Relationships between yield components and lint yield are complicated because of interrelationships among them. Traditionally, the exploration of these interrelationships was analyzed by path coefficients which requires a priori knowledge of the cause and effect relationships. Commonality analysis is a method of multiple regression to dissect the total effects of yield components to yield into direct effects and indirect effects. This study was designed to dissect relationships of yield components to yield based on commonality analysis and determine correlated selection responses of yield to selections of different yield components. Selections were made within 300 F3 plants in 2017 for the top seventy-five plants by LP and six within-boll yield components, lint weight per seed, seeds per boll, seed surface area, lint weight per fiber (LWF), lint weight per unit seed surface area, and lint number per unit seed surface area. F4 progenies were evaluated in field with two replicates in 2018. Direct coefficients of the seven single yield components ranged from 0.00 to 0.18 with LP as the largest contributor. Indirect coefficients of multiple components ranged from − 0.04 to 0.08. Five single yield components and five multiple yield components were chosen for selections based on their relatively large coefficients to yield. The correlated selection response (CR) of lint yield, 1684 kg ha−1, in F4 was significantly positive to selections by LP, but the CR of seed size and fiber length was negative to the selection by LP. The CR of lint yield, 1769 kg ha−1, to selections by multiple yield components of LP-LWF, had 5% increase compared with the selection by LP alone. There was no significant CR of seed size and fiber length to these selections. This study was a first application of commonality analysis in crop breeding and results provide evidence for its feasibility in exploration of interrelationships among yield components in breeding.