AN ALTERNATIVE DISTRIBUTION OF INTERNAL STUDENTIZED RESIDUAL AND IDENTIFICATION OF OUTLIERS THROUGH EVIDENCE PLOTS

David Sam Jayakumar, Sulthan A

Abstract


This paper proposed the exact distribution of internal studentized residual which used to evaluate the outliers in X and Y space in linear multiple regression analysis. The authors explored the relationship between the internal studentized residual in terms of two independent t-ratio, F-ratio’s and they show the derived density function of the residual in terms of Gauss hyper-geometric function. Moreover, the new form of the distribution is symmetric, first two moments of the distribution are derived and the authors computed the critical points of internal studentized residual at 5% and 1% significance level for different sample sizes and varying no.of predictors. Evidence plots were also proposed to evaluate the exact position and location of the outliers. Finally, the numerical example shows the results extracted from the proposed approaches are more scientific, systematic in identifying the outliers in both spaces(X and Y) and its exactness outperforms the traditional Weisberg test.


Keywords


Internal studentized residual, X,Y space, outliers, t-ratio, F-ratio, Gauss hyper-geometric function moments, critical points, evidence plots, Weisberg test

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