/* NIST/ITL StRD Dataset Name: Gauss3 (Gauss3.dat) File Format: ASCII Starting Values (lines 41 to 48) Certified Values (lines 41 to 53) Data (lines 61 to 310) Procedure: Nonlinear Least Squares Regression Description: The data are two strongly-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 Average 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 = 94.9 96.0 9.8940368970E+01 5.3005192833E-01 b2 = 0.009 0.0096 1.0945879335E-02 1.2554058911E-04 b3 = 90.1 80.0 1.0069553078E+02 8.1256587317E-01 b4 = 113.0 110.0 1.1163619459E+02 3.5317859757E-01 b5 = 20.0 25.0 2.3300500029E+01 3.6584783023E-01 b6 = 73.8 74.0 7.3705031418E+01 1.2091239082E+00 b7 = 140.0 139.0 1.4776164251E+02 4.0488183351E-01 b8 = 20.0 25.0 1.9668221230E+01 3.7806634336E-01 Residual Sum of Squares: 1.2444846360E+03 Residual Standard Deviation: 2.2677077625E+00 Degrees of Freedom: 242 Number of Observations: 250 */ clear scalar N = 250 scalar df_r = 242 scalar df_m = 8 scalar rss = 1.2444846360E+03 scalar rmse = 2.2677077625E+00 scalar b1 = 9.8940368970E+01 scalar seb1 = 5.3005192833E-01 scalar b2 = 1.0945879335E-02 scalar seb2 = 1.2554058911E-04 scalar b3 = 1.0069553078E+02 scalar seb3 = 8.1256587317E-01 scalar b4 = 1.1163619459E+02 scalar seb4 = 3.5317859757E-01 scalar b5 = 2.3300500029E+01 scalar seb5 = 3.6584783023E-01 scalar b6 = 7.3705031418E+01 scalar seb6 = 1.2091239082E+00 scalar b7 = 1.4776164251E+02 scalar seb7 = 4.0488183351E-01 scalar b8 = 1.9668221230E+01 scalar seb8 = 3.7806634336E-01 qui input double(y x) 97.58776 1.000000 97.76344 2.000000 96.56705 3.000000 92.52037 4.000000 91.15097 5.000000 95.21728 6.000000 90.21355 7.000000 89.29235 8.000000 91.51479 9.000000 89.60965 10.000000 86.56187 11.00000 85.55315 12.00000 87.13053 13.00000 85.67938 14.00000 80.04849 15.00000 82.18922 16.00000 87.24078 17.00000 80.79401 18.00000 81.28564 19.00000 81.56932 20.00000 79.22703 21.00000 79.43259 22.00000 77.90174 23.00000 76.75438 24.00000 77.17338 25.00000 74.27296 26.00000 73.11830 27.00000 73.84732 28.00000 72.47746 29.00000 71.92128 30.00000 66.91962 31.00000 67.93554 32.00000 69.55841 33.00000 69.06592 34.00000 66.53371 35.00000 63.87094 36.00000 69.70526 37.00000 63.59295 38.00000 63.35509 39.00000 59.99747 40.00000 62.64843 41.00000 65.77345 42.00000 59.10141 43.00000 56.57750 44.00000 61.15313 45.00000 54.30767 46.00000 62.83535 47.00000 56.52957 48.00000 56.98427 49.00000 58.11459 50.00000 58.69576 51.00000 58.23322 52.00000 54.90490 53.00000 57.91442 54.00000 56.96629 55.00000 51.13831 56.00000 49.27123 57.00000 52.92668 58.00000 54.47693 59.00000 51.81710 60.00000 51.05401 61.00000 52.51731 62.00000 51.83710 63.00000 54.48196 64.00000 49.05859 65.00000 50.52315 66.00000 50.32755 67.00000 46.44419 68.00000 50.89281 69.00000 52.13203 70.00000 49.78741 71.00000 49.01637 72.00000 54.18198 73.00000 53.17456 74.00000 53.20827 75.00000 57.43459 76.00000 51.95282 77.00000 54.20282 78.00000 57.46687 79.00000 53.60268 80.00000 58.86728 81.00000 57.66652 82.00000 63.71034 83.00000 65.24244 84.00000 65.10878 85.00000 69.96313 86.00000 68.85475 87.00000 73.32574 