On thinking quantitatively of complex diseases, there are at least three statistical strategies for association studies: one single-nucleotide polymorphism (SNP) on a single trait, gene or region (with multiple SNPs) on a single trait, and gene or region on multiple traits. The third approach is the most general in dissecting genetic mechanisms underlying complex diseases underpinning multiple quantitative traits. Gene or region association methods based on partial least square (PLS) approaches have been shown to have apparent power advantage. However, few approaches have been developed for multiple quantitative phenotypes or traits underlying a condition or disease, and the performance of various PLS approaches used in association studies for multiple quantitative traits have not been assessed. Here we exploit association between multiple SNPs and multiple phenotypes or traits, from a regression perspective, through exhaustive scan statistics (sliding window) using PLS and sparse PLS regressions. Simulations were conducted to assess the performance of the proposed scan statistics and compare them with existing methods. The proposed methods were applied to 12 regions of genome-wide association study data from the European Prospective Investigation of Cancer-Norfolk study.