Linear Algebra and Its Applications · Problem 3.3.18

Orthogonality — Gilbert Strang

Mathematics · least-squares-plane-fit

Problem

We want to fit a plane y=C+Dt+Ezy = C + Dt + Ez to the four points y=3 at t=1,z=1y=6 at t=0,z=3y = 3 \text{ at } t = 1, z = 1 \qquad y = 6 \text{ at } t = 0, z = 3 y=5 at t=2,z=1y=0 at t=0,z=0.y = 5 \text{ at } t = 2, z = 1 \qquad y = 0 \text{ at } t = 0, z = 0. (a) Find 4 equations in 3 unknowns to pass a plane through the points (if there is such a plane). (b) Find 3 equations in 3 unknowns for the best least-squares solution.

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