> Procedure:     Nonlinear Least Squares Regression
> 
> Description:   These data are the result of a NIST study regarding
>                dental research in monomolecular adsorption.  The
>                response variable is volume, and the predictor
>                variable is pressure.
> 
> Reference:     Misra, D., NIST (1978).
>                Dental Research Monomolecular Adsorption Study.
> 
> 
> Data:          1 Response Variable  (y = volume)
>                1 Predictor Variable (x = pressure)
>                14 Observations
>                Lower Level of Difficulty
>                Observed Data
> 
> Model:         Exponential Class
>                2 Parameters (b1 and b2)
> 
>                y = b1*(1-exp[-b2*x])  +  e
> 
> 
>           Starting values                  Certified Values
> 
>         Start 1     Start 2           Parameter     Standard Deviation
>   b1 =   500         250           2.3894212918E+02  2.7070075241E+00
>   b2 =     0.0001      0.0005      5.5015643181E-04  7.2668688436E-06
> 
> Residual Sum of Squares:                    1.2455138894E-01
> Residual Standard Deviation:                1.0187876330E-01
> Degrees of Freedom:                                12
> Number of Observations:                            14
> */
. 
. clear

. 
. scalar N         = 14

. scalar df_r      = 12

. scalar df_m      = 2

. 
. scalar rss       = 1.2455138894E-01

. scalar rmse      = 1.0187876330E-01

. 
. scalar b1        = 2.3894212918E+02

. scalar seb1      = 2.7070075241E+00

. scalar b2        = 5.5015643181E-04

. scalar seb2      = 7.2668688436E-06

. 
. qui input double (y x)

. 
. nl ( y = {b1}*(1-exp(-{b2}*x)) ), init(b1 500 b2 0.0001) eps(1e-10)
(obs = 14)

Iteration 0:  residual SS =  10697.62
Iteration 1:  residual SS =  10640.08
Iteration 2:  residual SS =  10497.53
Iteration 3:  residual SS =  10374.65
Iteration 4:  residual SS =  10230.61
Iteration 5:  residual SS =  9280.129
Iteration 6:  residual SS =  2951.824
Iteration 7:  residual SS =  2188.115
Iteration 8:  residual SS =  .7215063
Iteration 9:  residual SS =  .6258301
Iteration 10:  residual SS =  .1245514
Iteration 11:  residual SS =  .1245514
Iteration 12:  residual SS =  .1245514
Iteration 13:  residual SS =  .1245514


      Source |      SS            df       MS
-------------+----------------------------------    Number of obs =         14
       Model |  33059.509          2  16529.7543    R-squared     =     1.0000
    Residual |  .12455139         12  .010379282    Adj R-squared =     1.0000
-------------+----------------------------------    Root MSE      =   .1018788
       Total |  33059.633         14  2361.40236    Res. dev.     =  -26.37904

------------------------------------------------------------------------------
           y | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         /b1 |   238.9421   2.707006    88.27   0.000     233.0441    244.8402
         /b2 |   .0005502   7.27e-06    75.71   0.000     .0005343     .000566
------------------------------------------------------------------------------

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

[b1]_b[_cons]        9.4
[b2]_b[_cons]        9.4
-------------------------
min                  9.4

[b1]_se[_cons]       6.4
[b2]_se[_cons]       6.5
-------------------------
min                  6.4

e(rmse)             10.6
e(rss)              10.5

. 
end of do-file