-It helps in the ranking because it will have your pages in the main index not in the supplemental index. Pages that do not have page rank data are placed in supplemental and would be very hard to rank.

-You can maximize your website potential during a link exchange process. This is because if you have 16 pages in the website and only one page (the homepage) got PR of 3 and the others are zero. You can actively promote only one page because some link exchange partners are selective of page rank. But if you have 16 pages with all in PR 3, imagine the potential link partners you could have.

-Page rank is highly correlated with crawling frequency as observed in high PR sites with high crawling frequencies than those lower ones or with no PR at all. This means that if you have a home page of PR 5, and you spread your PR throughout the internal pages. This will increase the probability of Googlebot crawling the internal pages.

I have done an experiment using a Java page rank simulator and I would like to establish the complete relationship among the number of links per page and the page rank of that page. Based on the experiment, below are the results:

a.)The links per page has some direct affect on page rank distribution.
b.)The higher variation of your links per page, the higher will be variation in the page rank of the site.

This suggests that:
-to have a consistent page rank in the pages use a consistent navigation per page and maintain a consistent number of links per page.

Below is a snapshot of the coefficient of variation analysis among page rank of every page and number of links in every page. This means that a 45% variation in links per page of the entire site will produce a 30% variation in page rank for the entire site pages.

Please see below for the plot of the analysis:

Based on this plot, apparently the variations among the statmax (mean + standard deviation) and statmin(mean-standard deviation) are very similar. Graphically we can say domain page rank has no significant affect on Google ranking. Now, to confirm this, a ANOVA is conducted with the following hypothesis:

Null Hypothesis: Domain Page rank has no effect on Google search engine ranking.
Alternative Hypothesis: Domain page rank has effect on Google search engine ranking.

Confidence level: 95%

Rejection/Acceptance of Hypothesis Criteria:
1. Accept null hypothesis if anova p-value is greater than 0.05
2. Reject null hypothesis if anova p-value is less than 0.05

Below are the ANOVA result:

Based on the result, p-value is about 0.65 so it means to accept the null hypothesis that domain page rank has no effect in Google search engine ranking.

What this study suggests in your quest for high search engine ranking?
1. Do not be obsessed with domain page rank when you want to rank high in Google.
2. Do not focus on increasing your page rank to increase your ranking.
3. High page rank does not mean high relevance (as high position results in Google are high relevant results to a search query).

PR tool bar = log (Backlinks) to the base X

where “Backlinks” is the total amount of backlinks from other domains pointing to the entire site.
“Base x” is the base of the logarithm not being solved so far. It is used to convert the actual back link data to a friendly Google Page rank measurement we seen in their toolbar, which will update every 3 months.

In this post I would like to calculate the value of “x”. So my objective will be to calculate the base of the logarithm used by Google to export it to the toolbar. Though this is not guaranteed to be accurate because the tool bar data is just a snapshot in time, it is not a real time one. So to define variables:

PR tool bar = log (Backlinks) to the base X , can be written as:

x ^ PR tool bar = backlinks , by principle of logarithm

then, taking the logarithm of both sides of the equation:

PR tool bar * log x = log (backlinks)

All logarithms are assuming at the base 10 above.

Then :

Log x = (log (backlinks))/ (PR toolbar)

Say we will equate:

Y = (log(backlinks))/ (PR toolbar)

Finally we can solve for x as:

x = 10 ^ Y
By principle of relationship in converting logarithmic to exponential and vice versa.

I do not know the value as it needs to gather actual data. But the principle is presented above.