/* 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) 92.9000E0 0.5000E0 78.7000E0 0.6250E0 64.2000E0 0.7500E0 64.9000E0 0.8750E0 57.1000E0 1.0000E0 43.3000E0 1.2500E0 31.1000E0 1.7500E0 23.6000E0 2.2500E0 31.0500E0 1.7500E0 23.7750E0 2.2500E0 17.7375E0 2.7500E0 13.8000E0 3.2500E0 11.5875E0 3.7500E0 9.4125E0 4.2500E0 7.7250E0 4.7500E0 7.3500E0 5.2500E0 8.0250E0 5.7500E0 90.6000E0 0.5000E0 76.9000E0 0.6250E0 71.6000E0 0.7500E0 63.6000E0 0.8750E0 54.0000E0 1.0000E0 39.2000E0 1.2500E0 29.3000E0 1.7500E0 21.4000E0 2.2500E0 29.1750E0 1.7500E0 22.1250E0 2.2500E0 17.5125E0 2.7500E0 14.2500E0 3.2500E0 9.4500E0 3.7500E0 9.1500E0 4.2500E0 7.9125E0 4.7500E0 8.4750E0 5.2500E0 6.1125E0 5.7500E0 80.0000E0 0.5000E0 79.0000E0 0.6250E0 63.8000E0 0.7500E0 57.2000E0 0.8750E0 53.2000E0 1.0000E0 42.5000E0 1.2500E0 26.8000E0 1.7500E0 20.4000E0 2.2500E0 26.8500E0 1.7500E0 21.0000E0 2.2500E0 16.4625E0 2.7500E0 12.5250E0 3.2500E0 10.5375E0 3.7500E0 8.5875E0 4.2500E0 7.1250E0 4.7500E0 6.1125E0 5.2500E0 5.9625E0 5.7500E0 74.1000E0 0.5000E0 67.3000E0 0.6250E0 60.8000E0 0.7500E0 55.5000E0 0.8750E0 50.3000E0 1.0000E0 41.0000E0 1.2500E0 29.4000E0 1.7500E0 20.4000E0 2.2500E0 29.3625E0 1.7500E0 21.1500E0 2.2500E0 16.7625E0 2.7500E0 13.2000E0 3.2500E0 10.8750E0 3.7500E0 8.1750E0 4.2500E0 7.3500E0 4.7500E0 5.9625E0 5.2500E0 5.6250E0 5.7500E0 81.5000E0 .5000E0 62.4000E0 .7500E0 32.5000E0 1.5000E0 12.4100E0 3.0000E0 13.1200E0 3.0000E0 15.5600E0 3.0000E0 5.6300E0 6.0000E0 78.0000E0 .5000E0 59.9000E0 .7500E0 33.2000E0 1.5000E0 13.8400E0 3.0000E0 12.7500E0 3.0000E0 14.6200E0 3.0000E0 3.9400E0 6.0000E0 76.8000E0 .5000E0 61.0000E0 .7500E0 32.9000E0 1.5000E0 13.8700E0 3.0000E0 11.8100E0 3.0000E0 13.3100E0 3.0000E0 5.4400E0 6.0000E0 78.0000E0 .5000E0 63.5000E0 .7500E0 33.8000E0 1.5000E0 12.5600E0 3.0000E0 5.6300E0 6.0000E0 12.7500E0 3.0000E0 13.1200E0 3.0000E0 5.4400E0 6.0000E0 76.8000E0 .5000E0 60.0000E0 .7500E0 47.8000E0 1.0000E0 32.0000E0 1.5000E0 22.2000E0 2.0000E0 22.5700E0 2.0000E0 18.8200E0 2.5000E0 13.9500E0 3.0000E0 11.2500E0 4.0000E0 9.0000E0 5.0000E0 6.6700E0 6.0000E0 75.8000E0 .5000E0 62.0000E0 .7500E0 48.8000E0 1.0000E0 35.2000E0 1.5000E0 20.0000E0 2.0000E0 20.3200E0 2.0000E0 19.3100E0 2.5000E0 12.7500E0 3.0000E0 10.4200E0 4.0000E0 7.3100E0 5.0000E0 7.4200E0 6.0000E0 70.5000E0 .5000E0 59.5000E0 .7500E0 48.5000E0 1.0000E0 35.8000E0 1.5000E0 21.0000E0 2.0000E0 21.6700E0 2.0000E0 21.0000E0 2.5000E0 15.6400E0 3.0000E0 8.1700E0 4.0000E0 8.5500E0 5.0000E0 10.1200E0 6.0000E0 78.0000E0 .5000E0 66.0000E0 .6250E0 62.0000E0 .7500E0 58.0000E0 .8750E0 47.7000E0 1.0000E0 37.8000E0 1.2500E0 20.2000E0 2.2500E0 21.0700E0 2.2500E0 13.8700E0 2.7500E0 9.6700E0 3.2500E0 7.7600E0 3.7500E0 5.4400E0 4.2500E0 4.8700E0 4.7500E0 4.0100E0 5.2500E0 3.7500E0 5.7500E0 24.1900E0 3.0000E0 25.7600E0 3.0000E0 18.0700E0 3.0000E0 11.8100E0 3.0000E0 12.0700E0 3.0000E0 16.1200E0 3.0000E0 70.8000E0 .5000E0 54.7000E0 .7500E0 48.0000E0 1.0000E0 39.8000E0 1.5000E0 29.8000E0 2.0000E0 23.7000E0 2.5000E0 29.6200E0 2.0000E0 23.8100E0 2.5000E0 17.7000E0 3.0000E0 11.5500E0 4.0000E0 12.0700E0 5.0000E0 8.7400E0 6.0000E0 80.7000E0 .5000E0 61.3000E0 .7500E0 47.5000E0 1.0000E0 29.0000E0 1.5000E0 24.0000E0 2.0000E0 17.7000E0 2.5000E0 24.5600E0 2.0000E0 18.6700E0 2.5000E0 16.2400E0 3.0000E0 8.7400E0 4.0000E0 7.8700E0 5.0000E0 8.5100E0 6.0000E0 66.7000E0 .5000E0 59.2000E0 .7500E0 40.8000E0 1.0000E0 30.7000E0 1.5000E0 25.7000E0 2.0000E0 16.3000E0 2.5000E0 25.9900E0 2.0000E0 16.9500E0 2.5000E0 13.3500E0 3.0000E0 8.6200E0 4.0000E0 7.2000E0 5.0000E0 6.6400E0 6.0000E0 13.6900E0 3.0000E0 81.0000E0 .5000E0 64.5000E0 .7500E0 35.5000E0 1.5000E0 13.3100E0 3.0000E0 4.8700E0 6.0000E0 12.9400E0 3.0000E0 5.0600E0 6.0000E0 15.1900E0 3.0000E0 14.6200E0 3.0000E0 15.6400E0 3.0000E0 25.5000E0 1.7500E0 25.9500E0 1.7500E0 81.7000E0 .5000E0 61.6000E0 .7500E0 29.8000E0 1.7500E0 29.8100E0 1.7500E0 17.1700E0 2.7500E0 10.3900E0 3.7500E0 28.4000E0 1.7500E0 28.6900E0 1.7500E0 81.3000E0 .5000E0 60.9000E0 .7500E0 16.6500E0 2.7500E0 10.0500E0 3.7500E0 28.9000E0 1.7500E0 28.9500E0 1.7500E0 end nl ( y = exp(-{b1}*x)/({b2}+{b3}*x) ), init(b1 1 b2 .01 b3 .02) eps(1e-10) 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