Explaining unique variance in multiple regression models I have a question about what explaining unique variance means in regression models and outputs.
I often read in research papers that "We found that outcomes E and F could not simply be explained by individual differences C and D. Each predictor, predictors A and B was uniquely related to one measure of outcomes E and F above and beyond individual differences C and D. ... Taken together, outcomes E and F may be shaped by individual differences C and D, but cannot be explained fully by those constructs."
Does this mean a multiple regression model was computed with A, B, C and D as predictors and E and F as outcomes? And if A and B explain unique variance, does that mean the correlation coefficients for those two predictors are significant?  Essentially, what does it mean that predictors A and B was uniquely related to one measure of outcomes E and F above and beyond individual differences C and D?
Here's the DOI to the paper: http://dx.doi.org/10.1037/emo0000927 and the public link. You can look at the first paragraph on page 10 under the "Discussion" section of Study 1 and the "Perceived benefits of IER Interactions" for analysis strategy under Study 1.
Sorry if the question is too abstract. I don't have access to the data nor the regression models. Happy to elaborate more, and I appreciate any input on this!

The example provided discusses the results from an exploratory factor analysis (EFA). The reason I asked for the example is because a single multiple regression model contains only one outcome (i.e., dependent variable) and therefore, it was unclear how to answer the question.
Now that we know the results did not in fact come from a multiple regression model, is the question about:

*

*unique variability in EFA

*unique variability in multiple regression

I didn't see a previous post directly getting at #1, but there is one about the comparison between principal components analysis and factor analysis. If that doesn't answer the question, I would recommend making a new post about variance in EFA.
If multiple regression is the question (although it is not the example), there are some previous posts that might answer the question:
shared vs. unique variance explained by regression predictors
partitioning SS
multiple regression and partial correlations
