I have a single dependent variable Y, K independent variables of interest (X1, X2... Xk), and a single independent variable of non-interest (Z).
I am interested in the relationship between Y and each X, while accounting for the effect of Z. In other words, I am interested in the partial correlations.
Further, I want to compare the slopes of each X to each other, both to evaluate whether some X's have a larger effect than others, and because I want to be able to talk about the presence/absence of a significant effect of each X without falling into the trap of "The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant".
Complicating factors:
- There is high co-linearity between many of the X variables. Because of this, and because I have a priori theoretical reasons to be interested in the non-unique variance explained by each X, I assess the effect of each X in a separate model (Y ~ X1 + Z, Y ~ X