___ ____ ____ ____ ____ (R) /__ / ____/ / ____/ ___/ / /___/ / /___/ 14.0 Copyright 1985-2015 StataCorp LP Statistics/Data Analysis StataCorp 4905 Lakeway Drive Special Edition College Station, Texas 77845 USA 800-STATA-PC http://www.stata.com 979-696-4600 stata@stata.com 979-696-4601 (fax) 10-user Stata network perpetual license: Serial number: 1 Licensed to: Stata Developer StataCorp LP 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. . 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