Relation between bitcoin price and other cryptocurrencies prices If bitcoin price goes up, Will that increase the value of the other cryptocurrencies? 

Edit: If yes, then WHY? Seems a mystery for me since I guess every coin has its independent price. 

Thank you
It depends, obviously. Short answer, yes.

Bitcoin used to make up a huge percentage of the value of all Cryptocurrencies, so obviously since Bitcoin was the largest and most used, if it were to crash or change in price drastically, obviously most of, if not all other cryptocurrencies would be affected.

Bitcoin still makes up a large percentage of the Cryptocurrency Market Cap, over 34% on January 25, 2018, followed by Ethereum with 18%.

This is important not to be mistaken though. Perception is what controls the price of Cryptocurrencies.

since bitcoin is the leader of all cryptos, if news were to come out that someone figured out how to exploit it's "proof of work" algorithm, or something giving Bitcoin a negative perception, it would loose value.

Because Bitcoin is so prominent in the crypto world, all other coins would be impacted too, because its literally the "leader".

of course if news comes out that a very small and unknown cryptocurrency would grant you super powers if you owned enough, just that cryptocurrency would go up, not really impacting others because it doesn't have a large market cap.

So in short, the larger market cap, the larger the impact on other currencies