A Classification of Single Influential Observation Statistics in Regression Analysis

The results of least squares fit of the general linear model Y=Xβ+ε 1 to given data set can be substantially influenced by omission or addition one or few observations. Therefore, the least squares method does not ensure that the regression model proposed is fully acceptable from the statistical and physical points of view. Usually one of the main problems is that all observations have not an equal influence in least squares fit and in the conclusions that result from such analysis. The detection, assessment, and understanding of influential observations are the major areas of interest in regression model building. It is important for a data analyst to be able to identify influential observations, assess and understanding their effects on various aspects of the analysis. They are rapidly gaining recognition and acceptance by practitioners as supplements to the traditional analysis of residuals. Residuals play an important role in regression diagnostics; no analysis is complete without a thorough examination of the residuals. The standard analysis of regression results is based on certain assumptions for more information we refer to [1], [2] . It is necessary to check the validity of these assumptions before drawing conclusions from an analysis [3].