On Multiple Linear Regression and Partial Correlation

I am conducting a study that involves A as the dependent variable (the DV) and B,C and D as the independent variables (the IVs).
In the first place, for hypothesis one, I have conducted a standard multiple regression of B,C and D (the IVs) on A (the DV).
After this, for hypothesis two, I have conducted partial correlation of A (the DV) and B partialling C and D.
For hypothesis three, I have conducted partial correlation of A (the DV) and C partialling B and D.
for hypothesis four, I have conducted partial correlation of A (the DV) and D partialling B and C.
Please confirm for me whether I am right to conduct the partial correlations after the multiple regression or otherwise. Please, I expect your reply.Thanks


Less is more. Stay pure. Stay poor.
You can typically run a single regression and just look at variance inflation factor or tolerance statistic to understand multicollinearity.

Does that address your pursuit.
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Thanks, hismith , I mean how to order the different hypotheses. Should the Multiple regression hypothesis come before the partial correlation hypotheses?


TS Contributor
OP: please provide more details for what you wish to achieve.

If I recall, partialling out would be that you regress B on C and D and save the residuals from this regression as Resid(B).
Repeat this so you regress C on B and D to get Resid(C). Then do this once more so you have D regressed on B and C to get Resid(D).

If you now regress A on Resid(B), A on Resid(C), and A on Resid(D) each in a simple regression, the coefficients should be equal to the coefficients obtained by regressing A on B,C, and D in a multiple linear regression. This is because each of the coefficients in MLR are interpreted as the effect of an X variable on Y after accounting for the other variables. By regressing B on C and D in an MLR and saving residuals, we found the part of B that is unrelated to the group of C and D (we have "accounted" for C and D).

Not sure if this helps at all, but do let us know more details for what you want to do.


Less is more. Stay pure. Stay poor.
Yes, there are many directions this could go without further description of the purpose. Are you trying to do structural equation modelling, partial R**2, mediation analysis (direct and non direct effects), etc.?