___ ____ ____ ____ ____ tm /__ / ____/ / ____/ ___/ / /___/ / /___/ 10.0 Copyright 1984-2007 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, PhD 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 lanczos1.do . /* NIST/ITL StRD > Dataset Name: Lanczos1 (Lanczos1.dat) > > File Format: ASCII > Starting Values (lines 41 to 46) > Certified Values (lines 41 to 51) > Data (lines 61 to 84) > > Procedure: Nonlinear Least Squares Regression > > Description: These data are taken from an example discussed in > Lanczos (1956). The data were generated to 14-digits > of accuracy using > f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) > + 1.5576*exp(-5*x). > > > Reference: Lanczos, C. (1956). > Applied Analysis. > Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. > > > > > Data: 1 Response (y) > 1 Predictor (x) > 24 Observations > Average Level of Difficulty > Generated Data > > Model: Exponential Class > 6 Parameters (b1 to b6) > > y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e > > > > Starting values Certified Values > > Start 1 Start 2 Parameter Standard Deviation > b1 = 1.2 0.5 9.5100000027E-02 5.3347304234E-11 > b2 = 0.3 0.7 1.0000000001E+00 2.7473038179E-10 > b3 = 5.6 3.6 8.6070000013E-01 1.3576062225E-10 > b4 = 5.5 4.2 3.0000000002E+00 3.3308253069E-10 > b5 = 6.5 4 1.5575999998E+00 1.8815731448E-10 > b6 = 7.6 6.3 5.0000000001E+00 1.1057500538E-10 > > Residual Sum of Squares: 1.4307867721E-25 > Residual Standard Deviation: 8.9156129349E-14 > Degrees of Freedom: 18 > Number of Observations: 24 > */ . . clear . . scalar N = 24 . scalar df_r = 18 . scalar df_m = 6 . . scalar rss = 1.4307867721E-25 . scalar rmse = 8.9156129349E-14 . . scalar b1 = 9.5100000027E-02 . scalar seb1 = 5.3347304234E-11 . scalar b2 = 1.0000000001E+00 . scalar seb2 = 2.7473038179E-10 . scalar b3 = 8.6070000013E-01 . scalar seb3 = 1.3576062225E-10 . scalar b4 = 3.0000000002E+00 . scalar seb4 = 3.3308253069E-10 . scalar b5 = 1.5575999998E+00 . scalar seb5 = 1.8815731448E-10 . scalar b6 = 5.0000000001E+00 . scalar seb6 = 1.1057500538E-10 . . qui input double(y x) . . nl ( y = {b1}*exp(-{b2}*x) + {b3}*exp(-{b4}*x) + {b5}*exp(-{b6}*x) ), /// > init(b1 1.2 b2 0.3 b3 5.6 b4 5.5 b5 6.5 b6 7.6) eps(1e-10) (obs = 24) Iteration 0: residual SS = 12.10782 Iteration 1: residual SS = .0161967 Iteration 2: residual SS = .0000417 Iteration 3: residual SS = .0000374 Iteration 4: residual SS = .0000328 Iteration 5: residual SS = .0000295 Iteration 6: residual SS = .0000187 Iteration 7: residual SS = 3.18e-06 Iteration 8: residual SS = 2.23e-06 Iteration 9: residual SS = 1.72e-06 Iteration 10: residual SS = 6.01e-07 Iteration 11: residual SS = 5.41e-13 Iteration 12: residual SS = 9.12e-24 Iteration 13: residual SS = 1.43e-25 Source | SS df MS -------------+------------------------------ Number of obs = 24 Model | 19.2786563 6 3.21310938 R-squared = 1.0000 Residual | 1.4295e-25 18 7.9415e-27 Adj R-squared = 1.0000 -------------+------------------------------ Root MSE = 8.91e-14 Total | 19.2786563 24 .803277346 Res. dev. = -1381.14 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /b1 | .0951 5.33e-11 1.8e+09 0.000 .0951 .0951 /b2 | 1 2.75e-10 3.6e+09 0.000 1 1 /b3 | .8607 1.36e-10 6.3e+09 0.000 .8607 .8607 /b4 | 3 3.33e-10 9.0e+09 0.000 3 3 /b5 | 1.5576 1.88e-10 8.3e+09 0.000 1.5576 1.5576 /b6 | 5 1.11e-10 4.5e+10 0.000 5 5 ------------------------------------------------------------------------------ . . 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 () /* > */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 /* > */ [b4]_se[_cons] seb4 [b5]_se[_cons] seb5 [b6]_se[_cons] seb6 () /* > */ e(rmse) rmse e(rss) rss [b1]_b[_cons] 11.4 [b2]_b[_cons] 10.6 [b3]_b[_cons] 11.3 [b4]_b[_cons] 10.9 [b5]_b[_cons] 10.6 [b6]_b[_cons] 11.6 ------------------------- min 10.6 [b1]_se[_cons] 3.3 [b2]_se[_cons] 3.3 [b3]_se[_cons] 3.3 [b4]_se[_cons] 3.3 [b5]_se[_cons] 3.3 [b6]_se[_cons] 3.3 ------------------------- min 3.3 e(rmse) 3.3 e(rss) 3.0 . . . end of do-file