/* NIST/ITL StRD Dataset Name: Thurber (Thurber.dat) File Format: ASCII Starting Values (lines 41 to 47) Certified Values (lines 41 to 52) Data (lines 61 to 97) Procedure: Nonlinear Least Squares Regression Description: These data are the result of a NIST study involving semiconductor electron mobility. The response variable is a measure of electron mobility, and the predictor variable is the natural log of the density. Reference: Thurber, R., NIST (197?). Semiconductor electron mobility modeling. Data: 1 Response Variable (y = electron mobility) 1 Predictor Variable (x = log[density]) 37 Observations Higher Level of Difficulty Observed Data Model: Rational Class (cubic/cubic) 7 Parameters (b1 to b7) y = (b1 + b2*x + b3*x**2 + b4*x**3) / (1 + b5*x + b6*x**2 + b7*x**3) + e Starting Values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 1000 1300 1.2881396800E+03 4.6647963344E+00 b2 = 1000 1500 1.4910792535E+03 3.9571156086E+01 b3 = 400 500 5.8323836877E+02 2.8698696102E+01 b4 = 40 75 7.5416644291E+01 5.5675370270E+00 b5 = 0.7 1 9.6629502864E-01 3.1333340687E-02 b6 = 0.3 0.4 3.9797285797E-01 1.4984928198E-02 b7 = 0.03 0.05 4.9727297349E-02 6.5842344623E-03 Residual Sum of Squares: 5.6427082397E+03 Residual Standard Deviation: 1.3714600784E+01 Degrees of Freedom: 30 Number of Observations: 37 */ clear scalar N = 37 scalar df_r = 30 scalar df_m = 7 scalar rss = 5.6427082397E+03 scalar rmse = 1.3714600784E+01 scalar b1 = 1.2881396800E+03 scalar seb1 = 4.6647963344E+00 scalar b2 = 1.4910792535E+03 scalar seb2 = 3.9571156086E+01 scalar b3 = 5.8323836877E+02 scalar seb3 = 2.8698696102E+01 scalar b4 = 7.5416644291E+01 scalar seb4 = 5.5675370270E+00 scalar b5 = 9.6629502864E-01 scalar seb5 = 3.1333340687E-02 scalar b6 = 3.9797285797E-01 scalar seb6 = 1.4984928198E-02 scalar b7 = 4.9727297349E-02 scalar seb7 = 6.5842344623E-03 qui input double(y x) 80.574E0 -3.067E0 84.248E0 -2.981E0 87.264E0 -2.921E0 87.195E0 -2.912E0 89.076E0 -2.840E0 89.608E0 -2.797E0 89.868E0 -2.702E0 90.101E0 -2.699E0 92.405E0 -2.633E0 95.854E0 -2.481E0 100.696E0 -2.363E0 101.060E0 -2.322E0 401.672E0 -1.501E0 390.724E0 -1.460E0 567.534E0 -1.274E0 635.316E0 -1.212E0 733.054E0 -1.100E0 759.087E0 -1.046E0 894.206E0 -0.915E0 990.785E0 -0.714E0 1090.109E0 -0.566E0 1080.914E0 -0.545E0 1122.643E0 -0.400E0 1178.351E0 -0.309E0 1260.531E0 -0.109E0 1273.514E0 -0.103E0 1288.339E0 0.010E0 1327.543E0 0.119E0 1353.863E0 0.377E0 1414.509E0 0.790E0 1425.208E0 0.963E0 1421.384E0 1.006E0 1442.962E0 1.115E0 1464.350E0 1.572E0 1468.705E0 1.841E0 1447.894E0 2.047E0 1457.628E0 2.200E0 end #delimit ; nl ( y = ({b1} + {b2}*x + {b3}*x^2 + {b4}*x^3) / (1 + {b5}*x + {b6}*x^2 + {b7}*x^3) ), init(b1 1000 b2 1000 b3 400 b4 40 b5 0.7 b6 0.3 b7 0.03) eps(1e-10) ; #delimit cr 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 [b7]_b[_cons] b7 () /* */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 [b4]_se[_cons] seb4 /* */ [b5]_se[_cons] seb5 [b6]_se[_cons] seb6 [b7]_se[_cons] seb7 () /* */ e(rmse) rmse e(rss) rss