# On Multiple Linear Regression and Partial Correlation

#### Etubom

##### New Member
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

#### hlsmith

##### Not a robit
You can typically run a single regression and just look at variance inflation factor or tolerance statistic to understand multicollinearity.

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#### Etubom

##### New Member
Thanks, hismith , I mean how to order the different hypotheses. Should the Multiple regression hypothesis come before the partial correlation hypotheses?

#### ondansetron

##### 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.

#### hlsmith

##### Not a robit
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.?