# What polynomial do I need for regression of such relations

I have following 4 graphs and for each I have to do regression.

The relation is clearly curvilinear. What term should I use for regression (eg y ~ x+x^2) for each of these?

• They all look like they could be fitted with 4-point Bezier curves, so I would suggest a cubic polynomial will probably be sufficient. – tristan Jun 7 '15 at 7:02
• In the graph on the wiki page en.wikipedia.org/wiki/B%C3%A9zier_curve and en.wikipedia.org/wiki/File:Bezier_basis.svg I could see B and D curves above but not A and C. – rnso Jun 7 '15 at 9:25
• A(x) = k - D(x) for some constant k. Likewise C is a reflection of B in the x axis then translated. – tristan Jun 7 '15 at 9:31
• What is the application by the way? – tristan Jun 7 '15 at 9:31
• And those basis curves are to do with calculating the curve, not the output. – tristan Jun 7 '15 at 9:33

I suggest you try your regression with $x$, $x^2$, $x^3$ and $x^4$ terms, but bear in mind that the fit is only for the range you fit - it probably shouldn't be used for any extrapolation without an understanding of the physical processes (if any) underlying.
• How can you get B and C with $x^2$ etc? – rnso Jun 7 '15 at 16:47