/* NIST/ITL StRD Dataset Name: MGH17 (MGH17.dat) File Format: ASCII Starting Values (lines 41 to 45) Certified Values (lines 41 to 50) Data (lines 61 to 93) Procedure: Nonlinear Least Squares Regression Description: This problem was found to be difficult for some very good algorithms. See More, J. J., Garbow, B. S., and Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software. 7(1): pp. 17-41. Reference: Osborne, M. R. (1972). Some aspects of nonlinear least squares calculations. In Numerical Methods for Nonlinear Optimization, Lootsma (Ed). New York, NY: Academic Press, pp. 171-189. Data: 1 Response (y) 1 Predictor (x) 33 Observations Average Level of Difficulty Generated Data Model: Exponential Class 5 Parameters (b1 to b5) y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5] + e Starting values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 50 0.5 3.7541005211E-01 2.0723153551E-03 b2 = 150 1.5 1.9358469127E+00 2.2031669222E-01 b3 = -100 -1 -1.4646871366E+00 2.2175707739E-01 b4 = 1 0.01 1.2867534640E-02 4.4861358114E-04 b5 = 2 0.02 2.2122699662E-02 8.9471996575E-04 Residual Sum of Squares: 5.4648946975E-05 Residual Standard Deviation: 1.3970497866E-03 Degrees of Freedom: 28 Number of Observations: 33 */ clear program drop _all scalar N = 33 scalar df_r = 28 scalar df_m = 5 scalar rss = 5.4648946975E-05 scalar rmse = 1.3970497866E-03 scalar b1 = 3.7541005211E-01 scalar seb1 = 2.0723153551E-03 scalar b2 = 1.9358469127E+00 scalar seb2 = 2.2031669222E-01 scalar b3 = -1.4646871366E+00 scalar seb3 = 2.2175707739E-01 scalar b4 = 1.2867534640E-02 scalar seb4 = 4.4861358114E-04 scalar b5 = 2.2122699662E-02 scalar seb5 = 8.9471996575E-04 program define nlbprog version 6 if "`1'"=="?" { global S_1 "b1 b2 b3 b4 b5" * first set of initial values do not lead to convergence for original nl global b1 .5 global b2 1.5 global b3 -1 global b4 .01 global b5 .02 exit } replace `1' = \$b1 + \$b2*exp(-(x*\$b4)) + \$b3*exp(-(x*\$b5)) end qui input double(y x) 8.440000E-01 0.000000E+00 9.080000E-01 1.000000E+01 9.320000E-01 2.000000E+01 9.360000E-01 3.000000E+01 9.250000E-01 4.000000E+01 9.080000E-01 5.000000E+01 8.810000E-01 6.000000E+01 8.500000E-01 7.000000E+01 8.180000E-01 8.000000E+01 7.840000E-01 9.000000E+01 7.510000E-01 1.000000E+02 7.180000E-01 1.100000E+02 6.850000E-01 1.200000E+02 6.580000E-01 1.300000E+02 6.280000E-01 1.400000E+02 6.030000E-01 1.500000E+02 5.800000E-01 1.600000E+02 5.580000E-01 1.700000E+02 5.380000E-01 1.800000E+02 5.220000E-01 1.900000E+02 5.060000E-01 2.000000E+02 4.900000E-01 2.100000E+02 4.780000E-01 2.200000E+02 4.670000E-01 2.300000E+02 4.570000E-01 2.400000E+02 4.480000E-01 2.500000E+02 4.380000E-01 2.600000E+02 4.310000E-01 2.700000E+02 4.240000E-01 2.800000E+02 4.200000E-01 2.900000E+02 4.140000E-01 3.000000E+02 4.110000E-01 3.100000E+02 4.060000E-01 3.200000E+02 end nl ( y = {b1} + {b2}*exp(-x*{b4}) + {b3}*exp(-x*{b5}) ), /// init(b1 .5 b2 1.5 b3 -1 b4 0.01 b5 0.02) eps(1e-10) assert N == e(N) assert df_r == e(df_r) assert df_m == e(df_m) lrecomp _b[b1] b1 _b[b2] b2 _b[b3] b3 /* */ _b[b4] b4 _b[b5] b5 () /* */ _se[b1] seb1 _se[b2] seb2 _se[b3] seb3 /* */ _se[b4] seb4 _se[b5] seb5 () /* */ e(rmse) rmse e(rss) rss