versioninfo()

using Random

Random.seed!(280) # seed

n, p = 5, 3
X = randn(n, p) # predictor matrix
y = randn(n)    # response vector

# finds the least squares solution
X \ y

using Random, LinearAlgebra

Random.seed!(280) # seed

y = randn(5)    # response vector
X = randn(5, 3) # predictor matrix

X \ y # least squares solution by QR

# same as
qr(X) \ y

cholesky(X'X) \ (X'y) # least squares solution by Cholesky

# QR factorization with column pivoting
xqr = qr(X, Val(true))

xqr \ y # least squares solution

# thin Q matrix multiplication (a sequence of Householder transforms)
norm(xqr.Q * xqr.R - X[:, xqr.p]) # recovers X (with columns permuted)