Is there a way to estimate the price based on the blockchain? Suppose I need a rough estimate of the current value of BTC in USD, is there anything in the blockchain that could be used for that? For example, is there some kind of correlation between block difficulty vs price, number of transaction vs price, etc?
I wrote a bitcoin price theory is about a correlation of number of bitcoin addresses 
(from blockchain) and the bitcoin price, with a law of networking use like the metcalfe law.

here I posted my study about your question

https://bitcointalk.org/index.php?topic=441336.0