QR and Cholesky decomposition

Question

A while ago I asked for help to develop a polynomial regression model using least squares, where the system was solved by cholesky decomposition, you can check it here Cholesky Polynomial Regression

Now I need to solve the same problem using rather than Cholesky Decomposition the QR decomposition. To save the work of remaking from scratch, I'll just change the parts that change from one procedure to another, then my doubts are

i) The least squares solution obtained through cholesky decomposition and QR decomposition are similar? I ask this because if they are pretty similar I would save a lot of work, making the graphics of various degree polynomials.

ii)The condition number in $A=QR$ decomposition is obtained from $R$ matriz right?

Thanks in advance

Answer 1

For Q the condition number cond(Q) = 1 since it is orthogonal, this is true for all orthogonal matrices so indeed the cond(A) = cond(QR) = cond(R).

I'm not sure I can answer the other parts of your question however, I hope this helps.