This work deal with biased estimation methods for estimating the parameters of general linear regression model when the data are ill-conditioned. We focus our attention on ordinary and generalized ridge regression estimators, Jackknife ridge estimators and principal components estimators. In chapter one introduction and historical review In chapter two basic concepts, definitions on linear regression model are presented. Moreover, the statistical properties of the ordinary least squares estimators are presented. Classes of biased estimators are discussed in chapter three when the data suffer...