This report from Shareaholic came out in March (https://blog.shareaholic.com/social-media-traffic-engagement-03-2014/) but it's worth repeating. Here's their findings:
"Although Google+ and LinkedIn drive the fewest social referrals, they bring in some of the best visitors. Google+ users, on average, find themselves spending north of 3 minutes diving into things shared by connections in their circles. They also visit 2.45 pages during each visit, and bounce only 50.63% of the time. LinkedIn users generally spend 2 minutes and 13 seconds on each link they click, viewing 2.23 pages with each visit and bouncing 51.28% of the time. Although many sites see minimal traffic from both Google+ and LinkedIn, now may be the time to invest in building communities within those networks if engagement really matters to your business."