13.2. Least Squares

The least squares problem \(y = A x + e\).

Computing the least squares (without an intercept term):

> A <- matrix(c(1, 2, -1, 3, -6, 9, -1, 2, 1), nrow=3)
> x <- c(1,2,3)
> y <- A %*% x
> lsfit(A, y, intercept=FALSE)
$coefficients
X1 X2 X3
 1  2  3

$residuals
[1] 0 0 0

$intercept
[1] FALSE

$qr
$qt
[1]  9.797959 16.970563  6.928203

$qr
             X1         X2         X3
[1,] -2.4494897  7.3484692 -0.8164966
[2,]  0.8164966  8.4852814  0.0000000
[3,] -0.4082483 -0.9120956  2.3094011

$qraux
[1] 1.408248 1.409978 2.309401

$rank
[1] 3

$pivot
[1] 1 2 3

$tol
[1] 1e-07

attr(,"class")
[1] "qr"