least squares method for the 3 unknowns

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Marek Rousek
Marek Rousek 2015-12-21
编辑： Renato Agurto 2015-12-21
Hi,
I have a problem how to calculate the 3 unknows using the least squares method.
I have a lot of same-looking equations like this: 46.2=C1*0.00134447+C2*0.006914+C3*0.01121469
where C1, C2 and C3 is unknow
How i can these unknow calculate with using the least squares method?
Here is code for example more equations
DMOS1=[46.2, 45.1, 47.3];
SSIM1=[0.00134447, 0.00114451, 0.00102085];
SSIM2=[0.006914, 0.006894, 0.007149];
SSIM3=[0.01121469, 0.01316054, 0.01604895];
A=[SSIM1; SSIM2; SSIM3];
A=A';
b=b';

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回答（2 个）

Renato Agurto
Renato Agurto 2015-12-21
Hello.
If
b = DMOS1'
then your solution is
A\b
  2 个评论
Marek Rousek
Marek Rousek 2015-12-21
when i tried for 1 equation:
DMOS1=[46.2, 45.1, 47.3];
SSIM1=[0.00134447, 0.00114451, 0.00102085];
SSIM2=[0.006914, 0.006894, 0.007149];
SSIM3=[0.01121469, 0.01316054, 0.01604895];
A=[SSIM1; SSIM2; SSIM3];
A=A';
b=DMOS1;
x=A/b;
C=x(1)*SSIM1(1)+x(2)*SSIM2(1)+x(3)*SSIM3(1);
result is 0,000003..., what is not 46,2!!!

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Marek Rousek
Marek Rousek 2015-12-21
编辑：Marek Rousek 2015-12-21
But these equations dont have a simple solution , I need to use the least squares method to find the most accurate solution , ideally also appear on the chart.
  1 个评论
Renato Agurto
Renato Agurto 2015-12-21
编辑：Renato Agurto 2015-12-21
A\b is least squares. you can try it with a larger number of equations

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