I come with a supplement to what you said if I can.
Page authority is a very important SEO factor for the performance of a web page in Google search results. Unlike Page Rank (another patented Google SEO factor and much more popular), which is a unit of measure from 1 to 10, the authority of the page (or page authority) is measured on a logarithmic scale from 1 to 100.
That means it's easier to get from 20 to 30 than from 80 to 90.
The authority of a page is an indicator for Google that that page provides quality content and is an online "authority" in the field. For example, Wikipedia's pages enjoy great authority, as well as those on newspaper websites, education sites, and so on.
How can you increase the authority of the page?
Algorithms after which Google calculates the authority of a page are complex, always change, and are not formally presented to the general public.
However, it can be deduced that the content value, the age of the site and the quality links (on pages with high authority) are the main elements that should be emphasized by a webmaster concerned with the growth of this SEO factor.
The more your site is perceived by Google as one that offers value to visitors, it provides useful content, and it will give you greater authority.
Comments and impressions, likes on FaceBook and + 1s in Google+, and other social networking activity visitors also tend to become more and more important for Google to indicate the value of a page's content.