/* NIST StRD benchmark from http://www.nist.gov/itl/div898/strd/ Nonlinear Regression Difficulty=Average Rational k=7 N=236 Observed Dataset Name: Hahn1 (Hahn1.dat) Procedure: Nonlinear Least Squares Regression Description: These data are the result of a NIST study involving the thermal expansion of copper. The response variable is the coefficient of thermal expansion, and the predictor variable is temperature in degrees kelvin. Reference: Hahn, T., NIST (197?). Copper Thermal Expansion Study. Data: 1 Response (y = coefficient of thermal expansion) 1 Predictor (x = temperature, degrees kelvin) 236 Observations Average Level of Difficulty Observed Data Model: Rational Class (cubic/cubic) 7 Parameters (b1 to b7) y = (b1+b2*x+b3*x**2+b4*x**3) / (1+b5*x+b6*x**2+b7*x**3) + e Starting values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 10 1 1.0776351733E+00 1.7070154742E-01 b2 = -1 -0.1 -1.2269296921E-01 1.2000289189E-02 b3 = 0.05 0.005 4.0863750610E-03 2.2508314937E-04 b4 = -0.00001 -0.000001 -1.4262662514E-06 2.7578037666E-07 b5 = -0.05 -0.005 -5.7609940901E-03 2.4712888219E-04 b6 = 0.001 0.0001 2.4053735503E-04 1.0449373768E-05 b7 = -0.000001 -0.0000001 -1.2314450199E-07 1.3027335327E-08 Residual Sum of Squares: 1.5324382854E+00 Residual Standard Deviation: 8.1803852243E-02 Degrees of Freedom: 229 Number of Observations: 236 */ clear scalar N = 236 scalar df_r = 229 scalar df_m = 7 scalar rss = 1.5324382854E+00 scalar rmse = 8.1803852243E-02 scalar b1 = 1.0776351733E+00 scalar seb1 = 1.7070154742E-01 scalar b2 = -1.2269296921E-01 scalar seb2 = 1.2000289189E-02 scalar b3 = 4.0863750610E-03 scalar seb3 = 2.2508314937E-04 scalar b4 = -1.4262662514E-06 scalar seb4 = 2.7578037666E-07 scalar b5 = -5.7609940901E-03 scalar seb5 = 2.4712888219E-04 scalar b6 = 2.4053735503E-04 scalar seb6 = 1.0449373768E-05 scalar b7 = -1.2314450199E-07 scalar seb7 = 1.3027335327E-08 qui input double (y x) .591E0 24.41E0 1.547E0 34.82E0 2.902E0 44.09E0 2.894E0 45.07E0 4.703E0 54.98E0 6.307E0 65.51E0 7.03E0 70.53E0 7.898E0 75.70E0 9.470E0 89.57E0 9.484E0 91.14E0 10.072E0 96.40E0 10.163E0 97.19E0 11.615E0 114.26E0 12.005E0 120.25E0 12.478E0 127.08E0 12.982E0 133.55E0 12.970E0 133.61E0 13.926E0 158.67E0 14.452E0 172.74E0 14.404E0 171.31E0 15.190E0 202.14E0 15.550E0 220.55E0 15.528E0 221.05E0 15.499E0 221.39E0 16.131E0 250.99E0 16.438E0 268.99E0 16.387E0 271.80E0 16.549E0 271.97E0 16.872E0 321.31E0 16.830E0 321.69E0 16.926E0 330.14E0 16.907E0 333.03E0 16.966E0 333.47E0 17.060E0 340.77E0 17.122E0 345.65E0 17.311E0 373.11E0 17.355E0 373.79E0 17.668E0 411.82E0 17.767E0 419.51E0 17.803E0 421.59E0 17.765E0 422.02E0 17.768E0 422.47E0 17.736E0 422.61E0 17.858E0 441.75E0 17.877E0 447.41E0 17.912E0 448.7E0 18.046E0 472.89E0 18.085E0 476.69E0 18.291E0 522.47E0 18.357E0 522.62E0 18.426E0 524.43E0 18.584E0 546.75E0 18.610E0 549.53E0 18.870E0 575.29E0 18.795E0 576.00E0 19.111E0 625.55E0 .367E0 20.15E0 .796E0 28.78E0 0.892E0 29.57E0 1.903E0 37.41E0 2.150E0 39.12E0 3.697E0 50.24E0 5.870E0 61.38E0 6.421E0 66.25E0 7.422E0 73.42E0 9.944E0 95.52E0 11.023E0 107.32E0 11.87E0 122.04E0 12.786E0 134.03E0 14.067E0 163.19E0 13.974E0 163.48E0 14.462E0 175.70E0 14.464E0 179.86E0 15.381E0 211.27E0 15.483E0 217.78E0 15.59E0 219.14E0 16.075E0 