topic Re: QR Decomposition in Intel® oneAPI Math Kernel Library

QR Decomposition

JohnNichols — Wed, 25 Oct 2023 17:03:20 GMT

If I use the QR decomposition to solve a multiple regression equation say

Y = A + BX + CZ

And I get values on B and C and A,

I cannot see how I get the error estimates on B,C and A. I could go back and zero out the BX by adjusting y and then do a linear regression on the data to get an A estimate and so on, but is there a better way.

Re:QR Decomposition

VarshaS_Intel — Fri, 27 Oct 2023 12:14:59 GMT

Hi,

Thanks for posting in Intel Communities.

Could you please get back to us with the Intel product details, the MKL version being used and the MKL routines being used?

And also, could you please elaborate on your issue, so that it helps us in understand the issue better?

Thanks & Regards,

Varsha

Re: QR Decomposition

mecej4 — Tue, 31 Oct 2023 14:16:19 GMT

See Example 2 in the IMSL C library manual page for the routine imsl_f_nonlin_least_squares(). The underlying theory is covered in Ratkowsky's book Nonlinear Regression Modelling.

I do not have ready-to-use Fortran or C implementations, but you can assemble one using routines from MKL.

Once you have the QR factorization, note that J^T J = R^T R, so you can use R to compute the variance-covariance matrix. Using that together with the Student-t value for 0.95 confidence and d.o.f. = number of data sets - number of regression coefficients, you can compute the confidence intervals for the regression coefficients, as shown in Example 2 of the IMSL manual that I mentioned above.

Re: QR Decomposition

VarshaS_Intel — Tue, 07 Nov 2023 16:24:32 GMT

Hi,

We have not heard back from you. From the solution provided by the black belt user "mecej4", could you please let us know if you have any other queries?

Thanks & Regards,

Varsha

Re:QR Decomposition

VarshaS_Intel — Wed, 15 Nov 2023 13:07:13 GMT

Hi,

We have not heard back from you. Could you please provide us with an update on your issue?

Thanks & Regards,

Varsha