It will not be a direct correlation. This is because puzzles only measures one aspect of the game of chess. That being tactics. As you increase your puzzle rating that will help you recognize tactics patterns, and being able to calculate more moves ahead with more concreteness. As you get better you will need to learn more aspects of the game. When you get to around 1000 range in rapid (maybe 900) you will need to start learn about other aspects of the game (just the basics at that time). You primarily should still work on tactics though because that is what decides most game.
Correlation between puzzles and rating
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I KNOW it’s not a direct one to one, but has anybody seen their rating increase as their puzzle rating went up? Obviously your play rating is a lagging indicator. Hard to tell when you get better at chess that it’s related to puzzles UNLESS you KNOW you saw a pattern similar in a puzzle and had an aha moment