At the bottom of vendor profile, there is an text box for you to insert your GA code.
Question: what does this do? What kind of stats am I expected to see in Google Analytics? I don't have the luxury of trial and error at the moment.
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If you list your Google Apps domain at your Google Analytics account, a key is generated (as your picture is showing: UA-??????-?)
This code can be entered into your Google Sites, to monitor web site behaviour:
If you enter this code for the vendors Marketplace app, then user behavior on document level, intranet level or web site level can be monitored.