st: equations-solution

 From "Andreas Aschbacher" To statalist@hsphsun2.harvard.edu Subject st: equations-solution Date Tue, 30 Mar 2004 10:16:12 +0200 (MEST)

dear fellows !

maybe the following /I am sure that it is/ is useful for someone :
for version 8
I do:
clear
set obs 3
input y
1. 1
2. 0
3. 0
then I type do faq:

. capture program drop nlfaq

. program nlfaq
1.    if "`1'" == "?" {
2.       global S_1 " A B C"
3.       global A=1
4.       global B=1
5.       global C=1
6.       exit
7.    }
8.    tempvar yh
9.    gen `yh'= exp(\$A) + \$B * \$C + cos(\$B)+ tan(\$B) - 2 in 1
10.    replace `yh'= \$A/\$B +\$C^2-log(\$B) in 2
11.    replace `yh'= \$A/(\$A+\$B+\$C)- sin(\$C) in 3
12.    replace `1' = `yh'
13.
. end

. nl faq y
(obs = 3)

Iteration 0:  residual SS =  12.18801
Iteration 1:  residual SS =  .5363988
Iteration 2:  residual SS =  .0919842
Iteration 3:  residual SS =  .0185061
Iteration 4:  residual SS =   .016263
Iteration 5:  residual SS =  .0000506
Iteration 6:  residual SS =  7.04e-06
Iteration 7:  residual SS =  3.92e-06
Iteration 8:  residual SS =  3.07e-06
Iteration 9:  residual SS =  3.84e-10
Iteration 10:  residual SS =  2.26e-10
Iteration 11:  residual SS =  3.20e-14

Source |       SS       df       MS            Number of obs =
3
-------------+------------------------------         F(  3,     0) =
.
Model |           1     3  .333333333         Prob > F      =
.
Residual |  1.4211e-14     0           .         R-squared     =
1.0000
.
Total |           1     3  .333333333         Root MSE      =
.
Res. dev.     =
-90.43652
(faq)
------------------------------------------------------------------------------
y |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
A |  -.0212359          .        .       .            .
.
B |    .978015          .        .       .            .
.
C |  -.0227374          .        .       .            .
.
------------------------------------------------------------------------------
(SEs, P values, CIs, and correlations are asymptotic approximations)

. di \$A/\$B +\$C^2,log(\$B)
-.02223023 -.02223023

. di \$A/(\$A+\$B+\$C),sin(\$C)
-.02273546 -.02273546

. di "                " exp(\$A) + \$B*\$C,3-cos(\$B)-tan(\$B)
.95675048 .95675034

as a solution of :
A/B + C^2 = log(B)
A/(A+B +C) = sin(C)
exp(A) + B*C = 3 - cos(B) -tan(B)

andreas aschbacher

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