How about I make a design matrix as follows:

1  d1,1  0   0     0   0     0   0   0
0    0   1   d1,2  0   0     0   0   0
0    0   0   0     1   d1,3  0   0   0
...
...

0    0    0  0     0   0  ...  ... 1  d1,12


The above matrix will work for the 1st row of Y data;

d1, 1 means the 1st column of the 1st row of data;
d1, 12 means the 12th column of the 1st row of data.


But now since I have N samples(rows) of Y data; how do I conceptually do a
3D design matrix?

On 11/15/06, John Fox <jfox@mcmaster.ca> wrote:
>
> Dear Michael,
>
> > -----Original Message-----
> > From: Michael [mailto:comtech.usa@gmail.com]
> > Sent: Wednesday, November 15, 2006 2:40 PM
> > To: John Fox
> > Cc: R-help@stat.math.ethz.ch
> > Subject: Re: [R] how to create this design matrix?
> >
> > There are 12 response variables, columns 1 to 12 are response
> > variables, i.e., these are y's, they all regress to the 13th
> > column, which is the predictor, i.e. the X.
> >
>
> Right.
>
> > Let's take column 1, call this Y1, and there are n rows(n
> > samples) of it,
> >
> > I need Y1= b0_1 + b1_1* X + epsilon, where X is the 13th column
> >
> > Similarly, for column 1 to column 12, we do the above,
> >
> > Y12= b0_12 + b1_12 * X + epsilon, where Y12 is the 12th column,
> >
> > they all have different b0's and b1's.
>
> Right.
>
> > Totally there are 24 b0's and b1's.
> >
>
> Yes.
>
> > I want a group regression, not separated regression...
> >
>
> I'm not sure what you mean by a "group regression" rather than "separated
> regressions." The multivarite linear regression that I suggested will give
> you 12 slopes and 12 intercepts. They are exactly what you'd get from 12
> individual least-squares regression of each Y on X, but the multivariate
> regression can also give you, e.g., the covariances among all of the
> coefficients (if you want them).
>
> John
>
> > Thanks
> >
> >
> >
> >
> > On 11/15/06, John Fox < jfox@mcmaster.ca> wrote:
> >
> >       Dear Michael,
> >
> >       This looks like a multivariate simple regression --
> > that is, 12 response
> >       variables, one predictor. If the data are in the matrix
> > X, then lm(X[,1:12]
> >       ~ X[,13]) should do the trick.
> >
> >       I hope this helps,
> >       John
> >
> >       --------------------------------
> >       John Fox
> >       Department of Sociology
> >       McMaster University
> >       Hamilton, Ontario
> >       Canada L8S 4M4
> >       905-525-9140x23604
> >       http://socserv.mcmaster.ca/jfox
> >       --------------------------------
> >
> >       > -----Original Message-----
> >       > From: r-help-bounces@stat.math.ethz.ch
> >       > [mailto: r-help-bounces@stat.math.ethz.ch
> > <mailto:r-help-bounces@stat.math.ethz.ch> ] On Behalf Of Michael
> >       > Sent: Wednesday, November 15, 2006 12:23 AM
> >       > To: R-help@stat.math.ethz.ch
> >       > Subject: [R] how to create this design matrix?
> >       >
> >       > Hi all,
> >       >
> >       > I have a multiple-linear regression problem.
> >       >
> >       > There are 13 columns of data, the whole data matrix is:  n x
> >       > 13, where n is the number of samples.
> >       >
> >       > Now I want to regress  EACH of the first 12 columns onto the
> >       > 13th column, with 2-parameter linear model  y_i = b0 + b1 *
> >       > x_i, where i goes from 1 to n, and b0 is the intercept.
> >       >
> >       > How do I create a design matrix to do the 12-column
> >       > regression collectively all at once using multiple
> > linear regressions?
> >       >
> >       > Thanks a lot
> >       >
> >       >       [[alternative HTML version deleted]]
> >       >
> >       > ______________________________________________
> >       > R-help@stat.math.ethz.ch mailing list
> >       > https://stat.ethz.ch/mailman/listinfo/r-help
> >       > PLEASE do read the posting guide
> >       > http://www.R-project.org/posting-guide.html
> > < http://www.R-project.org/posting-guide.html>
> >       > and provide commented, minimal, self-contained,
> > reproducible code.
> >
> >
> >
> >
> >
>
>

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