/* NIST/ITL StRD Nonlinear Regression Difficulty=Lower Exponential k=8 N=250 Generated Dataset Name: Gauss1 (Gauss1.dat) Procedure: Nonlinear Least Squares Regression Description: The data are two well-separated 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 = 97.0 94.0 9.8778210871E+01 5.7527312730E-01 b2 = 0.009 0.0105 1.0497276517E-02 1.1406289017E-04 b3 = 100.0 99.0 1.0048990633E+02 5.8831775752E-01 b4 = 65.0 63.0 6.7481111276E+01 1.0460593412E-01 b5 = 20.0 25.0 2.3129773360E+01 1.7439951146E-01 b6 = 70.0 71.0 7.1994503004E+01 6.2622793913E-01 b7 = 178.0 180.0 1.7899805021E+02 1.2436988217E-01 b8 = 16.5 20.0 1.8389389025E+01 2.0134312832E-01 Residual Sum of Squares: 1.3158222432E+03 Residual Standard Deviation: 2.3317980180E+00 Degrees of Freedom: 242 Number of Observations: 250 */ clear scalar N = 250 scalar df_r = 242 scalar df_m = 8 scalar rss = 1.3158222432E+03 scalar rmse = 2.3317980180E+00 scalar b1 = 9.8778210871E+01 scalar seb1 = 5.7527312730E-01 scalar b2 = 1.0497276517E-02 scalar seb2 = 1.1406289017E-04 scalar b3 = 1.0048990633E+02 scalar seb3 = 5.8831775752E-01 scalar b4 = 6.7481111276E+01 scalar seb4 = 1.0460593412E-01 scalar b5 = 2.3129773360E+01 scalar seb5 = 1.7439951146E-01 scalar b6 = 7.1994503004E+01 scalar seb6 = 6.2622793913E-01 scalar b7 = 1.7899805021E+02 scalar seb7 = 1.2436988217E-01 scalar b8 = 1.8389389025E+01 scalar seb8 = 2.0134312832E-01 qui input double (y x) 97.62227 1.000000 97.80724 2.000000 96.62247 3.000000 92.59022 4.000000 91.23869 5.000000 95.32704 6.000000 90.35040 7.000000 89.46235 8.000000 91.72520 9.000000 89.86916 10.000000 86.88076 11.00000 85.94360 12.00000 87.60686 13.00000 86.25839 14.00000 80.74976 15.00000 83.03551 16.00000 88.25837 17.00000 82.01316 18.00000 82.74098 19.00000 83.30034 20.00000 81.27850 21.00000 81.85506 22.00000 80.75195 23.00000 80.09573 24.00000 81.07633 25.00000 78.81542 26.00000 78.38596 27.00000 79.93386 28.00000 79.48474 29.00000 79.95942 30.00000 76.10691 31.00000 78.39830 32.00000 81.43060 33.00000 82.48867 34.00000 81.65462 35.00000 80.84323 36.00000 88.68663 37.00000 84.74438 38.00000 86.83934 39.00000 85.97739 40.00000 91.28509 41.00000 97.22411 42.00000 93.51733 43.00000 94.10159 44.00000 101.91760 45.00000 98.43134 46.00000 110.4214 47.00000 107.6628 48.00000 111.7288 49.00000 116.5115 50.00000 120.7609 51.00000 123.9553 52.00000 124.2437 53.00000 130.7996 54.00000 133.2960 55.00000 130.7788 56.00000 132.0565 57.00000 138.6584 58.00000 142.9252 59.00000 142.7215 60.00000 144.1249 61.00000 147.4377 62.00000 148.2647 63.00000 152.0519 64.00000 147.3863 65.00000 149.2074 66.00000 148.9537 67.00000 144.5876 68.00000 148.1226 69.00000 148.0144 70.00000 143.8893 71.00000 140.9088 72.00000 143.4434 73.00000 139.3938 74.00000 135.9878 75.00000 136.3927 76.00000 126.7262 77.00000 124.4487 78.00000 122.8647 79.00000 113.8557 80.00000 113.7037 81.00000 106.8407 82.00000 107.0034 83.00000 102.46290 84.00000 96.09296 85.00000 94.57555 86.00000 86.98824 87.00000 84.90154 88.00000 81.18023 89.00000 76.40117 90.00000 67.09200 91.00000 72.67155 92.00000 68.10848 93.00000 67.99088 94.00000 63.34094 95.00000 60.55253 96.00000 