/* NIST StRD benchmark from http://www.nist.gov/itl/div898/strd/ Nonlinear Regression Difficulty=Lower Miscellaneous k=2 N=6 Observed Dataset Name: DanielWood (DanielWood.dat) Procedure: Nonlinear Least Squares Regression Description: These data and model are described in Daniel and Wood (1980), and originally published in E.S.Keeping, "Introduction to Statistical Inference," Van Nostrand Company, Princeton, NJ, 1962, p. 354. The response variable is energy radieted from a carbon filament lamp per cm**2 per second, and the predictor variable is the absolute temperature of the filament in 1000 degrees Kelvin. Reference: Daniel, C. and F. S. Wood (1980). Fitting Equations to Data, Second Edition. New York, NY: John Wiley and Sons, pp. 428-431. Data: 1 Response Variable (y = energy) 1 Predictor Variable (x = temperature) 6 Observations Lower Level of Difficulty Observed Data Model: Miscellaneous Class 2 Parameters (b1 and b2) y = b1*x**b2 + e Starting values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 1 0.7 7.6886226176E-01 1.8281973860E-02 b2 = 5 4 3.8604055871E+00 5.1726610913E-02 Residual Sum of Squares: 4.3173084083E-03 Residual Standard Deviation: 3.2853114039E-02 Degrees of Freedom: 4 Number of Observations: 6 */ clear scalar N = 6 scalar df_r = 4 scalar df_m = 2 scalar rss = 4.3173084083E-03 scalar rmse = 3.2853114039E-02 scalar b1 = 7.6886226176E-01 scalar seb1 = 1.8281973860E-02 scalar b2 = 3.8604055871E+00 scalar seb2 = 5.1726610913E-02 qui input double (y x) 2.138E0 1.309E0 3.421E0 1.471E0 3.597E0 1.490E0 4.340E0 1.565E0 4.882E0 1.611E0 5.660E0 1.680E0 end nl ( y = {b1}*x^{b2} ), init(b1 1 b2 5) 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 () /* */ _se[b1] seb1 _se[b2] seb2 () /* */ e(rmse) rmse e(rss) rss