___ ____ ____ ____ ____ (R)
/__ / ____/ / ____/
___/ / /___/ / /___/ 11.0 Copyright 1984-2009
Statistics/Data Analysis StataCorp
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Serial number: 999
Licensed to: Brian P. Poi
StataCorp LP
Notes:
1. (-m# option or -set memory-) 10.00 MB allocated to data
2. Command line editing disabled
3. Stata running in batch mode
running /home/bpp/bin/profile.do ...
. do chwirut1.do
. /* NIST StRD benchmark from http://www.nist.gov/itl/div898/strd/
>
> Nonlinear Regression
>
> Difficulty=Lower Exponential k=3 N=214 Observed
>
> Dataset Name: Chwirut1 (Chwirut1.dat)
>
> File Format: ASCII
> Starting Values (lines 41 to 43)
> Certified Values (lines 41 to 48)
> Data (lines 61 to 274)
>
> Procedure: Nonlinear Least Squares Regression
>
> Description: These data are the result of a NIST study involving
> ultrasonic calibration. The response variable is
> ultrasonic response, and the predictor variable is
> metal distance.
>
> Reference: Chwirut, D., NIST (197?).
> Ultrasonic Reference Block Study.
>
> Data: 1 Response Variable (y = ultrasonic response)
> 1 Predictor Variable (x = metal distance)
> 214 Observations
> Lower Level of Difficulty
> Observed Data
>
> Model: Exponential Class
> 3 Parameters (b1 to b3)
>
> y = exp[-b1*x]/(b2+b3*x) + e
>
>
> Starting values Certified Values
>
> Start 1 Start 2 Parameter Standard Deviation
> b1 = 0.1 0.15 1.9027818370E-01 2.1938557035E-02
> b2 = 0.01 0.008 6.1314004477E-03 3.4500025051E-04
> b3 = 0.02 0.010 1.0530908399E-02 7.9281847748E-04
>
> Residual Sum of Squares: 2.3844771393E+03
> Residual Standard Deviation: 3.3616721320E+00
> Degrees of Freedom: 211
> Number of Observations: 214
> */
.
. clear
.
. scalar N = 214
. scalar df_r = 211
. scalar df_m = 3
.
. scalar rss = 2.3844771393E+03
. scalar rmse = 3.3616721320E+00
.
. scalar b1 = 1.9027818370E-01
. scalar seb1 = 2.1938557035E-02
. scalar b2 = 6.1314004477E-03
. scalar seb2 = 3.4500025051E-04
. scalar b3 = 1.0530908399E-02
. scalar seb3 = 7.9281847748E-04
.
. qui input double (y x)
.
. nl ( y = exp(-{b1}*x)/({b2}+{b3}*x) ), init(b1 1 b2 .01 b3 .02) eps(1e-10)
(obs = 214)
Iteration 0: residual SS = 103077.7
Iteration 1: residual SS = 38669.29
Iteration 2: residual SS = 5678.076
Iteration 3: residual SS = 2453.61
Iteration 4: residual SS = 2384.491
Iteration 5: residual SS = 2384.477
Iteration 6: residual SS = 2384.477
Iteration 7: residual SS = 2384.477
Iteration 8: residual SS = 2384.477
Iteration 9: residual SS = 2384.477
Iteration 10: residual SS = 2384.477
Source | SS df MS
-------------+------------------------------ Number of obs = 214
Model | 313023.796 3 104341.265 R-squared = 0.9924
Residual | 2384.47714 211 11.3008395 Adj R-squared = 0.9923
-------------+------------------------------ Root MSE = 3.361672
Total | 315408.273 214 1473.87043 Res. dev. = 1123.208
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/b1 | .1902782 .0219386 8.67 0.000 .1470313 .233525
/b2 | .0061314 .000345 17.77 0.000 .0054513 .0068115
/b3 | .0105309 .0007928 13.28 0.000 .008968 .0120938
------------------------------------------------------------------------------
.
. 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] 7.6
[b2]_b[_cons] 8.0
[b3]_b[_cons] 7.8
-------------------------
min 7.6
[b1]_se[_cons] 6.6
[b2]_se[_cons] 6.3
[b3]_se[_cons] 6.3
-------------------------
min 6.3
e(rmse) 10.9
e(rss) 11.4
.
end of do-file