How accurate the solution of over-determined linear system of equation could be using least square method?

Question

I have read the theory of least square method. It is used to minimize the Frobenius norm of equation residual vector. but I searched the internet and I did not find how to determine the actual value of $||A\times x-b||_F$ during QR or SVD factorization. There must be some internal quality of matrix $A$ determines how accurate the solution could be.