Using least squares, find the expression of a plane $z=f(x,y) \,$, that passes through the origin
and is the best fit for the following points:
$$\begin{array}{|c|c|c|} \hline f(x,y) & 5.7 & 3.75 & 8.9 \\ \hline x & 1 & 0 & 1.5 \\ \hline y & 1 & 0.5 & 1.5 \\ \hline \end{array}$$
The values of z have a dispersion of 0.5 and the variables x and y are measured with no error.
So, first of all, what does it mean when it says dispersion?. As it could be the variance or the standard deviation.
Second, the way I tried to find the plane is using linear least squares ($\vec{z} = \vec{\eta} + \vec{\epsilon}$, where $\vec{\eta}=A\vec{x}$).
Since the ecuation of a plane is $z=f(x,y)=Ax + By + C \,$; I wrote the desing matrix like this:
$$A=\begin{bmatrix} 1 & 1 & 1 \\ 0 & 0.5 & 1 \\ 1.5 & 1.5 & 1 \end{bmatrix}$$
and then used the least square method but don't where to use the fact that the plane has to pass through the origin. Any advice is welcome. Thanks