This is simply the correlation between two variables after their correlation with another variable is removed. This is quite useful as a way to disentangle relationships between variables in any particular dataset where many variables may be correlated statistically significantly, i.e. may have non-random relationships with each other.
Details #
Say you are interested in the relationship between quality of life and physical disability and you have values for these things in a good sized dataset. You can compute the simple correlation between them and probably find that quality of life is inversely related to physical disability: they greater someone’s disability, the lower their quality of life is likely to me. But suppose you also have values for each individual’s annual income, you might think that might impinge on the relationship between disability and quality of life. One way to address this is partial correlation: instead of computing the correlation between disability and quality of life you compute the linear regression of quality of life on annual income and then compuite the linear regression of disability on annual income; now you compute the correlation between the residuals from that first regression and those from the second regression. Now you have the correlation between quality of life and disability with any linear effects of annual income on either quality of life and disability removed, you have “partialled it out”.
I suspect you would find that the relationship between quality of life and disability is still statistically significant, but reduced by removing the impact of annual income.
The correlation usually used is the Pearson correlation and the regression usually used is a linear regression. There are other methods but they are very small print.
Try also #
Chapters #
Not covered in the OMbook.
Online resources #
Not yet but this really needs a worked example in my Rblog and perhaps a new Shiny app.
Dates #
First created 28.i.25, exact method corrected 29.i.25!
