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regressionlinear-regressionplane

Normal vector from least squares-derived plane

I have a set of points and I can derive a least squares solution in the form:

z = Ax + By + C

The coefficients I compute are correct, but how would I get the vector normal to the plane in an equation of this form? Simply using A, B and C coefficients from this equation don't seem correct as a normal vector using my test dataset.

Solution

  • Following on from dmckee's answer:

    a x b = (a2b3 − a3b2), (a3b1 − a1b3), (a1b2 − a2b1)

    In your case a1=1, a2=0 a3=A b1=0 b2=1 b3=B

    so = (-A), (-B), (1)