I'm exploring how 7 system parameters spanning mechanical, electrical, and physical (size) properties are related. I gathered the 7 specs of 36 different systems, and I plotted every parameter combination to see what, if any, correlations existed.

  • Each column has the same x-axis parameter as identified in the bottom row
  • Each row has the same y-axis parameter as identified in the first column

Factor effects chart


Some of the plots verify known relations: I knew beforehand that parameter 3 & 4's are positively correlated and parameter's 2 & 7's are inversely correlated.

I also know that I have an incomplete picture. For example, parameter 1 is a product of parameter 3 and two other parameters that I don't have data for. One (or potentially both!) of these unknown parameters significantly affects parameter 2. I don't know how, but I know the correlation exists.


I'm curious if the mid-trend "splits"/divergences in some plots--eg: p5 vs p4, p5 vs p6, p7 vs p6--are the effects of those unknown parameters.

  1. What, if anything, do these splits indicate?
  2. What are some additional tests I can run to reveal more concrete info?

PS: Please let me know how I can improve my chart!


As Nuclear Wang and DWin suggested, I investigate my data for subgroups. I also added data from another discrete variable, so my total number of parameters is 8.

Parameters 5 and 6 (diameter and length) are both volumetric specs, so I divided all points based on their D/L ratio. This actually resolved most of the "divergences"!

  • The flat and wide systems (D/L > 1) are blue
  • The long and skinny systems (D/L <= 1) are orange

Subgrouped factor effects


When I see a plot like that, my thinking immediately goes toward sample subgroups. It seems like you have two different sample groups, each with a visually apparent trend line. Are all your samples similar, or are there some categorical differences between them? Suppose one of your divergent graphs represents price vs. capacity of hard drives. The two sample groups might represent different manufacturers, one with cheap products and a low dollar/GB slope, and one with more expensive products and a high dollar/GB slope.

To characterize this further, you can label the samples on one of the divergent lines and plot out those sample labels on the other graphs as well. If you consistently see the same samples falling onto the separate trend lines across several variables, that suggests there's some sort of categorical difference that's driving the behavior across several of your observed variables.

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There is at least one discrete variable, parm3 and it's possible that there are other un-labeled groupings. I'd start by redo that graphic while labeling the parm3 values with color coding. Ten you can quickly see whether one or two colors fall into the "splits" that are apparent.

That appears to be a "pairs" plot. In R you could do something like:

pairs(  data , bg= rainbow(10)[parm3], other parameters)

That call to rainbow function would give you 10 colors across the visible spectrum.and the values of parm3 would get individually "painted".

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