___ ____ ____ ____ ____ (R)
/__ / ____/ / ____/
___/ / /___/ / /___/ 15.1 Copyright 1985-2017 StataCorp LLC
Statistics/Data Analysis StataCorp
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Special Edition College Station, Texas 77845 USA
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Single-user Stata perpetual license:
Serial number: 15
Licensed to: Kreshna Gopal
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 5000; see help set_maxvar.
running /home/krg/bin/profile.do ...
Compile number 629
. do mgh17.do
. /* NIST/ITL StRD
> Dataset Name: MGH17 (MGH17.dat)
>
> File Format: ASCII
> Starting Values (lines 41 to 45)
> Certified Values (lines 41 to 50)
> Data (lines 61 to 93)
>
> Procedure: Nonlinear Least Squares Regression
>
> Description: This problem was found to be difficult for some very
> good algorithms.
>
> See More, J. J., Garbow, B. S., and Hillstrom, K. E.
> (1981). Testing unconstrained optimization software.
> ACM Transactions on Mathematical Software. 7(1):
> pp. 17-41.
>
> Reference: Osborne, M. R. (1972).
> Some aspects of nonlinear least squares
> calculations. In Numerical Methods for Nonlinear
> Optimization, Lootsma (Ed).
> New York, NY: Academic Press, pp. 171-189.
>
> Data: 1 Response (y)
> 1 Predictor (x)
> 33 Observations
> Average Level of Difficulty
> Generated Data
>
> Model: Exponential Class
> 5 Parameters (b1 to b5)
>
> y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] + e
>
>
>
> Starting values Certified Values
>
> Start 1 Start 2 Parameter Standard Deviation
> b1 = 50 0.5 3.7541005211E-01 2.0723153551E-03
> b2 = 150 1.5 1.9358469127E+00 2.2031669222E-01
> b3 = -100 -1 -1.4646871366E+00 2.2175707739E-01
> b4 = 1 0.01 1.2867534640E-02 4.4861358114E-04
> b5 = 2 0.02 2.2122699662E-02 8.9471996575E-04
>
> Residual Sum of Squares: 5.4648946975E-05
> Residual Standard Deviation: 1.3970497866E-03
> Degrees of Freedom: 28
> Number of Observations: 33
> */
.
. clear
. program drop _all
.
. scalar N = 33
. scalar df_r = 28
. scalar df_m = 5
.
. scalar rss = 5.4648946975E-05
. scalar rmse = 1.3970497866E-03
.
. scalar b1 = 3.7541005211E-01
. scalar seb1 = 2.0723153551E-03
. scalar b2 = 1.9358469127E+00
. scalar seb2 = 2.2031669222E-01
. scalar b3 = -1.4646871366E+00
. scalar seb3 = 2.2175707739E-01
. scalar b4 = 1.2867534640E-02
. scalar seb4 = 4.4861358114E-04
. scalar b5 = 2.2122699662E-02
. scalar seb5 = 8.9471996575E-04
.
. program define nlbprog
1. version 6
2. if "`1'"=="?" {
3. global S_1 "b1 b2 b3 b4 b5"
4.
. * first set of initial values do not lead to convergence for original nl
. global b1 .5
5. global b2 1.5
6. global b3 -1
7. global b4 .01
8. global b5 .02
9. exit
10. }
11.
. replace `1' = $b1 + $b2*exp(-(x*$b4)) + $b3*exp(-(x*$b5))
12. end
.
. qui input double(y x)
.
. nl ( y = {b1} + {b2}*exp(-x*{b4}) + {b3}*exp(-x*{b5}) ), ///
> init(b1 .5 b2 1.5 b3 -1 b4 0.01 b5 0.02) eps(1e-10)
(obs = 33)
Iteration 0: residual SS = .0018987
Iteration 1: residual SS = .0017038
Iteration 2: residual SS = .0010161
Iteration 3: residual SS = .0003689
Iteration 4: residual SS = .0000547
Iteration 5: residual SS = .0000546
Iteration 6: residual SS = .0000546
Iteration 7: residual SS = .0000546
Iteration 8: residual SS = .0000546
Iteration 9: residual SS = .0000546
Iteration 10: residual SS = .0000546
Source | SS df MS
-------------+---------------------------------- Number of obs = 33
Model | 14.28459 5 2.85691807 R-squared = 1.0000
Residual | .00005465 28 1.9517e-06 Adj R-squared = 1.0000
-------------+---------------------------------- Root MSE = .001397
Total | 14.284645 33 .43286803 Res. dev. = -345.616
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/b1 | .3754101 .0020723 181.15 0.000 .3711651 .379655
/b2 | 1.935847 .2203166 8.79 0.000 1.484549 2.387145
/b4 | .0128675 .0004486 28.68 0.000 .0119486 .0137865
/b3 | -1.464687 .221757 -6.60 0.000 -1.918936 -1.010438
/b5 | .0221227 .0008947 24.73 0.000 .02029 .0239554
------------------------------------------------------------------------------
.
. 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 () /*
> */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 /*
> */ [b4]_se[_cons] seb4 [b5]_se[_cons] seb5 () /*
> */ e(rmse) rmse e(rss) rss
[b1]_b[_cons] 8.5
[b2]_b[_cons] 7.1
[b3]_b[_cons] 7.0
[b4]_b[_cons] 7.7
[b5]_b[_cons] 7.6
-------------------------
min 7.0
[b1]_se[_cons] 6.2
[b2]_se[_cons] 6.3
[b3]_se[_cons] 6.3
[b4]_se[_cons] 6.4
[b5]_se[_cons] 6.1
-------------------------
min 6.1
e(rmse) 11.9
e(rss) 11.5
.
.
.
end of do-file