Using correlations to re-label data from Google Analytics In my Google Analytics data a lot of traffic gets mis-labelled as "Direct" because Google doesn't know the original traffic source.
I've taken 6 months worth of our "Direct" traffic data and calculated the correlation of that to other traffic channels, such as Organic and Social. There is a moderate correlation between Social and Direct.

My question is... is there a way to adjust the traffic numbers for "Social" (in a spreadsheet) to include some of the traffic from "Direct", knowing that there's a correlation between them?
Eg, say GA currently reports 1,000 social visits and 5,000 direct, can I attribute some of the direct to social, like: Social might now be 2,000.
Although I know the levels of correlation, there's no way of telling how much Direct is actually direct of course, so I don't know if this calculation is possible, or if there is a scientific way of going about the process.
I accept this wont be truly accurate or definitive, I'm looking at this as more of an indicator.
Thanks!
 A: The total amount of Traffic is a deterministic function of Social, Direct, Referral, and Z (just pretend Z is all other sources combined - you can split them out separately yourself if you want).
$$\text{Traffic} = \text{Social} + \text{Direct} + \text{Referral} + \text{Direct}$$
Now what I believe would be useful to your situation is an estimate of the indirect effect of the amount of Social traffic on the other sources. I'm pretty ignorant of SEO, but I imagine getting mentioned alot on popular social network sites boosts your page rank, and so indirectly increases traffic from either higher search results (or other unknown sources). We can illustrate this is a path model as below:

Because Traffic is deterministic I simply placed 1's on those paths. The indirect effect then of social on the total amount of traffic through direct is the first path multiplied by the second path (in linear models), which is simply $1 \cdot d = d$. To fill in the blanks for $d$, $r$, and $z$ you need the covariances between Social and the indirect paths. 
There are actually more informative ways to draw the diagram though, but it all stems from estimating these variances and covariances. It is typical to estimate the correlations and then fill in the paths based on the correlations and partial correlations. Another informative way though may be after you estimate the partial correlations is to rescale the diagram so that all arrows going into Traffic sum to 100. Then the direct effects on Traffic can be interpreted as percentage totals, and the indirect effects can be interpreted as the decomposition of the indirect effect of social. (This interpretation gets a bit strange though if you have negative correlations.)
This is of course a simplification. It is likely that the arrows between social and the indirect effects are not single headed, there could certainly be reciprocal effects. But I'm hoping this is a useful abstraction.
