/* NIST StRD benchmark from http://www.nist.gov/itl/div898/strd/ Nonlinear Regression Difficulty=Lower Exponential k=2 N=14 Observed Dataset Name: Misra1a (Misra1a.dat) Procedure: Nonlinear Least Squares Regression Description: These data are the result of a NIST study regarding dental research in monomolecular adsorption. The response variable is volume, and the predictor variable is pressure. Reference: Misra, D., NIST (1978). Dental Research Monomolecular Adsorption Study. Data: 1 Response Variable (y = volume) 1 Predictor Variable (x = pressure) 14 Observations Lower Level of Difficulty Observed Data Model: Exponential Class 2 Parameters (b1 and b2) y = b1*(1-exp[-b2*x]) + e Starting values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 500 250 2.3894212918E+02 2.7070075241E+00 b2 = 0.0001 0.0005 5.5015643181E-04 7.2668688436E-06 Residual Sum of Squares: 1.2455138894E-01 Residual Standard Deviation: 1.0187876330E-01 Degrees of Freedom: 12 Number of Observations: 14 */ clear scalar N = 14 scalar df_r = 12 scalar df_m = 2 scalar rss = 1.2455138894E-01 scalar rmse = 1.0187876330E-01 scalar b1 = 2.3894212918E+02 scalar seb1 = 2.7070075241E+00 scalar b2 = 5.5015643181E-04 scalar seb2 = 7.2668688436E-06 qui input double (y x) 10.07E0 77.6E0 14.73E0 114.9E0 17.94E0 141.1E0 23.93E0 190.8E0 29.61E0 239.9E0 35.18E0 289.0E0 40.02E0 332.8E0 44.82E0 378.4E0 50.76E0 434.8E0 55.05E0 477.3E0 61.01E0 536.8E0 66.40E0 593.1E0 75.47E0 689.1E0 81.78E0 760.0E0 end nl ( y = {b1}*(1-exp(-{b2}*x)) ), init(b1 500 b2 0.0001) 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 () /* */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 () /* */ e(rmse) rmse e(rss) rss