: Multiple regression with correlated explanatory variable is relevant to a board range of problems in the physical , chemical and engineering sciences. Researcher from different branches of science in particular have made heavy use of principal components regression and related procedures for predicting a response variable from a large number of highly correlated variables. A response variable from a large number of highly correlated explanatory variables. In multiple regression models, regression coefficient estimator may perform poorly when there are near multicollinearrties in the matrix of explanatory variable. Increasing the number of variables also lead to increase the number of correlation coefficient. So we need those methods which decrease the dimention of variables. In this thesis principal component regression is considered as main method with target of decreasing dimention of variables. Using this method these principal components will be selected, that yield estimates of regression coefficients with low mean squared error.