Is regulations among the key factors that affects the price of Bitcoin
It would be foolish to say it woudn't affect. You can deduct that yourself just by thinking.
Let me put this as simplified as i can:
Ask yourself few questions:
Would rules of the marketplace affect to how people behave in the marketplaces?
Would fear of jail sanctions make these people follow the rules?
Would people be more inclined to buy stuff with low taxation in opposition to low taxed?
Would banning some of the customers and marketplaces in general affect sales?
Would people in general trust more to CEXes if they had more oversight and legal protection?
Would institutional investors rather invest in regulated serious market in cexes, rather than depositing their money to potential exit scams?
Answer is yes to all of these, and they are basically same question as yours sectioned in different parts.
HOW is it affecting to price depends on what the regulations are. It can be positive or negative.
Imho there are more upsides with regulations than downsides, even when we are talking about just the price.