least squares method for the 3 unknowns

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';

Answer 1

[Renato Agurto]

Hello.

If

 b = DMOS1'

then your solution is

 A\b

[Marek Rousek]

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!!!

[Renato Agurto]

b = DMOS1'; %transposed
x=A\b; %not A/b!!

Answer 2

[Marek Rousek]

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.

[Renato Agurto]

A\b is least squares. you can try it with a larger number of equations