also racket brand is categorical data thus it cant necessary be compared to the unforced errors which are quantitative and correlation doesn't imply causation so.
It is always true that correlation does not imply causation.
But most of the time the scientific method works by disproving hypotheses, not by proving them. The longer a hypothesis survives and the more tests that fail to disprove a scientific hypothesis, the more likely there is to be something to it.
So while correlation does not imply causation, the absence of correlation does disprove a hypothesis of causation in a properly designed experiment. Experiments that disprove or fail to disprove an interesting hypothesis are themselves relevant and interesting and commonly published. In contrast, I almost always recommend rejection of papers that claim to have proved something. Failing to disprove something is
support, not proof.
In most cases, a strong correlation can be said to
support a hypothesis in a well designed experiment.
Racquet brand is categorical data, and in most cases of sporting equipment, it is better to use exact make and model. However, a lot of pro equipment is so specialized that make and model are no longer meaningful, which would then require an experimental design that defined some class features that could be known and quantified. But in most cases, the data will not be available for this design.
Most well designed stats experiments hope that potential confounding factors (like athlete ability in this case) cancel each other out through equivalent pools and good sample sizes. I doubt that will be the case with sporting equipment, because in most cases, one manufacturer spends a lot more money paying athletes to use their equipment so the pool of players using one brand is not comparable to the pool of players using another brand.
