I ran into trouble trying to remove the effects of one variable on other variables doing the writing my reanalysis of the Noble et al 2015 paper. It was not completely obvious which exact method to use. The authors in their own paper used OLS aka. standard linear regression. However, since I wanted to plot the results at the case-level, this was not useful to me. Before doing this I did not really understand how partial correlations worked, or what semi-partial correlations were, or how multiple regression works exactly. I still don't understand the last, but the others I will explain with example results.