The hip and lumbosacral joint centre (HJC and LSJC) predictions are required to analyse the lumbo-pelvic-hip dynamics during various human motions. Some HJC and LSJC regression equations based on pelvic dimension have been developed; however, the pre-existing methods need to be re-evaluated, and methodological reconsideration may improve the regression methods. Here we show that pre-existing methods produce biased predictions of the LSJC and HJC in 23 male and 24 female Japanese adults, and that the biases in the LSJC differ between sexes, using magnetic resonance imaging (MRI) around the pelvis. Compared with directly measured locations on MRI, the pre-existing regression equations predict LSJC to be more posterior in males and more inferior and posterior in females, and HJC to be more medial in both sexes. The better pre-existing regression equation for LSJC height differs between sexes, with pelvic-width-base better in males and pelvic-depth-base better in females, respectively. We suggest the unsuitability of pre-existing methods to our dataset consisting of Japanese adults and the importance of considering sex differences in regression methods. We propose regression equations to predict HJC and LSJC, considering soft-tissue thickness, sex differences, and a height-directional measure, using least absolute shrinkage and selection operator regression. We validate them using leave-one-out cross-validation (LOOCV). LOOCV shows that our model produces negligible biases and smaller absolute errors than the pre-existing regressions; in particular, the anteroposterior absolute error for LSJC is less than half that of the pre-existing regression. Our regression equation can be a powerful solution for accurate motion analysis.