QR Decomposition

[JohnNichols]

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. 

[VarshaS_Intel]

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

[mecej4]

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.

[VarshaS_Intel]

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

[VarshaS_Intel]

Hi,

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

Thanks & Regards,

Varsha