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#1
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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 |
#2
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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) |
#3
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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) |
#4
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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 |
#5
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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) |
#6
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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) |
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