MATLAB Central Newsreader - linear regression

linear regression

fas — Fri, 16 May 2008 13:19:53 -0400

Hi
I want to do linear regression
X_vec=a*Y_vec + b
.
.
.

where X_vec(1....100) and Y_vec (1..100) are vectors (say of size
100). So I have an overdetermined system where each vector value gives
me one equation and I want to determine 'a' and 'b' after regression.
I am bit novice any help?

Re: linear regression

Steven Lord — Fri, 16 May 2008 13:28:29 -0400

"fas" <faisalmufti@gmail.com> wrote in message
news:13a0ad36-75d8-4ca0-b585-727d3a8ce1a9@w8g2000prd.googlegroups.com...
> Hi
> I want to do linear regression
> X_vec=a*Y_vec + b
> .
> .
> .
>
> where X_vec(1....100) and Y_vec (1..100) are vectors (say of size
> 100). So I have an overdetermined system where each vector value gives
> me one equation and I want to determine 'a' and 'b' after regression.
> I am bit novice any help?

Look at the Interactive Fitting and Programmatic Fitting sections of the
Data Analysis documentation:

http://www.mathworks.com/access/helpdesk/help/techdoc/data_analysis/f1-6010.html

The first example on the Programmatic Fitting page does basically what you
want.

--
Steve Lord
slord@mathworks.com

Re: linear regression

John D'Errico — Fri, 16 May 2008 13:31:01 -0400

fas <faisalmufti@gmail.com> wrote in message <13a0ad36-75d8-4ca0-b585-
727d3a8ce1a9@w8g2000prd.googlegroups.com>...
> Hi
> I want to do linear regression
> X_vec=a*Y_vec + b
> .
> .
> .
>
> where X_vec(1....100) and Y_vec (1..100) are vectors (say of size
> 100). So I have an overdetermined system where each vector value gives
> me one equation and I want to determine 'a' and 'b' after regression.
> I am bit novice any help?

polyfit

John

Re: linear regression

fas — Sat, 17 May 2008 11:12:46 -0400

On May 16, 11:31 pm, "John D'Errico" <woodch...@rochester.rr.com>
wrote:
> fas <faisalmu...@gmail.com> wrote in message <13a0ad36-75d8-4ca0-b585-
>
> 727d3a8ce...@w8g2000prd.googlegroups.com>...
>
> > Hi
> > I want to do linear regression
> > X_vec=a*Y_vec + b
> > .
> > .
> > .
>
> > where X_vec(1....100) and Y_vec (1..100) are vectors (say of size
> > 100). So I have an overdetermined system where each vector value gives
> > me one equation and I want to determine 'a' and 'b' after regression.
> > I am bit novice any help?
>
> polyfit
>
> John

My data is 100x100, 2D which I have converted to X(:) as same for Y,
but it seems its not the right approach to run 1D polyfit on it. Any
idea what to do now

Re: linear regression

John D'Errico — Sat, 17 May 2008 11:51:02 -0400

fas <faisalmufti@gmail.com> wrote in message <4c336df8-f903-4db2-
bb4a-7a8cf785ec45@j33g2000pri.googlegroups.com>...
> On May 16, 11:31 pm, "John D'Errico" <woodch...@rochester.rr.com>
> wrote:
> > fas <faisalmu...@gmail.com> wrote in message <13a0ad36-75d8-
4ca0-b585-
> >
> > 727d3a8ce...@w8g2000prd.googlegroups.com>...
> >
> > > Hi
> > > I want to do linear regression
> > > X_vec=a*Y_vec + b
> > > .
> > > .
> > > .
> >
> > > where X_vec(1....100) and Y_vec (1..100) are vectors (say of size
> > > 100). So I have an overdetermined system where each vector value
gives
> > > me one equation and I want to determine 'a' and 'b' after regression.
> > > I am bit novice any help?
> >
> > polyfit
> >
> > John
>
> My data is 100x100, 2D which I have converted to X(:) as same for Y,
> but it seems its not the right approach to run 1D polyfit on it. Any
> idea what to do now

You need to think about what you want to
do, or at least explain yourself more clearly.
You will find that learning to explain yourself
clearly will often bring you directly to the
answer that you need.

