Attributing causality to single quasi-independent variable Apologies if this isn't the correct place to ask - I'm not sure if this fits best with Stats or Data Science.

I'm using analytics to help marketers identify attributes of their users correspond to successful conversions (such as someone buying a product, signing up for a newsletter, or subscribing to a service). Attributes could be things like which site they came from (referrer), their location, time/day of week, device type, browser, etc.

What I'd like to say (although I'm not certain it's possible) is to isolate differences in conversion rate to an individual attribute, something like, '11% of your users from Facebook converted whereas only 3% of non-Facebook users converted', which would mean that the attribute 'referrer' and the level of the attribute 'Facebook' are responsible for driving conversions.

Given that I may have 100s of quasi-independent variables, is it even possible to isolate the effect to one variable and one level of that variable? As opposed to a combination of them that is more likely to be driving the difference? If so, what technique or conceptual paradigm do I use to identify which variable-level is responsible for the greatest lift in my dependent variable, conversion rate?
I would suggest you to consider either direct dimensionality reduction approach. Check my relevant answer on this site. Another valid option is to use latent variable modeling, for example, structural equation modeling. You can start with relevant articles on Wikipedia (this and this, correspondingly) and then, as needed, read more specialized or more practical articles, papers and books.