How to increase google page rank?

Why there is an inverse relationship between page rank and keywords rank in google?
When keywords rank increases, page rank in google decreases. Do you know the relationship between page rank and keywords rank in google?

It is just coincidence, I'm sure. A lot of high PR sites are on page 1 of SERP.

With that, to answer the question on the title of your post, you need to add more links from high PR pages.

Not really sure what you are asking....

Your actual PR does not greatly effect your ranking for specific keywords.

In my opinion, PR is more of an evaluation of onsite factors while keyword rank is based more off of off site factors such as backlinks (of course, onsite optimization is important too).

maybe this thread can help me to understand better in SEO. i'm still learning seo