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Notes:
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running /home/bpp/bin/profile.do ...
. do ratkow2.do
. /* 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)
.
. nl ( y = {b1} / (1+exp({b2}-{b3}*x)) ), init(b1 100 b2 1 b3 0.1) eps(1e-10)
(obs = 9)
Iteration 0: residual SS = 6184.434
Iteration 1: residual SS = 6178.702
Iteration 2: residual SS = 6175.971
Iteration 3: residual SS = 6167.185
Iteration 4: residual SS = 6164.692
Iteration 5: residual SS = 6142.645
Iteration 6: residual SS = 6111.21
Iteration 7: residual SS = 6028.496
Iteration 8: residual SS = 5985.768
Iteration 9: residual SS = 4696.54
Iteration 10: residual SS = 1943.7
Iteration 11: residual SS = 1210.456
Iteration 12: residual SS = 10.19422
Iteration 13: residual SS = 8.056614
Iteration 14: residual SS = 8.056523
Iteration 15: residual SS = 8.056523
Iteration 16: residual SS = 8.056523
Iteration 17: residual SS = 8.056523
Iteration 18: residual SS = 8.056523
Iteration 19: residual SS = 8.056523
Source | SS df MS
-------------+------------------------------ Number of obs = 9
Model | 18215.3637 3 6071.78789 R-squared = 0.9996
Residual | 8.05652293 6 1.34275382 Adj R-squared = 0.9993
-------------+------------------------------ Root MSE = 1.158773
Total | 18223.4202 9 2024.82447 Res. dev. = 24.54421
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/b1 | 72.46224 1.734027 41.79 0.000 68.21923 76.70525
/b2 | 2.618077 .0882953 29.65 0.000 2.402026 2.834128
/b3 | .0673592 .0034466 19.54 0.000 .0589258 .0757926
------------------------------------------------------------------------------
.
. 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
[b1]_b[_cons] 8.0
[b2]_b[_cons] 7.8
[b3]_b[_cons] 7.6
-------------------------
min 7.6
[b1]_se[_cons] 6.2
[b2]_se[_cons] 6.0
[b3]_se[_cons] 6.3
-------------------------
min 6.0
e(rmse) 10.4
e(rss) 11.8
.
.
end of do-file