well for the past decade that bitcoin market existed it never depended on any other market and has never been affected by any of them. there is no reason for it to start now either so checking these things is pointless.
the only thing i personally consider when buying bitcoin is first the benefits of using bitcoin as the only available decentralized censorship resistance global currency and the long term potential that it offers.
Hmm but the general trend is that when US market tends to do well, Bitcoin prices will rise too. As for the correlation, I'm not too sure about that because I don't have the specific market data to test for the correlation. I feel that it could also be the case whereby the news that benefits the US economy tends to paint Bitcoin in a more positive outlook as well. The recent rise can no doubt be attributed to the purchase of Bitcoin by the investment firms but it could also be related to the upbeat news of Covid vaccine as well.
Would be great if any economist or someone with skills that relate to the expertise to weigh in on this though.