R help - Apr 2004 - Solving linear equations

Is there a simple method under R to solve an overdetermined system of linear 
equations Ax=b with A being a matrix m*n? I know that solve() seems to work 
for m*m matrices, but I had no luck with overdetermined systems.

Mlod

On Tue, 27 Apr 2004 23:02:37 +0000, "Tomek R" <rtomek at
hotmail.com>
wrote:
>Is there a simple method under R to solve an overdetermined system of linear
>equations Ax=b with A being a matrix m*n? I know that solve() seems to work 
>for m*m matrices, but I had no luck with overdetermined systems.
Isn't that just a linear regression problem?  You can get x as

lm.fit(A, b)$coefficients

or go lower level and use 

qr.coef(qr(A), b)

Duncan Murdoch

How do you wish to decide how to resolve the likely 
inconsistencies in the overdetermined system?  If you assume the 
vertical deviations from a linear fit are normally distributed with 
constant variance, then "lm" should do what you want. 

      hope this helps.  spencer graves

Tomek R wrote:
> Is there a simple method under R to solve an overdetermined system of 
> linear equations Ax=b with A being a matrix m*n? I know that solve() 
> seems to work for m*m matrices, but I had no luck with overdetermined 
> systems.
>
> Mlod
>
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lm.fit(A, b)$coefficients seems to do what I want, but, as you have rightly 
pointed out, the deviations most probably will not have constant variance 
(but should be normally distributed).  Basically, I make measurements from 
which I obtain the vector b with variance in each of the values v.  How 
would I fit my data then? (A is known and fixed). What's the best book to 
look at for solving those problems?

Thanks,

Tomek

>      How do you wish to decide how to resolve the likely inconsistencies 
>in the overdetermined system?  If you assume the vertical deviations from a 
>linear fit are normally distributed with constant variance, then 
>"lm" should do what you want.
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