___ ____ ____ ____ ____ tm /__ / ____/ / ____/ ___/ / /___/ / /___/ 9.0 Copyright 1984-2005 Statistics/Data Analysis StataCorp 4905 Lakeway Drive College Station, Texas 77845 USA 800-STATA-PC http://www.stata.com 979-696-4600 stata@stata.com 979-696-4601 (fax) 3-user Stata for Linux64 (network) perpetual license: Serial number: 999 Licensed to: Brian P. Poi, Ph.D. StataCorp LP Notes: 1. (-m# option or -set memory-) 1.00 MB allocated to data 2. Command line editing disabled 3. Stata running in batch mode running /home/bpp/bin/profile.do ... . do gauss2.do . /* NIST StRD benchmark from http://www.nist.gov/itl/div898/strd/ > > Nonlinear Regression > > Difficulty=Lower Exponential k=8 N=250 Generated > > Dataset Name: Gauss2 (Gauss2.dat) > > Procedure: Nonlinear Least Squares Regression > > Description: The data are two slightly-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 > Lower 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 = 96.0 98.0 9.9018328406E+01 5.3748766879E-01 > b2 = 0.009 0.0105 1.0994945399E-02 1.3335306766E-04 > b3 = 103.0 103.0 1.0188022528E+02 5.9217315772E-01 > b4 = 106.0 105.0 1.0703095519E+02 1.5006798316E-01 > b5 = 18.0 20.0 2.3578584029E+01 2.2695595067E-01 > b6 = 72.0 73.0 7.2045589471E+01 6.1721965884E-01 > b7 = 151.0 150.0 1.5327010194E+02 1.9466674341E-01 > b8 = 18.0 20.0 1.9525972636E+01 2.6416549393E-01 > > Residual Sum of Squares: 1.2475282092E+03 > Residual Standard Deviation: 2.2704790782E+00 > Degrees of Freedom: 242 > Number of Observations: 250 > */ . . clear . . scalar N = 250 . scalar df_r = 242 . scalar df_m = 8 . . scalar rss = 1.2475282092E+03 . scalar rmse = 2.2704790782E+00 . . scalar b1 = 9.9018328406E+01 . scalar seb1 = 5.3748766879E-01 . scalar b2 = 1.0994945399E-02 . scalar seb2 = 1.3335306766E-04 . scalar b3 = 1.0188022528E+02 . scalar seb3 = 5.9217315772E-01 . scalar b4 = 1.0703095519E+02 . scalar seb4 = 1.5006798316E-01 . scalar b5 = 2.3578584029E+01 . scalar seb5 = 2.2695595067E-01 . scalar b6 = 7.2045589471E+01 . scalar seb6 = 6.1721965884E-01 . scalar b7 = 1.5327010194E+02 . scalar seb7 = 1.9466674341E-01 . scalar b8 = 1.9525972636E+01 . scalar seb8 = 2.6416549393E-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 96 b2 0.009 b3 103 b4 106 b5 18 b6 72 b7 151 b8 18) > eps(1e-10) ; (obs = 250) Iteration 0: residual SS = 9158.14 Iteration 1: residual SS = 1613.56 Iteration 2: residual SS = 1248.662 Iteration 3: residual SS = 1247.528 Iteration 4: residual SS = 1247.528 Iteration 5: residual SS = 1247.528 Iteration 6: residual SS = 1247.528 Iteration 7: residual SS = 1247.528 Source | SS df MS Number of obs = 250 -------------+------------------------------ F( 8, 242) = 30791.27 Model | 1269850.46 8 158731.307 Prob > F = 0.0000 Residual | 1247.52821 242 5.15507524 R-squared = 0.9990 -------------+------------------------------ Adj R-squared = 0.9990 Total | 1271097.99 250 5084.39194 Root MSE = 2.270479 Res. dev. = 1111.334 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- b1 | 99.01833 .5374877 184.22 0.000 97.95958 100.0771 b2 | .0109949 .0001334 82.45 0.000 .0107323 .0112576 b3 | 101.8802 .592173 172.04 0.000 100.7138 103.0467 b4 | 107.031 .150068 713.22 0.000 106.7353 107.3266 b5 | 23.57858 .2269559 103.89 0.000 23.13152 24.02565 b6 | 72.04559 .6172196 116.73 0.000 70.82978 73.2614 b7 | 153.2701 .1946668 787.35 0.000 152.8866 153.6536 b8 | 19.52597 .2641658 73.92 0.000 19.00561 20.04633 ------------------------------------------------------------------------------ (SEs, P values, CIs, and correlations are asymptotic approximations) . #delimit cr delimiter now cr . . assert N == e(N) . assert df_r == e(df_r) . assert df_m == e(df_m) . . lrecomp _b[b1] b1 _b[b2] b2 _b[b3] b3 /* > */ _b[b4] b4 _b[b5] b5 _b[b6] b6 /* > */ _b[b7] b7 _b[b8] b8 () /* > */ _se[b1] seb1 _se[b2] seb2 _se[b3] seb3 /* > */ _se[b4] seb4 _se[b5] seb5 _se[b6] seb6 /* > */ _se[b7] seb7 _se[b8] seb8 () /* > */ e(rmse) rmse e(rss) rss _b[b1] 9.5 _b[b2] 9.9 _b[b3] 9.2 _b[b4] 9.4 _b[b5] 8.4 _b[b6] 9.6 _b[b7] 9.4 _b[b8] 8.2 ------------------------- min 8.2 _se[b1] 6.9 _se[b2] 6.3 _se[b3] 6.5 _se[b4] 6.8 _se[b5] 6.4 _se[b6] 6.8 _se[b7] 6.9 _se[b8] 5.9 ------------------------- min 5.9 e(rmse) 10.7 e(rss) 10.6 . end of do-file