# Find correlation from biased observations

I have a set of observations of a variable Z (shown as the colormap) as a function of two other variables A and B. I want to study how Z varies with respect to A, B, and both A and B (eg. if A increases, does Z increase or decrease? Same with respect to B?)

The only problem is that my observations of Z are highly biased, i.e., for low A, B is high, and vice-versa.

Is there any way I can disentangle both dimensions (A and B)?

Right now, I have just studied Z for A < 1.75, as A doesn't vary too much in this window.

• What do you mean by Z being biased for low A - high B? How do you know that? Is it really biased or did you mean that the variability is different? Also a 3D plot of the three variables might help. Feb 12 at 14:54
• From what you are describing, both A and B and correlated somehow. Have you explored this further ? Feb 12 at 16:06
• To my understanding of this plot, the observations of Z are biased (maybe not the best term here ^^) in the sense that when observing Z for low A, B is high (vice-versa). This observation bias makes any analysis of the trend of Z versus A and B hard. And the plot already show a 3D dataset? And to answer @CaroZ, indeed the observations of A and B are correlated. Feb 13 at 8:08
• How strongly are A and B correlated, could you upload a plot ? And what exactly is your research question ? Feb 13 at 10:51
• You may want to look in the direction of PCA in particular and dimensionality reduction in general.
– Cryo
Feb 14 at 5:25