I just signed up with a hosting program, and they are offering PR6 links on their site for clients. If I just submit a link to them that has no relevance to hosting, will Google treat my link from their site as having no value in the PageRank algorithm?
i think the pr of your site would play more of a role than whether or not you're in the same niche. for example, i'd rather get an irrelevant pr6 than a relevant pr2 link.
like what shockie already said, prioritize the pr over relevancy. it would be a good help if they offer a follow link so their pr juice goes to your site, and also they are also linked up by higher pr sites as well.
PR and SERP ranking are 2 different things. getting a PR6 link will certainly increase your site PR. how much that will benefit you in terms of SERP ranking is hard to tell but surely it will help
I think that you can try that aqnd look how it is going. I think that would be quite difficult to decide without trying
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Basically it isn't really a major factor in the PR algorithm if the site linking back to you is in your niche or not since if it were working ideally (and there weren't link sellers, etc), people would just link to sites they find useful from their own site which isn't necessarily relevant.
PR is based on number of dofollow links pointing to you. PR is also dependent on the number of outgoing links on the page where your link would be placed. The more outgoing links - the less PR juice you would recieve.
It is worth trying of course if it is relevent to your site it will be seen as higher value, but either way a link for nothing is a good link especially from a PR 6 site.
Google tries to return the most relevant results for a given search. One way Google does so is by searching for and analyzing keywords on pages of other websites that link to your site. What other sites “say” about your site through their link text, the title of their Links page, and the content of their Links page can be almost as important as what your own web pages say! This means that the quality of links may be as important as the quantity of links to your site.
You could have hundreds of pages linking to your site, but if the text of those links doesn’t match your keywords, or if the linking page content is not related to your site, those links by themselves probably won’t add any appreciable boost to your ranking.