You have an array X and an array Y. Originally
you said that X and Y were vectors of length
100. Now you are telling us that they are
arrays of size 100x100. It cannot be both.

Try a little harder. Explain your problem.

John

Re: linear regression

fas — Sun, 18 May 2008 00:35:42 -0400

On May 17, 9:51 pm, "John D'Errico" <woodch...@rochester.rr.com>
wrote:
> fas <faisalmu...@gmail.com> wrote in message <4c336df8-f903-4db2-
>
> bb4a-7a8cf785e...@j33g2000pri.googlegroups.com>...
>
>
>
> > On May 16, 11:31 pm, "John D'Errico" <woodch...@rochester.rr.com>
> > wrote:
> > > fas <faisalmu...@gmail.com> wrote in message <13a0ad36-75d8-
> 4ca0-b585-
>
> > > 727d3a8ce...@w8g2000prd.googlegroups.com>...
>
> > > > Hi
> > > > I want to do linear regression
> > > > X_vec=a*Y_vec + b
> > > > .
> > > > .
> > > > .
>
> > > > where X_vec(1....100) and Y_vec (1..100) are vectors (say of size
> > > > 100). So I have an overdetermined system where each vector value
> gives
> > > > me one equation and I want to determine 'a' and 'b' after regression.
> > > > I am bit novice any help?
>
> > > polyfit
>
> > > John
>
> > My data is 100x100, 2D which I have converted to X(:) as same for Y,
> > but it seems its not the right approach to run 1D polyfit on it. Any
> > idea what to do now
>
> You need to think about what you want to
> do, or at least explain yourself more clearly.
> You will find that learning to explain yourself
> clearly will often bring you directly to the
> answer that you need.
>
> You have an array X and an array Y. Originally
> you said that X and Y were vectors of length
> 100. Now you are telling us that they are
> arrays of size 100x100. It cannot be both.
>
> Try a little harder. Explain your problem.
>
> John

Ok, X and Y were for an example case are of size 100. In actual X and
Y are both of 2D of size (100x100 again example case). I converted
them to vectorized form as 10000x1. So I have 10000 equations each for
one point and now I want to fit polyfit. But the problem is that as
they are converted from 2D matrix. If I plot in 1D they do not appear
right and hence I believe polyfit may not work. The other option I can
think of is to sort it after converting it into vectorized form, so
that then can come in some order (for of some curve). Will it be ok to
apply polyfit on it. Will the coefficient that I find will have same
meaning or if the regression is done on the same 2D function (some
how)
Thanks,

