Regression/linear equation solving

I have a set of over defined equations that do not fit perfectly. The problem resembles this simpler problem in nature:

x1 = 0.8 + x2,

x1 = 1.2 + x2

x2 = 1.5 + x3

x3 = -3 + x1

x4 = -1.5 + x2

x4 = -1.7 +x2

I'm trying to solve for the x's, and they have values which are relative to one another, so i can assume for example that one of the x's is 0.

Because this is over defined, I would need to do a regression of some sort.

I'm feeling a bit foggy today, but I'm sure there's got to be a way to do this in MATLAB. Can anyone provide me with some sample code?

Answer 1

[Tom Lane]

Bring all the x's over to the left of the equal sign. Then a matrix representation of those equations is this:

       1    -1     0     0
       1    -1     0     0
       0     1    -1     0
      -1     0     1     0
       0    -1     0     1
       0    -1     0     1

Let this be A, and define a vector b that is is the vector of constant terms, and your least squares solution is A\b. MATLAB will automatically set one of the x values to zero for you.

[Matt]

Thanks, this is exactly what I was looking for