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___/ / /___/ / /___/ 15.1 Copyright 1985-2017 StataCorp LLC
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Serial number: 15
Licensed to: Kreshna Gopal
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Notes:
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running /home/krg/bin/profile.do ...
Compile number 629
. do ratkow3.do
. /* NIST/ITL StRD
> Dataset Name: Ratkowsky3 (Ratkowsky3.dat)
>
> File Format: ASCII
> Starting Values (lines 41 to 44)
> Certified Values (lines 41 to 49)
> Data (lines 61 to 75)
>
> 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 the dry weight of onion bulbs
> and tops, and the predictor variable is growing time.
>
>
> Reference: Ratkowsky, D.A. (1983).
> Nonlinear Regression Modeling.
> New York, NY: Marcel Dekker, pp. 62 and 88.
>
>
>
>
>
> Data: 1 Response (y = onion bulb dry weight)
> 1 Predictor (x = growing time)
> 15 Observations
> Higher Level of Difficulty
> Observed Data
>
> Model: Exponential Class
> 4 Parameters (b1 to b4)
>
> y = b1 / ((1+exp[b2-b3*x])**(1/b4)) + e
>
>
>
> Starting Values Certified Values
>
> Start 1 Start 2 Parameter Standard Deviation
> b1 = 100 700 6.9964151270E+02 1.6302297817E+01
> b2 = 10 5 5.2771253025E+00 2.0828735829E+00
> b3 = 1 0.75 7.5962938329E-01 1.9566123451E-01
> b4 = 1 1.3 1.2792483859E+00 6.8761936385E-01
>
> Residual Sum of Squares: 8.7864049080E+03
> Residual Standard Deviation: 2.8262414662E+01
> Degrees of Freedom: 9 *** should be 11 ***
> Number of Observations: 15
> */
.
. clear
. program drop _all
.
. scalar N = 15
. scalar df_r = 11
. scalar df_m = 4
.
. scalar rss = 8.7864049080E+03
. scalar rmse = 2.8262414662E+01
.
. scalar b1 = 6.9964151270E+02
. scalar seb1 = 1.6302297817E+01
. scalar b2 = 5.2771253025E+00
. scalar seb2 = 2.0828735829E+00
. scalar b3 = 7.5962938329E-01
. scalar seb3 = 1.9566123451E-01
. scalar b4 = 1.2792483859E+00
. scalar seb4 = 6.8761936385E-01
.
. qui input double(y x)
.
. /* The following starting values led to convergence problems:
>
> nl ( y = {b1} / ( ( 1 + exp( {b2} - {b3}*x ) )^(1/{b4})) ), ///
> init(b1 100 b2 10 b3 1 b4 1)
>
> */
.
. nl ( y = {b1} / ( ( 1 + exp( {b2} - {b3}*x ) )^(1/{b4})) ), ///
> init(b1 700 b2 5 b3 0.75 b4 1.3) eps(1e-10)
(obs = 15)
Iteration 0: residual SS = 8838.785
Iteration 1: residual SS = 8788.805
Iteration 2: residual SS = 8786.424
Iteration 3: residual SS = 8786.406
Iteration 4: residual SS = 8786.405
Iteration 5: residual SS = 8786.405
Iteration 6: residual SS = 8786.405
Iteration 7: residual SS = 8786.405
Iteration 8: residual SS = 8786.405
Iteration 9: residual SS = 8786.405
Iteration 10: residual SS = 8786.405
Source | SS df MS
-------------+---------------------------------- Number of obs = 15
Model | 3755359.3 4 938839.82 R-squared = 0.9977
Residual | 8786.4049 11 798.764083 Adj R-squared = 0.9968
-------------+---------------------------------- Root MSE = 28.26241
Total | 3764145.7 15 250943.046 Res. dev. = 138.1618
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/b1 | 699.6415 16.3023 42.92 0.000 663.7604 735.5226
/b2 | 5.277129 2.082889 2.53 0.028 .6927216 9.861536
/b3 | .7596297 .1956631 3.88 0.003 .3289782 1.190281
/b4 | 1.27925 .6876225 1.86 0.090 -.2341974 2.792697
------------------------------------------------------------------------------
.
. 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 (
> ) /*
> */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 [b3]_se[_cons] seb3 [b4]_se[_cons]
> seb4 () /*
> */ e(rmse) rmse e(rss) rss
[b1]_b[_cons] 7.8
[b2]_b[_cons] 6.2
[b3]_b[_cons] 6.4
[b4]_b[_cons] 6.0
-------------------------
min 6.0
[b1]_se[_cons] 6.4
[b2]_se[_cons] 5.1
[b3]_se[_cons] 5.0
[b4]_se[_cons] 5.3
-------------------------
min 5.0
e(rmse) 11.0
e(rss) 11.4
.
.
end of do-file