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I have written this book for those students studying statistics and mathematics.The need for this book as become apparent in many years with several students having only classical back ground. We consider when it missing in Y,The aim of this book is to help in solving the problem when missing in both side and outliers exist.This book proposes simple but very interesting robust single imputation technique which gives more accurate estimates over the classical single imputation technique in the presence of outliers. we also considered a situation in which observations are missing in the X explanatory variable. In this respect, the Dummy Variable (DV) approach is one of the best approaches to predict the missing data model. However, this approach also becomes poor in the presence of outliers. As an alternative, Robust Inverse Regression Technique is proposed to get the better estimate. By examining the real data and Monte Carlo Simulation studies, it revealed that our proposed robust methods perform better than the classical methods.