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running /home/krg/bin/profile.do ...
Compile number 785
. do gauss3.do
. /* NIST/ITL StRD
> Dataset Name: Gauss3 (Gauss3.dat)
>
> File Format: ASCII
> Starting Values (lines 41 to 48)
> Certified Values (lines 41 to 53)
> Data (lines 61 to 310)
>
> Procedure: Nonlinear Least Squares Regression
>
> Description: The data are two strongly-blended Gaussians on a
> decaying exponential baseline plus normally
> distributed zero-mean noise with variance = 6.25.
>
> Reference: Rust, B., NIST (1996).
>
>
>
>
>
>
>
>
>
> Data: 1 Response (y)
> 1 Predictor (x)
> 250 Observations
> Average Level of Difficulty
> Generated Data
>
> Model: Exponential Class
> 8 Parameters (b1 to b8)
>
> y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
> + b6*exp( -(x-b7)**2 / b8**2 ) + e
>
>
> Starting values Certified Values
>
> Start 1 Start 2 Parameter Standard Deviation
> b1 = 94.9 96.0 9.8940368970E+01 5.3005192833E-01
> b2 = 0.009 0.0096 1.0945879335E-02 1.2554058911E-04
> b3 = 90.1 80.0 1.0069553078E+02 8.1256587317E-01
> b4 = 113.0 110.0 1.1163619459E+02 3.5317859757E-01
> b5 = 20.0 25.0 2.3300500029E+01 3.6584783023E-01
> b6 = 73.8 74.0 7.3705031418E+01 1.2091239082E+00
> b7 = 140.0 139.0 1.4776164251E+02 4.0488183351E-01
> b8 = 20.0 25.0 1.9668221230E+01 3.7806634336E-01
>
> Residual Sum of Squares: 1.2444846360E+03
> Residual Standard Deviation: 2.2677077625E+00
> Degrees of Freedom: 242
> Number of Observations: 250
> */
.
. clear
.
. scalar N = 250
. scalar df_r = 242
. scalar df_m = 8
.
. scalar rss = 1.2444846360E+03
. scalar rmse = 2.2677077625E+00
.
. scalar b1 = 9.8940368970E+01
. scalar seb1 = 5.3005192833E-01
. scalar b2 = 1.0945879335E-02
. scalar seb2 = 1.2554058911E-04
. scalar b3 = 1.0069553078E+02
. scalar seb3 = 8.1256587317E-01
. scalar b4 = 1.1163619459E+02
. scalar seb4 = 3.5317859757E-01
. scalar b5 = 2.3300500029E+01
. scalar seb5 = 3.6584783023E-01
. scalar b6 = 7.3705031418E+01
. scalar seb6 = 1.2091239082E+00
. scalar b7 = 1.4776164251E+02
. scalar seb7 = 4.0488183351E-01
. scalar b8 = 1.9668221230E+01
. scalar seb8 = 3.7806634336E-01
.
. qui input double(y x)
.
. #delimit ;
delimiter now ;
. nl ( y = {b1}*exp( -{b2}*x ) + {b3}*exp( -(x-{b4})^2 / {b5}^2 )
> + {b6}*exp( -(x-{b7})^2 / {b8}^2 ) ) ,
> init(b1 94.9 b2 0.009 b3 90.1 b4 113.0 b5 20.0 b6 73.8 b7 140.0 b8 20
> )
> eps(1e-10);
(obs = 250)
Iteration 0: residual SS = 4278.011
Iteration 1: residual SS = 1476.725
Iteration 2: residual SS = 1245.232
Iteration 3: residual SS = 1244.485
Iteration 4: residual SS = 1244.485
Iteration 5: residual SS = 1244.485
Iteration 6: residual SS = 1244.485
Iteration 7: residual SS = 1244.485
Iteration 8: residual SS = 1244.485
Source | SS df MS
-------------+---------------------------------- Number of obs = 250
Model | 1316109.3 8 164513.657 R-squared = 0.9991
Residual | 1244.4846 242 5.1424985 Adj R-squared = 0.9990
-------------+---------------------------------- Root MSE = 2.267708
Total | 1317353.7 250 5269.41496 Res. dev. = 1110.723
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/b1 | 98.94037 .530052 186.66 0.000 97.89626 99.98447
/b2 | .0109459 .0001255 87.19 0.000 .0106986 .0111932
/b3 | 100.6955 .8125678 123.92 0.000 99.09492 102.2961
/b4 | 111.6362 .3531785 316.09 0.000 110.9405 112.3319
/b5 | 23.3005 .3658472 63.69 0.000 22.57985 24.02115
/b6 | 73.70503 1.20912 60.96 0.000 71.32329 76.08677
/b7 | 147.7616 .4048817 364.95 0.000 146.9641 148.5592
/b8 | 19.66822 .3780672 52.02 0.000 18.9235 20.41294
------------------------------------------------------------------------------
. #delimit cr
delimiter now cr
.
. 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 /*
> */ [b4]_b[_cons] b4 [b5]_b[_cons] b5 [b6]_b[_cons] b6 [b7]_b[_cons] b7 /*
> */ [b8]_b[_cons] b8 () /*
> */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 /*
> */ [b4]_se[_cons] seb4 [b5]_se[_cons] seb5 [b6]_se[_cons] seb6 [b7]_se[_cons]
> seb7 /*
> */ [b8]_se[_cons] seb8 () /*
> */ e(rmse) rmse e(rss) rss
[b1]_b[_cons] 10.1
[b2]_b[_cons] 9.1
[b3]_b[_cons] 9.0
[b4]_b[_cons] 9.0
[b5]_b[_cons] 8.2
[b6]_b[_cons] 8.3
[b7]_b[_cons] 9.1
[b8]_b[_cons] 8.4
-------------------------
min 8.2
[b1]_se[_cons] 6.9
[b2]_se[_cons] 6.3
[b3]_se[_cons] 5.6
[b4]_se[_cons] 6.6
[b5]_se[_cons] 5.8
[b6]_se[_cons] 5.5
[b7]_se[_cons] 6.5
[b8]_se[_cons] 5.6
-------------------------
min 5.5
e(rmse) 10.8
e(rss) 11.0
.
.
end of do-file