Re: linear regression

Greg Heath — Sun, 18 May 2008 09:39:30 -0400

On May 17, 8:35=A0pm, fas <faisalmu...@gmail.com> wrote:
> On May 17, 9:51 pm, "John D'Errico" <woodch...@rochester.rr.com>
> wrote:
>
>
>
>
>
> > fas <faisalmu...@gmail.com> wrote in message <4c336df8-f903-4db2-
>
> > bb4a-7a8cf785e...@j33g2000pri.googlegroups.com>...
>
> > > On May 16, 11:31 pm, "John D'Errico" <woodch...@rochester.rr.com>
> > > wrote:
> > > > fas <faisalmu...@gmail.com> wrote in message <13a0ad36-75d8-
> > 4ca0-b585-
>
> > > > 727d3a8ce...@w8g2000prd.googlegroups.com>...
>
> > > > > Hi
> > > > > I want to do linear regression
> > > > > X_vec=3Da*Y_vec + b
> > > > > .
> > > > > .
> > > > > .
>
> > > > > where X_vec(1....100) and Y_vec (1..100) are vectors (say of size
> > > > > 100). So I have an overdetermined system where each vector value
> > gives
> > > > > me one equation and I want to determine 'a' and 'b' after regressi=
on.
> > > > > I am bit novice any help?
>
> > > > polyfit
>
> > > > John
>
> > > My data is 100x100, 2D which I have converted to X(:) as same for Y,
> > > but it seems its not the right approach to run 1D polyfit on it. Any
> > > idea what to do now
>
> > You need to think about what you want to
> > do, or at least explain yourself more clearly.
> > You will find that learning to explain yourself
> > clearly will often bring you directly to the
> > answer that you need.
>
> > You have an array X and an array Y. Originally
> > you said that X and Y were vectors of length
> > 100. Now you are telling us that they are
> > arrays of size 100x100. It cannot be both.
>
> > Try a little harder. Explain your problem.
>
> > John
>
> Ok, X and Y were for an example case are of size 100. In actual X and
> Y are both of 2D of size (100x100 =A0again example case). I converted
> them to vectorized form as 10000x1. So I have 10000 equations each for
> one point and now I want to fit polyfit. But the problem is that as
> they are converted from 2D matrix. If I plot in 1D they do not appear
> right and hence I believe polyfit may not work. The other option I can
> think of is to sort it after converting it into vectorized form, so
> that then can come in some order (for of some curve). Will it be ok to
> apply polyfit on it. Will the coefficient that I find will have same
> meaning or if the regression is done on the same 2D function (some
> how)
> Thanks,-

Why is it more difficult than solving

Y =3D W*[ones(100);X]

for W?

Hope this helps.

Greg

Re: linear regression

fas — Sun, 18 May 2008 10:18:46 -0400

On May 18, 7:39 pm, Greg Heath <he...@alumni.brown.edu> wrote:
> On May 17, 8:35 pm, fas <faisalmu...@gmail.com> wrote:
>
>
>
> > On May 17, 9:51 pm, "John D'Errico" <woodch...@rochester.rr.com>
> > wrote:
>
> > > fas <faisalmu...@gmail.com> wrote in message <4c336df8-f903-4db2-
>
> > > bb4a-7a8cf785e...@j33g2000pri.googlegroups.com>...
>
> > > > On May 16, 11:31 pm, "John D'Errico" <woodch...@rochester.rr.com>
> > > > wrote:
> > > > > fas <faisalmu...@gmail.com> wrote in message <13a0ad36-75d8-
> > > 4ca0-b585-
>
> > > > > 727d3a8ce...@w8g2000prd.googlegroups.com>...
>
> > > > > > Hi
> > > > > > I want to do linear regression
> > > > > > X_vec=a*Y_vec + b
> > > > > > .
> > > > > > .
> > > > > > .
>
> > > > > > where X_vec(1....100) and Y_vec (1..100) are vectors (say of size
> > > > > > 100). So I have an overdetermined system where each vector value
> > > gives
> > > > > > me one equation and I want to determine 'a' and 'b' after regression.
> > > > > > I am bit novice any help?
>
> > > > > polyfit
>
> > > > > John
>
> > > > My data is 100x100, 2D which I have converted to X(:) as same for Y,
> > > > but it seems its not the right approach to run 1D polyfit on it. Any
> > > > idea what to do now
>
> > > You need to think about what you want to
> > > do, or at least explain yourself more clearly.
> > > You will find that learning to explain yourself
> > > clearly will often bring you directly to the
> > > answer that you need.
>
> > > You have an array X and an array Y. Originally
> > > you said that X and Y were vectors of length
> > > 100. Now you are telling us that they are
> > > arrays of size 100x100. It cannot be both.
>
> > > Try a little harder. Explain your problem.
>
> > > John
>
> > Ok, X and Y were for an example case are of size 100. In actual X and
> > Y are both of 2D of size (100x100 again example case). I converted
> > them to vectorized form as 10000x1. So I have 10000 equations each for
> > one point and now I want to fit polyfit. But the problem is that as
> > they are converted from 2D matrix. If I plot in 1D they do not appear
> > right and hence I believe polyfit may not work. The other option I can
> > think of is to sort it after converting it into vectorized form, so
> > that then can come in some order (for of some curve). Will it be ok to
> > apply polyfit on it. Will the coefficient that I find will have same
> > meaning or if the regression is done on the same 2D function (some
> > how)
> > Thanks,-
>
> Why is it more difficult than solving
>
> Y = W*[ones(100);X]
>
> for W?
>
> Hope this helps.
>
> Greg

Sorry I could not get you completely. ?

