Background: The objectives of this study were to (1) simultaneously estimate genetic parameters for BW, feed intake (FI), and body weight gain (Gain) during a FI test in broiler chickens using multi-trait Bayesian analysis; (2) derive phenotypic and genetic residual feed intake (RFI) and estimate genetic parameters of the resulting traits; and (3) compute a Bayesian measure of direct and correlated superiority of a group selected on phenotypic or genetic residual feed intake. A total of 56,649 male and female broiler chickens were measured at one of two ages (t or t- 6 days). BW, FI, and Gain of males and females at the two ages were considered as separate traits, resulting in a 12-trait model. Phenotypic RFI (RFI P(RFI P) and genetic RFI (RFI RFI G) were estimated from a conditional distribution of FI given BW and Gain using partial phenotypic and partial genetic regression coefficients, respectively. Results: Posterior means of heritability for BW, FI and Gain were moderately high and estimates were significantly different between males and females at the same age for all traits. In addition, the genetic correlations between male and female traits at the same age were significantly different from 1, which suggests a sex-by-genotype interaction. Genetic correlations between RFI RFI P and RFIG RFI G were significantly different from 1 at an older age but not at a younger age. Conclusions: The results of the multivariate Bayesian analyses in this study showed that genetic evaluation for production and feed efficiency traits should take sex and age differences into account to increase accuracy of selection and genetic gain. Moreover, for communicating with stakeholders, it is easier to explain results from selection on RFI RFI G than selection on RFI RFI P, since RFI RFI G is genetically independent of production traits and it explains the efficiency of birds in nutrient utilization independently of energy requirements for production and maintenance.