It doesn’t seem unplausible, but that’s not the point of doing research. The causality could be the other way round (people who are mentally fit also enjoy spor

It doesn’t seem unplausible, but that’s not the point of doing research. The causality could be the other way round (people who are mentally fit also enjoy sports more, or see more benefits in doing it), or it could be driven by unobserved variables, like influence from your family or friends that leads you to both study and work out hard. What you’re interested in is the treatment effect of doing sports vs not doing sports. With enough and the right kind of data you could try to estimate this effect while accounting for the potential endogeneity. Randomized experiments are a good way of generating such data, but even then the inference is tricky (subjects will know whether they are in the treatment or control group,...).