performing least squares
 

Hello,

I have the following data;

y x1 x2
12 1 10
23 2 20
34 3 30
45 4 40
56 5 50


And I would like to fit the following formula to this dataset; "x1^2 + x2 *
x1 = y"

Can anybody give me a pointer on how to do this, preferebly without having
to linearize the dataset first? The "algorithm" proposed should however be
able to fit any formula / model to the dataset, eg be general about this.

Kind regards, Darius Blaszijk

On Thu, 17 Mar 2005 00:25:44 +0100, "Darius Blaszijk"
wrote:

Hello,

I have the following data;

y x1 x2
12 1 10
23 2 20
34 3 30
45 4 40
56 5 50


And I would like to fit the following formula to this dataset; "x1^2 + x2 *
x1 = y"

Can anybody give me a pointer on how to do this, preferebly without having
to linearize the dataset first? The "algorithm" proposed should however be
able to fit any formula / model to the dataset, eg be general about this.

Kind regards, Darius Blaszijk


You seem to be missing something. You can't fit the formula as you wrote it.

What coefficients are you trying to determine? Do you really mean you are
trying to find "a" and "b" that best fit the equation y = a*x1^2 b*x1*x2,
or y= a*x1*(x1 + b*x2) or y= x1*(a*x1+b*x2), or something else?

--
Jay.
(remove dashes for legal email address)

Jay,

What I meant was the following; y = a*x1^2 b*x1*x2. But in fact it does not
matter as I need a general method.

Kind regards, Darius Blaszijk




"Jay Somerset" schreef in bericht
...
On Thu, 17 Mar 2005 00:25:44 +0100, "Darius Blaszijk"
wrote:

Hello,

I have the following data;

y x1 x2
12 1 10
23 2 20
34 3 30
45 4 40
56 5 50


And I would like to fit the following formula to this dataset; "x1^2 +
x2 *
x1 = y"

Can anybody give me a pointer on how to do this, preferebly without
having
to linearize the dataset first? The "algorithm" proposed should however
be
able to fit any formula / model to the dataset, eg be general about
this.

Kind regards, Darius Blaszijk


You seem to be missing something. You can't fit the formula as you wrote
it.

What coefficients are you trying to determine? Do you really mean you
are
trying to find "a" and "b" that best fit the equation y = a*x1^2 b*x1*x2,
or y= a*x1*(x1 + b*x2) or y= x1*(a*x1+b*x2), or something else?

--
Jay.
(remove dashes for legal email address)

x2 is a multiple of x1 so neither y = x1 + x2 nor y = x1^2 + x2*x1 have
uniquely determined coefficients.

If x2 were not a multiple of x1, then
LINEST(A2:A6,B2:B6*B2:C6)
would do the trick, assuming that column labels are in A1:C1 with data
in A2:C6.

Jerry

Darius Blaszijk wrote:

Hello,

I have the following data;

y x1 x2
12 1 10
23 2 20
34 3 30
45 4 40
56 5 50


And I would like to fit the following formula to this dataset; "x1^2 + x2 *
x1 = y"

Can anybody give me a pointer on how to do this, preferebly without having
to linearize the dataset first? The "algorithm" proposed should however be
able to fit any formula / model to the dataset, eg be general about this.

Kind regards, Darius Blaszijk

On Thu, 17 Mar 2005 09:48:39 +0100, "Darius Blaszijk"
wrote:

Jay,

What I meant was the following; y = a*x1^2 b*x1*x2. But in fact it does not
matter as I need a general method.

It certainly does matter. But if you have already decided that you don't
need a definitive expression with coefficients, then no amount of advice is
going to help you. Sad to say, it seems as though you do not understand
least squares fits.


Kind regards, Darius Blaszijk




"Jay Somerset" schreef in bericht
...
On Thu, 17 Mar 2005 00:25:44 +0100, "Darius Blaszijk"
wrote:

Hello,

I have the following data;

y x1 x2
12 1 10
23 2 20
34 3 30
45 4 40
56 5 50


And I would like to fit the following formula to this dataset; "x1^2 +
x2 *
x1 = y"

Can anybody give me a pointer on how to do this, preferebly without
having
to linearize the dataset first? The "algorithm" proposed should however
be
able to fit any formula / model to the dataset, eg be general about
this.

Kind regards, Darius Blaszijk


You seem to be missing something. You can't fit the formula as you wrote
it.

What coefficients are you trying to determine? Do you really mean you
are
trying to find "a" and "b" that best fit the equation y = a*x1^2 b*x1*x2,
or y= a*x1*(x1 + b*x2) or y= x1*(a*x1+b*x2), or something else?

--
Jay.
(remove dashes for legal email address)


--
Jay.
(remove dashes for legal email address)

Darius,

If you want a "general" method then why not use solver? I've used this
in the past when fitting a dataset (assuming this is experimental
data) to one or more models. Works fine.

Tim


"Jay Somerset" wrote in message
...
On Thu, 17 Mar 2005 09:48:39 +0100, "Darius Blaszijk"
wrote:

Jay,

What I meant was the following; y = a*x1^2 b*x1*x2. But in fact it
does not
matter as I need a general method.

It certainly does matter. But if you have already decided that you
don't
need a definitive expression with coefficients, then no amount of
advice is
going to help you. Sad to say, it seems as though you do not
understand
least squares fits.


Kind regards, Darius Blaszijk




"Jay Somerset" schreef in bericht
...
On Thu, 17 Mar 2005 00:25:44 +0100, "Darius Blaszijk"
wrote:

Hello,

I have the following data;

y x1 x2
12 1 10
23 2 20
34 3 30
45 4 40
56 5 50


And I would like to fit the following formula to this dataset;
"x1^2 +
x2 *
x1 = y"

Can anybody give me a pointer on how to do this, preferebly
without
having
to linearize the dataset first? The "algorithm" proposed should
however
be
able to fit any formula / model to the dataset, eg be general
about
this.

Kind regards, Darius Blaszijk


You seem to be missing something. You can't fit the formula as
you wrote
it.

What coefficients are you trying to determine? Do you really
mean you
are
trying to find "a" and "b" that best fit the equation y = a*x1^2
b*x1*x2,
or y= a*x1*(x1 + b*x2) or y= x1*(a*x1+b*x2), or something else?

--
Jay.
(remove dashes for legal email address)


--
Jay.
(remove dashes for legal email address)