56.18687 97.00000 53.64482 98.00000 53.70307 99.00000 48.07893 100.00000 42.21258 101.00000 45.65181 102.00000 41.69728 103.00000 41.24946 104.00000 39.21349 105.00000 37.71696 106.0000 36.68395 107.0000 37.30393 108.0000 37.43277 109.0000 37.45012 110.0000 32.64648 111.0000 31.84347 112.0000 31.39951 113.0000 26.68912 114.0000 32.25323 115.0000 27.61008 116.0000 33.58649 117.0000 28.10714 118.0000 30.26428 119.0000 28.01648 120.0000 29.11021 121.0000 23.02099 122.0000 25.65091 123.0000 28.50295 124.0000 25.23701 125.0000 26.13828 126.0000 33.53260 127.0000 29.25195 128.0000 27.09847 129.0000 26.52999 130.0000 25.52401 131.0000 26.69218 132.0000 24.55269 133.0000 27.71763 134.0000 25.20297 135.0000 25.61483 136.0000 25.06893 137.0000 27.63930 138.0000 24.94851 139.0000 25.86806 140.0000 22.48183 141.0000 26.90045 142.0000 25.39919 143.0000 17.90614 144.0000 23.76039 145.0000 25.89689 146.0000 27.64231 147.0000 22.86101 148.0000 26.47003 149.0000 23.72888 150.0000 27.54334 151.0000 30.52683 152.0000 28.07261 153.0000 34.92815 154.0000 28.29194 155.0000 34.19161 156.0000 35.41207 157.0000 37.09336 158.0000 40.98330 159.0000 39.53923 160.0000 47.80123 161.0000 47.46305 162.0000 51.04166 163.0000 54.58065 164.0000 57.53001 165.0000 61.42089 166.0000 62.79032 167.0000 68.51455 168.0000 70.23053 169.0000 74.42776 170.0000 76.59911 171.0000 81.62053 172.0000 83.42208 173.0000 79.17451 174.0000 88.56985 175.0000 85.66525 176.0000 86.55502 177.0000 90.65907 178.0000 84.27290 179.0000 85.72220 180.0000 83.10702 181.0000 82.16884 182.0000 80.42568 183.0000 78.15692 184.0000 79.79691 185.0000 77.84378 186.0000 74.50327 187.0000 71.57289 188.0000 65.88031 189.0000 65.01385 190.0000 60.19582 191.0000 59.66726 192.0000 52.95478 193.0000 53.87792 194.0000 44.91274 195.0000 41.09909 196.0000 41.68018 197.0000 34.53379 198.0000 34.86419 199.0000 33.14787 200.0000 29.58864 201.0000 27.29462 202.0000 21.91439 203.0000 19.08159 204.0000 24.90290 205.0000 19.82341 206.0000 16.75551 207.0000 18.24558 208.0000 17.23549 209.0000 16.34934 210.0000 13.71285 211.0000 14.75676 212.0000 13.97169 213.0000 12.42867 214.0000 14.35519 215.0000 7.703309 216.0000 10.234410 217.0000 11.78315 218.0000 13.87768 219.0000 4.535700 220.0000 10.059280 221.0000 8.424824 222.0000 10.533120 223.0000 9.602255 224.0000 7.877514 225.0000 6.258121 226.0000 8.899865 227.0000 7.877754 228.0000 12.51191 229.0000 10.66205 230.0000 6.035400 231.0000 6.790655 232.0000 8.783535 233.0000 4.600288 234.0000 8.400915 235.0000 7.216561 236.0000 10.017410 237.0000 7.331278 238.0000 6.527863 239.0000 2.842001 240.0000 10.325070 241.0000 4.790995 242.0000 8.377101 243.0000 6.264445 244.0000 2.706213 245.0000 8.362329 246.0000 8.983658 247.0000 3.362571 248.0000 1.182746 249.0000 4.875359 250.0000 end #delimit ; nl ( y = {b1}*exp( -{b2}*x ) + {b3}*exp( -(x-{b4})^2 / {b5}^2 ) + {b6}*exp( -(x-{b7})^2 / {b8}^2 ) ), init(b1 97.0 b2 0.009 b3 100.0 b4 65.0 b5 20.0 b6 70.0 b7 178.0 b8 16.5) 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 [b8]_b[_cons] b8 () /* */ [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 [b8]_se[_cons] seb8 () /* */ e(rmse) rmse e(rss) rss