I made a study on the exact relationship between Page rank and Back links published here:
http://www.seochat.com/c/a/Google-Optimization-Help/Back-Links-and-Google-Page-Rank/.
Basically it does not convince to be page rank freaks as it does not offer as much useful value like content , web page loading time and conversion rate.
Anyway, it was fun. And this is the raw data that is used in the experiment.
You can do your own analysis and experiments. I am using the native Google page rank toolbar and Yahoo site explorer for data gathering since it involves a lot of websites, and I cannot use Google webmaster tools data.
Google page rank is so much depreciated nowadays it is not even provided under Google webmaster tools report. But I still believe Page rank is still a measurement of domain authority which has been admitted frequently by Google like in this page: http://www.mattcutts.com/blog/google-search-event/. So if Page rank strongly correlates with backlinks it means that to become an authority or increase your authority, you simply need links.
Lot of mistakes in SEO commonly focuses on getting links ignoring value in content. The golden rule is to write content to get links, not get links then getting content after.
