hi, I don't think so Google PR is updated based on quality of the web site, load time and also Content.
SERP's mostly depends on your content and how frequent you update it but PR mostly depend on the backlinks.
According to my experience google PR update have influence on search engine ranking. If your site backlinks gets Good PR then Your site automatically go to top in search engine. thanks
Focus on getting quality links to your blog and focus on writing quality content, and you will soon experience an increase in pagerank and search engine traffic.
Well there are different point of views mentioned above. still i believe that the first thing that effect are keyword density, after that backlinks, then PR and finally the domain age. In case the websites are of same age then they will be ranked on the basis of good PR taking all else features constant.
Google page rank doesn't effect your site ranking but you just need quality backlinks to improve your site serp results.
PR of the website does not increase serp, but a link from a good pr page with specific anchor text does increase serp for that keyword
google page rank is necessary for get good rankings and increase the site's reputation in search engine. Page rand totally depends on website's inbound links.
Google page rank & search engine ranking both are different assets, page rank is issued depending upon the site performance, design, quality, content etc, while search engine ranking means, for which keywords the site is optimized to show up in serp's, even a low PR website can rank high in serp, so don't worry.