2. the correlation for facebook likes is 0.27. that's lower, but not by much.
3. its possible the causality runs the other direction: high quality results get more +1s
2. the correlation for facebook likes is 0.27. that's lower, but not by much.
3. its possible the causality runs the other direction: high quality results get more +1s
Your point #3 is critical: high quality things get more +1s (and tweets, and Facebook likes or comments or shares).
This brings up the interesting question of why other social media is used less for promotion of effective pages. More zombie / spammers / scammers / PR firms manipulating facebook likes than +1s? This seems extremely likely given the known "underground" like-market and incentives WRT FB.
The .3 correlation with a large sample size means something is happening. I agree with what Matt is saying: that content that gets +1s also gets links and mentions and everything else that Google might use to calculate rankings.
So how much is 'weak' or not depends on the situation. If you have something that is influenced by multiple causes, then it is impossible to have any single high correlation. But any correlation, if statistically significant (i.e. highly unlikely to be caused by chance) can be important.
The question is, how much is an 'interesting' amount of the total variance, in the given situation.
(In the topic under discussion here, I have no idea.)
The other possibility is a good piece of content earns links, has great user metrics for certain keywords, lives on a great site, etc. and ranks well. It then accumulates social shares on top of that, further confirming the quality of the content. Thus...you get a situation like #3. Social signals make sense for indexation, but beyond that, until you start to understand the importance of the author (cough, AuthorRank, cough) then you can't use them for much more then understanding what the "mob" is finding valuable at the moment. And it might be a very fleeting fascination on a subject that really doesn't deserve to hold a ranking.