Find a 3d equation that goes through a series of points?

Question

I have a series of points in 3d space and I need to find an equation that goes through all of them. What would be the best way to do this?

Points: (3.7, 0.45, 0.7) (5.2, 0.8, 0.96) (6, 1.04, 1.15) (7.5, 1.4, 1.4) (10, 2.1, 1.8) (30, 16, 6.6)

Answer 1

The given data points seem to be aligned on a curve. The first five are in a straight line but the sixth deviates noticeably.

For simplicity, we can admit that the relation between $M$ and $S$ is relatively linear and through the origin,

$$S\approx rM,$$ where $r=\dfrac{6.6}{30}$.

Then the $(M,R)$ relation can be approximated with a parabola which passes through the origin, of the form $$R\approx aM^2+bM.$$

We can obtain it by a Lagrangian interpolation through the origin and the points $5$ and $6$, and we get $a=\dfrac{9.7}{600},b=\dfrac{29}{600}$.