88.00000 76.21241 89.00000 78.06311 90.00000 75.37701 91.00000 87.54449 92.00000 89.50588 93.00000 95.82098 94.00000 97.48390 95.00000 100.86070 96.00000 102.48510 97.00000 105.7311 98.00000 111.3489 99.00000 111.0305 100.00000 110.1920 101.00000 118.3581 102.00000 118.8086 103.00000 122.4249 104.00000 124.0953 105.00000 125.9337 106.0000 127.8533 107.0000 131.0361 108.0000 133.3343 109.0000 135.1278 110.0000 131.7113 111.0000 131.9151 112.0000 132.1107 113.0000 127.6898 114.0000 133.2148 115.0000 128.2296 116.0000 133.5902 117.0000 127.2539 118.0000 128.3482 119.0000 124.8694 120.0000 124.6031 121.0000 117.0648 122.0000 118.1966 123.0000 119.5408 124.0000 114.7946 125.0000 114.2780 126.0000 120.3484 127.0000 114.8647 128.0000 111.6514 129.0000 110.1826 130.0000 108.4461 131.0000 109.0571 132.0000 106.5308 133.0000 109.4691 134.0000 106.8709 135.0000 107.3192 136.0000 106.9000 137.0000 109.6526 138.0000 107.1602 139.0000 108.2509 140.0000 104.96310 141.0000 109.3601 142.0000 107.6696 143.0000 99.77286 144.0000 104.96440 145.0000 106.1376 146.0000 106.5816 147.0000 100.12860 148.0000 101.66910 149.0000 96.44254 150.0000 97.34169 151.0000 96.97412 152.0000 90.73460 153.0000 93.37949 154.0000 82.12331 155.0000 83.01657 156.0000 78.87360 157.0000 74.86971 158.0000 72.79341 159.0000 65.14744 160.0000 67.02127 161.0000 60.16136 162.0000 57.13996 163.0000 54.05769 164.0000 50.42265 165.0000 47.82430 166.0000 42.85748 167.0000 42.45495 168.0000 38.30808 169.0000 36.95794 170.0000 33.94543 171.0000 34.19017 172.0000 31.66097 173.0000 23.56172 174.0000 29.61143 175.0000 23.88765 176.0000 22.49812 177.0000 24.86901 178.0000 17.29481 179.0000 18.09291 180.0000 15.34813 181.0000 14.77997 182.0000 13.87832 183.0000 12.88891 184.0000 16.20763 185.0000 16.29024 186.0000 15.29712 187.0000 14.97839 188.0000 12.11330 189.0000 14.24168 190.0000 12.53824 191.0000 15.19818 192.0000 11.70478 193.0000 15.83745 194.0000 10.035850 195.0000 9.307574 196.0000 12.86800 197.0000 8.571671 198.0000 11.60415 199.0000 12.42772 200.0000 11.23627 201.0000 11.13198 202.0000 7.761117 203.0000 6.758250 204.0000 14.23375 205.0000 10.63876 206.0000 8.893581 207.0000 11.55398 208.0000 11.57221 209.0000 11.58347 210.0000 9.724857 211.0000 11.43854 212.0000 11.22636 213.0000 10.170150 214.0000 12.50765 215.0000 6.200494 216.0000 9.018902 217.0000 10.80557 218.0000 13.09591 219.0000 3.914033 220.0000 9.567723 221.0000 8.038338 222.0000 10.230960 223.0000 9.367358 224.0000 7.695937 225.0000 6.118552 226.0000 8.793192 227.0000 7.796682 228.0000 12.45064 229.0000 10.61601 230.0000 6.001000 231.0000 6.765096 232.0000 8.764652 233.0000 4.586417 234.0000 8.390782 235.0000 7.209201 236.0000 10.012090 237.0000 7.327461 238.0000 6.525136 239.0000 2.840065 240.0000 10.323710 241.0000 4.790035 242.0000 8.376431 243.0000 6.263980 244.0000 2.705892 245.0000 8.362109 246.0000 8.983507 247.0000 3.362469 248.0000 1.182678 249.0000 4.875312 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 94.9 b2 0.009 b3 90.1 b4 113.0 b5 20.0 b6 73.8 b7 140.0 b8 20) 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