When stating the results of previous research (the "findings") in academic writing, the word "found" is a completely acceptable and very commonly used term, so your original sentence is fine. In fact "found" is more conventional than either "noted" or "reported" in the context of academic writing, both of which sound less certain than "found". They might be more likely to be used to describe something that was mentioned in a research paper but wasn't part of the main results (e.g. "it was noted that participants in the study appeared anxious").
Also, although this wasn't your original question, it might be a good idea to be more specific about the nature of the association between x and y. It sounds like perhaps you mean "correlated" but that isn't clear, as two variables can be "associated" in different ways and it's important when reporting research findings to be clear about this.