I would like to know that if we convert a nxm (matrix ) function to 1D
and then sort it and then polyfit . Can we use the result. As in a 3D
format( nxm) matrix I cannot use polyfit :(

Re: linear regression

John D'Errico — Sun, 18 May 2008 11:23:01 -0400

fas <faisalmufti@gmail.com> wrote in message <f4a869df-f422-47d9-
bda7-1daafa173bb1@z16g2000prn.googlegroups.com>...

> > Why is it more difficult than solving
> >
> > Y = W*[ones(100);X]
> >
> > for W?
> >
> > Hope this helps.
> >
> > Greg
>
> Sorry I could not get you completely. ?
>
> I would like to know that if we convert a nxm (matrix ) function to 1D
> and then sort it and then polyfit . Can we use the result. As in a 3D
> format( nxm) matrix I cannot use polyfit :(

Why do you state that it does not work?

If your model is

   X =a*Y + b

then polyfit as applied to

  ab = polyfit(Y(:),X(:),1);

will work. Equally as well, if you use backslash,

  ab = [Y(:),ones(numel(Y),1)]\X(:);

this will also work.

John

Re: linear regression

John D'Errico — Sun, 18 May 2008 11:29:02 -0400

fas <faisalmufti@gmail.com> wrote in message <2e7d4e65-1ce4-4bf3-
8ab3-81f0bae4638c@c19g2000prf.googlegroups.com>...

> Ok, X and Y were for an example case are of size 100. In actual X and
> Y are both of 2D of size (100x100 again example case). I converted
> them to vectorized form as 10000x1. So I have 10000 equations each for
> one point and now I want to fit polyfit. But the problem is that as
> they are converted from 2D matrix. If I plot in 1D they do not appear
> right and hence I believe polyfit may not work. The other option I can
> think of is to sort it after converting it into vectorized form, so
> that then can come in some order (for of some curve). Will it be ok to
> apply polyfit on it. Will the coefficient that I find will have same
> meaning or if the regression is done on the same 2D function (some
> how)
> Thanks,

What does not "appear" right?

If your model is as stated, then this is correct.

I think that you are asking to do a 2-d regression,
in both the x and y directinos, but for some reason
do not realize that is what you want to do. Or, you
just don't want to admit it.

John

Re: linear regression

fas — Mon, 19 May 2008 04:51:40 -0400

On May 18, 9:29 pm, "John D'Errico" <woodch...@rochester.rr.com>
wrote:
> fas <faisalmu...@gmail.com> wrote in message <2e7d4e65-1ce4-4bf3-
>
> 8ab3-81f0bae46...@c19g2000prf.googlegroups.com>...
>
> > Ok, X and Y were for an example case are of size 100. In actual X and
> > Y are both of 2D of size (100x100 again example case). I converted
> > them to vectorized form as 10000x1. So I have 10000 equations each for
> > one point and now I want to fit polyfit. But the problem is that as
> > they are converted from 2D matrix. If I plot in 1D they do not appear
> > right and hence I believe polyfit may not work. The other option I can
> > think of is to sort it after converting it into vectorized form, so
> > that then can come in some order (for of some curve). Will it be ok to
> > apply polyfit on it. Will the coefficient that I find will have same
> > meaning or if the regression is done on the same 2D function (some
> > how)
> > Thanks,
>
> What does not "appear" right?
>
> If your model is as stated, then this is correct.
>
> I think that you are asking to do a 2-d regression,
> in both the x and y directinos, but for some reason
> do not realize that is what you want to do. Or, you
> just don't want to admit it.
>
> John

I admit that I wan to to do 2D regression. So if I want to to do that
then doing a vectorization and sorting and then regression may not be
right (Is it?). So in that case how to to 2D regression ?