/* NIST/ITL StRD Dataset Name: Lanczos2 (Lanczos2.dat) File Format: ASCII Starting Values (lines 41 to 46) Certified Values (lines 41 to 51) Data (lines 61 to 84) Procedure: Nonlinear Least Squares Regression Description: These data are taken from an example discussed in Lanczos (1956). The data were generated to 6-digits of accuracy using f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x) + 1.5576*exp(-5*x). Reference: Lanczos, C. (1956). Applied Analysis. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280. Data: 1 Response (y) 1 Predictor (x) 24 Observations Average Level of Difficulty Generated Data Model: Exponential Class 6 Parameters (b1 to b6) y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e Starting values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 1.2 0.5 9.6251029939E-02 6.6770575477E-04 b2 = 0.3 0.7 1.0057332849E+00 3.3989646176E-03 b3 = 5.6 3.6 8.6424689056E-01 1.7185846685E-03 b4 = 5.5 4.2 3.0078283915E+00 4.1707005856E-03 b5 = 6.5 4 1.5529016879E+00 2.3744381417E-03 b6 = 7.6 6.3 5.0028798100E+00 1.3958787284E-03 Residual Sum of Squares: 2.2299428125E-11 Residual Standard Deviation: 1.1130395851E-06 Degrees of Freedom: 18 Number of Observations: 24 */ clear scalar N = 24 scalar df_r = 18 scalar df_m = 6 scalar rss = 2.2299428125E-11 scalar rmse = 1.1130395851E-06 scalar b1 = 9.6251029939E-02 scalar seb1 = 6.6770575477E-04 scalar b2 = 1.0057332849E+00 scalar seb2 = 3.3989646176E-03 scalar b3 = 8.6424689056E-01 scalar seb3 = 1.7185846685E-03 scalar b4 = 3.0078283915E+00 scalar seb4 = 4.1707005856E-03 scalar b5 = 1.5529016879E+00 scalar seb5 = 2.3744381417E-03 scalar b6 = 5.0028798100E+00 scalar seb6 = 1.3958787284E-03 qui input double(y x) 2.51340E+00 0.00000E+00 2.04433E+00 5.00000E-02 1.66840E+00 1.00000E-01 1.36642E+00 1.50000E-01 1.12323E+00 2.00000E-01 9.26890E-01 2.50000E-01 7.67934E-01 3.00000E-01 6.38878E-01 3.50000E-01 5.33784E-01 4.00000E-01 4.47936E-01 4.50000E-01 3.77585E-01 5.00000E-01 3.19739E-01 5.50000E-01 2.72013E-01 6.00000E-01 2.32497E-01 6.50000E-01 1.99659E-01 7.00000E-01 1.72270E-01 7.50000E-01 1.49341E-01 8.00000E-01 1.30070E-01 8.50000E-01 1.13812E-01 9.00000E-01 1.00042E-01 9.50000E-01 8.83321E-02 1.00000E+00 7.83354E-02 1.05000E+00 6.97669E-02 1.10000E+00 6.23931E-02 1.15000E+00 end nl ( y = {b1}*exp(-{b2}*x) + {b3}*exp(-{b4}*x) + {b5}*exp(-{b6}*x) ), /// init(b1 1.2 b2 0.3 b3 5.6 b4 5.5 b5 6.5 b6 7.6) 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 /* */ [b4]_b[_cons] b4 [b5]_b[_cons] b5 [b6]_b[_cons] b6 () /* */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 /* */ [b4]_se[_cons] seb4 [b5]_se[_cons] seb5 [b6]_se[_cons] seb6 () /* */ e(rmse) rmse e(rss) rss