This chapter focuses on the joint estimation of the regression parameters and the intraclass correlation (ICC), and shows how measured covariates affect the point estimation and the precision of the ICC. Regression analysis is among the most commonly used methods of statistical analysis to model the relationship between variables. Its objective is to describe the relationship of response with independent or explanatory variables. It is well known that the method of least squares is the most preferred method of estimation of the parameter of the regression model. The chapter analyses the sib-ship data that have two levels of hierarchy; the first is observations from sibs and the second is formed by the family identifiers. For family study, the clusters are formed by families, and in the second example a cluster comprises the repeated observations for a child. Clusters are aggregates of individuals or items that are the subject of investigation.