performing least squares

[Darius Blaszijk]

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

 

[Jay Somerset]

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?

 

[Darius Blaszijk]

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

 

[Jerry W. Lewis]

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

 

[Jay Somerset]

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

 

[Tim Williams]

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,

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.