I know Pearson's correlation is considered to be a linear measure of association, for it is intimately linked to simple least square regression. It is known to have poor performance on non-linear data vectors x and y.
And I also know partial (Pearson's) correlation can be used to control for a confounding variables, say z, and is linked to multiple least square regression.
So, is it sensible to claim partial correlation is a ``linear'' measure in the sense that it is still capturing a linear type of relationship between x and y? If x and y and z all has non-linear relationships between them (say, in the sense of scatter plot), how would partial correlation perform in this instance? Is there a simulation study done on partial correlation through a simulation study?