/* NIST/ITL StRD Dataset Name: MGH09 (MGH09.dat) File Format: ASCII Starting Values (lines 41 to 44) Certified Values (lines 41 to 49) Data (lines 61 to 71) Procedure: Nonlinear Least Squares Regression Description: This problem was found to be difficult for some very good algorithms. There is a local minimum at (+inf, -14.07..., -inf, -inf) with final sum of squares 0.00102734.... 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: Kowalik, J.S., and M. R. Osborne, (1978). Methods for Unconstrained Optimization Problems. New York, NY: Elsevier North-Holland. Data: 1 Response (y) 1 Predictor (x) 11 Observations Higher Level of Difficulty Generated Data Model: Rational Class (linear/quadratic) 4 Parameters (b1 to b4) y = b1*(x**2+x*b2) / (x**2+x*b3+b4) + e Starting values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 25 0.25 1.9280693458E-01 1.1435312227E-02 b2 = 39 0.39 1.9128232873E-01 1.9633220911E-01 b3 = 41.5 0.415 1.2305650693E-01 8.0842031232E-02 b4 = 39 0.39 1.3606233068E-01 9.0025542308E-02 Residual Sum of Squares: 3.0750560385E-04 Residual Standard Deviation: 6.6279236551E-03 Degrees of Freedom: 7 Number of Observations: 11 */ clear scalar N = 11 scalar df_r = 7 scalar df_m = 4 scalar rss = 3.0750560385E-04 scalar rmse = 6.6279236551E-03 scalar b1 = 1.9280693458E-01 scalar seb1 = 1.1435312227E-02 scalar b2 = 1.9128232873E-01 scalar seb2 = 1.9633220911E-01 scalar b3 = 1.2305650693E-01 scalar seb3 = 8.0842031232E-02 scalar b4 = 1.3606233068E-01 scalar seb4 = 9.0025542308E-02 qui input double(y x) 1.957000E-01 4.000000E+00 1.947000E-01 2.000000E+00 1.735000E-01 1.000000E+00 1.600000E-01 5.000000E-01 8.440000E-02 2.500000E-01 6.270000E-02 1.670000E-01 4.560000E-02 1.250000E-01 3.420000E-02 1.000000E-01 3.230000E-02 8.330000E-02 2.350000E-02 7.140000E-02 2.460000E-02 6.250000E-02 end /* The following starting values led to convergence problems: nl ( y = {b1}*(x^2 + x*{b2}) / (x^2 + x*{b3} + {b4}) ), /// init(b1 25 b2 39 b3 41.5 b4 39) */ nl ( y = {b1}*(x^2 + x*{b2}) / (x^2 + x*{b3} + {b4}) ), /// init(b1 0.25 b2 0.39 b3 0.415 b4 0.39) 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 () /* */ _se[b1] seb1 _se[b2] seb2 _se[b3] seb3 _se[b4] seb4 () /* */ e(rmse) rmse e(rss) rss