[R] Finding solution

[peter dalgaard]

On Oct 9, 2011, at 14:02 , Bogaso Christofer wrote:

> Dear all, I have a system of simultaneous equations with 2 unknowns as
> follows:
> 
> 
> 
> x*y + (1-x) = 0.05
> 
> x*(y - .5)^2 + (1-x)*0.6 = 0.56^2
> 
> 
> 
> Ofcourse I can do it manually however wondering whether there is any direct
> way in R available to get the solution of this system?


Not really (can't vouch for all 3000+ packages, though...)

You can sometimes get away with converting  to a minimization problem:

> f <- function(xy,x=xy[1],y=xy[2])(x*y + (1-x) - 0.05)^2+(x*(y - .5)^2 + (1-x)*0.6 - 0.56^2)^2
> optim(par=c(0,0),f,method="BFGS")$par
[1]  0.91674574 -0.03627402

$value
[1] 5.351777e-13

$counts
function gradient 
     39       13 

$convergence
[1] 0

$message
NULL


Notice that there is some risk of falling into a local minimum which has nothing to do with the solution. Always check that the minimum actually comes out as zero.


> 
> 
> 
> Thanks and regards,
> 
> 
> 
> 
> 	[[alternative HTML version deleted]]
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com