262.52E0 16.347E0 268.01E0 16.181E0 268.62E0 16.915E0 336.25E0 17.003E0 337.23E0 16.978E0 339.33E0 17.756E0 427.38E0 17.808E0 428.58E0 17.868E0 432.68E0 18.481E0 528.99E0 18.486E0 531.08E0 19.090E0 628.34E0 16.062E0 253.24E0 16.337E0 273.13E0 16.345E0 273.66E0 16.388E0 282.10E0 17.159E0 346.62E0 17.116E0 347.19E0 17.164E0 348.78E0 17.123E0 351.18E0 17.979E0 450.10E0 17.974E0 450.35E0 18.007E0 451.92E0 17.993E0 455.56E0 18.523E0 552.22E0 18.669E0 553.56E0 18.617E0 555.74E0 19.371E0 652.59E0 19.330E0 656.20E0 0.080E0 14.13E0 0.248E0 20.41E0 1.089E0 31.30E0 1.418E0 33.84E0 2.278E0 39.70E0 3.624E0 48.83E0 4.574E0 54.50E0 5.556E0 60.41E0 7.267E0 72.77E0 7.695E0 75.25E0 9.136E0 86.84E0 9.959E0 94.88E0 9.957E0 96.40E0 11.600E0 117.37E0 13.138E0 139.08E0 13.564E0 147.73E0 13.871E0 158.63E0 13.994E0 161.84E0 14.947E0 192.11E0 15.473E0 206.76E0 15.379E0 209.07E0 15.455E0 213.32E0 15.908E0 226.44E0 16.114E0 237.12E0 17.071E0 330.90E0 17.135E0 358.72E0 17.282E0 370.77E0 17.368E0 372.72E0 17.483E0 396.24E0 17.764E0 416.59E0 18.185E0 484.02E0 18.271E0 495.47E0 18.236E0 514.78E0 18.237E0 515.65E0 18.523E0 519.47E0 18.627E0 544.47E0 18.665E0 560.11E0 19.086E0 620.77E0 0.214E0 18.97E0 0.943E0 28.93E0 1.429E0 33.91E0 2.241E0 40.03E0 2.951E0 44.66E0 3.782E0 49.87E0 4.757E0 55.16E0 5.602E0 60.90E0 7.169E0 72.08E0 8.920E0 85.15E0 10.055E0 97.06E0 12.035E0 119.63E0 12.861E0 133.27E0 13.436E0 143.84E0 14.167E0 161.91E0 14.755E0 180.67E0 15.168E0 198.44E0 15.651E0 226.86E0 15.746E0 229.65E0 16.216E0 258.27E0 16.445E0 273.77E0 16.965E0 339.15E0 17.121E0 350.13E0 17.206E0 362.75E0 17.250E0 371.03E0 17.339E0 393.32E0 17.793E0 448.53E0 18.123E0 473.78E0 18.49E0 511.12E0 18.566E0 524.70E0 18.645E0 548.75E0 18.706E0 551.64E0 18.924E0 574.02E0 19.1E0 623.86E0 0.375E0 21.46E0 0.471E0 24.33E0 1.504E0 33.43E0 2.204E0 39.22E0 2.813E0 44.18E0 4.765E0 55.02E0 9.835E0 94.33E0 10.040E0 96.44E0 11.946E0 118.82E0 12.596E0 128.48E0 13.303E0 141.94E0 13.922E0 156.92E0 14.440E0 171.65E0 14.951E0 190.00E0 15.627E0 223.26E0 15.639E0 223.88E0 15.814E0 231.50E0 16.315E0 265.05E0 16.334E0 269.44E0 16.430E0 271.78E0 16.423E0 273.46E0 17.024E0 334.61E0 17.009E0 339.79E0 17.165E0 349.52E0 17.134E0 358.18E0 17.349E0 377.98E0 17.576E0 394.77E0 17.848E0 429.66E0 18.090E0 468.22E0 18.276E0 487.27E0 18.404E0 519.54E0 18.519E0 523.03E0 19.133E0 612.99E0 19.074E0 638.59E0 19.239E0 641.36E0 19.280E0 622.05E0 19.101E0 631.50E0 19.398E0 663.97E0 19.252E0 646.9E0 19.89E0 748.29E0 20.007E0 749.21E0 19.929E0 750.14E0 19.268E0 647.04E0 19.324E0 646.89E0 20.049E0 746.9E0 20.107E0 748.43E0 20.062E0 747.35E0 20.065E0 749.27E0 19.286E0 647.61E0 19.972E0 747.78E0 20.088E0 750.51E0 20.743E0 851.37E0 20.83E0 845.97E0 20.935E0 847.54E0 21.035E0 849.93E0 20.93E0 851.61E0 21.074E0 849.75E0 21.085E0 850.98E0 20.935E0 848.23E0 end #delimit ; nl (y = ({b1} + {b2}*x + {b3}*x^2 + {b4}*x^3) / (1 + {b5}*x + {b6}*x^2 + {b7}*x^3) ) , initial(b1 10 b2 -1 b3 0.05 b4 -0.00001 b5 -0.05 b6 0.001 b7 -0.000001) eps(1e-10) ; #delimit cr 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 [b7]_b[_cons] b7 () /* */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 /* */ [b4]_se[_cons] seb4 [b5]_se[_cons] seb5 [b6]_se[_cons] seb6 [b7]_se[_cons] seb7 () /* */ e(rmse) rmse e(rss) rss