I've got some data with a very high density of data points in one area, and I'm trying to produce an effective fit.

I'm being quite crude (stuck doing it this way for now) by "binning" the data in our dependent variable and performing a fit on each set of data in order to compare the impact. For example, here's three separate bins for comparison:

enter image description here

I'm expecting to see a larger difference in the curves at the top end of this, and it looks visually like there's data points that should be shifting the green curve away from the red & blue one - which is what I'm expecting.

I'm uncomfortable having to use 4th order polynomials to try get a sensible fit, I'm having trouble finding a curve that can fit the very high density data in the middle/left and the lower density (but very important) right.

I began to wonder whether using the y axis (quick Wikipedia came up with "ordinary least squares") to judge fit quality might be an issue. It's judging performance based on the red lines, rather than what might make more sense in the orange lines:

enter image description here

Wikipedia tells me this is a geometric fit, however, when researching this I'm getting many multivariate PCA type analysis, and maybe performing geometric fits for linear data.

I can't seem to find any resources on polynomial geometric fitting though - is it possible/good practice?

I'm sure there's a better way of going about this, can anyone point me in the right direction? My high school level knowledge of statistics is showing...


One possibility is using wave height as a fitting variable and fitting the data to a 3D surface, as in:

z = f(x,y)

so that there is no need for grouping. If you are unfamiliar with surface fitting, post a link to the raw data and I and others who read these questions can give it a try.

I would point out that the center of the plot shows a data point with what appears to be a Y value of zero, this might be a typographical error in the data and is worth a quick check to verify the value.


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