The following sample values from the function z = f(x,y) were obtained from experimental observations:
f(1,1) = −1.1 f(1,2) = 0.9
f(2,1) = 0.2 f(2,2) = 2.0
f(3,1) = 0.9 f(3,2) = 3.1
We would like to approximate the surface z = f(x,y) by a plane of the form z = ax + by + c. Use a least-squares criterion to choose the parameters a, b, and c.