A firm handshake is associated with confidence and assertiveness. Those qualities can also come from being physically strong, and a study of Brazilian soldiers published in the journal Medicina dello Sport suggests there might be a relationship between grip strength and total muscular strength.
Researchers tested 50 subjects for the grip strength of both dominant and non-dominant hands. They also measured core strength along with upper and lower body limb strength. The strongest correlations were between grip strength and dominant limb strength as well as grip strength and total muscular strength.