[R] least squares solution to linear system

[Berend Hasselman]

On 04-02-2012, at 19:14, Alaios wrote:

> Dear all
> I am having a linear system of the form
> A*X=B and I want to find the X by using least squares.
> For example my A is of dimension [205,3] and my B is of dimension[205,1]
> 
>  I am looking for the X matrix which is of the size [3,1]. In the matlab I was doing that by the function
> 
> 
>  X = LSCOV(A,B) returns the ordinary least squares solution to the
>     linear system of equations A*X = B, i.e., X is the N-by-1 vector that
>     minimizes the sum of squared errors (B - A*X)'*(B - A*X), where A is
>     M-by-N, and B is M-by-1
> 
> 
> for example for the matrices
> 
> A =
> 
>      1     2     3
>      4     5     6
>      7     8     9
> 
> K>> B=[1 2 3]
> 
> B =
> 
>      1     2     3
> 
> 
>>> lscov(A,B')
> 
> ans =
> 
>    -0.0000
>          0
>     0.3333
> 
> How I can get the same in R? I know about the lm function but it looks complicated to me how to insert formula and how to get exactly back only what I need

?qr

Example:

A <- matrix(runif(15),5)
b <- 1:5

solve(qr(A, LAPACK=TRUE), b)

or

lm(b ~ 0 + A)

Berend