I have read some examples of least squares fitting of data, for example there is a an example stating that Hooke's spring law relates the length of a uniform spring x as a linear function of the force y applied to it:
So it then goes on to form the matrix based on applying four forces, 0, 2, 4, and 6 N, and then taking the respective spring length measurements, so that the matrix and y vector,
look like this
for the system , where
I understand that example fine, but I want to fit some data into a least squares form, but I'm just not sure how to start.
The equation is as follows,
Here my parameters are,
My y vector in this case will be,
is an average that is included in every solution to so the first columb of the A matrix is all 1'a. From the equation above I can see that, take for example, is a linear combination of the parameters and . So I'm thinking the linear combination of the top line of the A matrix should look something like this:
But I can't see how this fits into the equation of a line model y = a + bx though. Am I going to have an equation like y = a + bx + cz? or something? Or am I doing something totally wrong?
Does anyone know how to help me fit this into a linear least squares model?