/* NIST/ITL StRD Dataset Name: Ratkowsky2 (Ratkowsky2.dat) File Format: ASCII Starting Values (lines 41 to 43) Certified Values (lines 41 to 48) Data (lines 61 to 69) Procedure: Nonlinear Least Squares Regression Description: This model and data are an example of fitting sigmoidal growth curves taken from Ratkowsky (1983). The response variable is pasture yield, and the predictor variable is growing time. Reference: Ratkowsky, D.A. (1983). Nonlinear Regression Modeling. New York, NY: Marcel Dekker, pp. 61 and 88. Data: 1 Response (y = pasture yield) 1 Predictor (x = growing time) 9 Observations Higher Level of Difficulty Observed Data Model: Exponential Class 3 Parameters (b1 to b3) y = b1 / (1+exp[b2-b3*x]) + e Starting Values Certified Values Start 1 Start 2 Parameter Standard Deviation b1 = 100 75 7.2462237576E+01 1.7340283401E+00 b2 = 1 2.5 2.6180768402E+00 8.8295217536E-02 b3 = 0.1 0.07 6.7359200066E-02 3.4465663377E-03 Residual Sum of Squares: 8.0565229338E+00 Residual Standard Deviation: 1.1587725499E+00 Degrees of Freedom: 6 Number of Observations: 9 */ clear scalar N = 9 scalar df_r = 6 scalar df_m = 3 scalar rss = 8.0565229338E+00 scalar rmse = 1.1587725499E+00 scalar b1 = 7.2462237576E+01 scalar seb1 = 1.7340283401E+00 scalar b2 = 2.6180768402E+00 scalar seb2 = 8.8295217536E-02 scalar b3 = 6.7359200066E-02 scalar seb3 = 3.4465663377E-03 qui input double(y x) 8.930E0 9.000E0 10.800E0 14.000E0 18.590E0 21.000E0 22.330E0 28.000E0 39.350E0 42.000E0 56.110E0 57.000E0 61.730E0 63.000E0 64.620E0 70.000E0 67.080E0 79.000E0 end nl ( y = {b1} / (1+exp({b2}-{b3}*x)) ), init(b1 100 b2 1 b3 0.1) 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