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running /home/bpp/bin/profile.do ...
. do boxbod.do
. /* NIST/ITL StRD
> Dataset Name: BoxBOD (BoxBOD.dat)
>
> File Format: ASCII
> Starting Values (lines 41 to 42)
> Certified Values (lines 41 to 47)
> Data (lines 61 to 66)
>
> Procedure: Nonlinear Least Squares Regression
>
> Description: These data are described in detail in Box, Hunter and
> Hunter (1978). The response variable is biochemical
> oxygen demand (BOD) in mg/l, and the predictor
> variable is incubation time in days.
>
>
> Reference: Box, G. P., W. G. Hunter, and J. S. Hunter (1978).
> Statistics for Experimenters.
> New York, NY: Wiley, pp. 483-487.
>
>
>
>
>
> Data: 1 Response (y = biochemical oxygen demand)
> 1 Predictor (x = incubation time)
> 6 Observations
> Higher Level of Difficulty
> Observed Data
>
> Model: Exponential Class
> 2 Parameters (b1 and b2)
>
> y = b1*(1-exp[-b2*x]) + e
>
>
>
> Starting values Certified Values
>
> Start 1 Start 2 Parameter Standard Deviation
> b1 = 1 100 2.1380940889E+02 1.2354515176E+01
> b2 = 1 0.75 5.4723748542E-01 1.0455993237E-01
>
> Residual Sum of Squares: 1.1680088766E+03
> Residual Standard Deviation: 1.7088072423E+01
> Degrees of Freedom: 4
> Number of Observations: 6
> */
.
. clear
.
. scalar N = 6
. scalar df_r = 4
. scalar df_m = 2
.
. scalar rss = 1.1680088766E+03
. scalar rmse = 1.7088072423E+01
.
. scalar b1 = 2.1380940889E+02
. scalar seb1 = 1.2354515176E+01
. scalar b2 = 5.4723748542E-01
. scalar seb2 = 1.0455993237E-01
.
. qui input double(y x)
.
. nl ( y = {b1}*(1-exp(-{b2}*x)) ), init(b1 1 b2 1) eps(1e-10)
(obs = 6)
Iteration 0: residual SS = 184700
Iteration 1: residual SS = 13388.66
Iteration 2: residual SS = 7327.64
Iteration 3: residual SS = 2375.331
Iteration 4: residual SS = 1388.389
Iteration 5: residual SS = 1168.01
Iteration 6: residual SS = 1168.009
Iteration 7: residual SS = 1168.009
Iteration 8: residual SS = 1168.009
Iteration 9: residual SS = 1168.009
Iteration 10: residual SS = 1168.009
Iteration 11: residual SS = 1168.009
Iteration 12: residual SS = 1168.009
Iteration 13: residual SS = 1168.009
Iteration 14: residual SS = 1168.009
Iteration 15: residual SS = 1168.009
Source | SS df MS
-------------+------------------------------ Number of obs = 6
Model | 187140.991 2 93570.4956 R-squared = 0.9938
Residual | 1168.00888 4 292.002219 Adj R-squared = 0.9907
-------------+------------------------------ Root MSE = 17.08807
Total | 188309 6 31384.8333 Res. dev. = 48.65504
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/b1 | 213.8094 12.35451 17.31 0.000 179.5078 248.111
/b2 | .5472375 .10456 5.23 0.006 .2569325 .8375425
------------------------------------------------------------------------------
.
. 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 () /*
> */ [b1]_se[_cons] seb1 [b2]_se[_cons] seb2 () /*
> */ e(rmse) rmse e(rss) rss
[b1]_b[_cons] 7.9
[b2]_b[_cons] 7.3
-------------------------
min 7.3
[b1]_se[_cons] 6.8
[b2]_se[_cons] 6.7
-------------------------
min 6.7
e(rmse) 11.1
e(rss) 10.4
.
.
end of do-file