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

enter image description here

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

  • $\begingroup$ They all look like they could be fitted with 4-point Bezier curves, so I would suggest a cubic polynomial will probably be sufficient. $\endgroup$ – tristan Jun 7 '15 at 7:02
  • $\begingroup$ 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. $\endgroup$ – rnso Jun 7 '15 at 9:25
  • $\begingroup$ A(x) = k - D(x) for some constant k. Likewise C is a reflection of B in the x axis then translated. $\endgroup$ – tristan Jun 7 '15 at 9:31
  • $\begingroup$ What is the application by the way? $\endgroup$ – tristan Jun 7 '15 at 9:31
  • $\begingroup$ And those basis curves are to do with calculating the curve, not the output. $\endgroup$ – tristan Jun 7 '15 at 9:33

I extracted a few points from curve A and fairly successfully fitted a quartic (degree 4) polynomial. Lower order didn't fit very well. I suspect it should fit the other curves equally well.

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.

Good luck!

  • $\begingroup$ How can you get B and C with $x^2$ etc? $\endgroup$ – rnso Jun 7 '15 at 16:47
  • $\begingroup$ You let the regression take care of that, just include the powers of x as additional variables. $\endgroup$ – tristan Jun 7 '15 at 16:48
  • $\begingroup$ And make sure you have a constant term as well $\endgroup$ – tristan Jun 7 '15 at 16:49

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