In this book, an attempt has been made to propose some new estimation procedures for the linear regression models such as elemental slopes methods, Grouping method, Hat diagonals method, and Dispersion and Correlation methods for estimating for estimating the parameters of the linear regression models. The proposed methods have been applied to two and three variables linear models for their validity.In this book Introduction given in the Chapter I, some important existing estimation procedures such as OLS, GLS, WLS, RLS and ML have been described in Chapter II. A brief about the review of the literature has been described in chapter III. In Chapter IV, some new estimation methods namely Elemental Slopes method, Grouping method, Hat diagonals method and Dispersion and Corrrelation methods have been proposed and applied to two and three variables linear models for their validity. The summary and conclusions besides the suggestions for future research, have been give in Chapter V. The slected list of research articles has been presented under Bibliography.