Meaning: a partial correlation between happiness and one of the correlates is that correlation, which remains after accounting for the contribution of the other influences, or some of them, to the total variability in the happiness scores.
Under that conditions
rpc > 0 « a higher correlate level corresponds with a higher happiness rating,
rpc < 0 « a higher correlate level corresponds with a lower happiness rating,
direct effects of sporting, physical health and psychological coping capacity partialed out