Heritability estimates a polygenic effect on a trait for a population. Reliable interpretation of heritability is critical in planning further genetic studies to locate a gene responsible for the trait. This study accommodates both single and multiple trait cases by employing regression models for correlation parameter to infer the heritability. Sharing the properties of regression approach, the proposed methods are exible to incorporate non-genetic and/or non-additive genetic information in the analysis. The performances of the proposed model are compared with those using the likelihood approach through simulations and carotid Intima Media Thickness analysis from Northern Manhattan family Study.