/* NIST/ITL StRD Dataset Name: MGH10 (MGH10.dat) File Format: ASCII Starting Values (lines 41 to 43) Certified Values (lines 41 to 48) Data (lines 61 to 76) 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: Meyer, R. R. (1970). Theoretical and computational aspects of nonlinear regression. In Nonlinear Programming, Rosen, Mangasarian and Ritter (Eds). New York, NY: Academic Press, pp. 465-486. Data: 1 Response (y) 1 Predictor (x) 16 Observations Higher Level of Difficulty Generated Data Model: Exponential Class 3 Parameters (b1 to b3) y = b1 * exp[b2/(x+b3)] + e Starting values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 2 0.02 5.6096364710E-03 1.5687892471E-04 b2 = 400000 4000 6.1813463463E+03 2.3309021107E+01 b3 = 25000 250 3.4522363462E+02 7.8486103508E-01 Residual Sum of Squares: 8.7945855171E+01 Residual Standard Deviation: 2.6009740065E+00 Degrees of Freedom: 13 Number of Observations: 16 */ clear scalar N = 16 scalar df_r = 13 scalar df_m = 3 scalar rss = 8.7945855171E+01 scalar rmse = 2.6009740065E+00 scalar b1 = 5.6096364710E-03 scalar seb1 = 1.5687892471E-04 scalar b2 = 6.1813463463E+03 scalar seb2 = 2.3309021107E+01 scalar b3 = 3.4522363462E+02 scalar seb3 = 7.8486103508E-01 qui input double(y x) 3.478000E+04 5.000000E+01 2.861000E+04 5.500000E+01 2.365000E+04 6.000000E+01 1.963000E+04 6.500000E+01 1.637000E+04 7.000000E+01 1.372000E+04 7.500000E+01 1.154000E+04 8.000000E+01 9.744000E+03 8.500000E+01 8.261000E+03 9.000000E+01 7.030000E+03 9.500000E+01 6.005000E+03 1.000000E+02 5.147000E+03 1.050000E+02 4.427000E+03 1.100000E+02 3.820000E+03 1.150000E+02 3.307000E+03 1.200000E+02 2.872000E+03 1.250000E+02 end /* The following starting values led to convergence problems: nl ( y = {b1} * exp({b2}/(x+{b3})) ), init(b1 2 b2 400000 b3 25000) eps(1e-10) */ nl ( y = {b1} * exp({b2}/(x+{b3})) ), init(b1 0.02 b2 4000 b3 250) eps(1e-10) 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 () /* */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 () /* */ e(rmse) rmse e(rss) rss