Joint impact of multiple observations on a subset of variables in multiple linear regression

In multiple linear regression analysis, each observation affects the fitted regression equation differently and has varying influences on the regression coefficients of the different variables. Chatterjee & Hadi (1988) have proposed some measures such as DSSEij (Impact on Residual Sum of Squares of simultaneously omitting the ith observation and the jth variable), Fj (Partial F-test for the jth variable) and Fj(i) (Partial F-test for the jth variable omitting the ith observation) to show the joint impact and the interrelationship that exists among a variable and an observation. In this paper we have proposed more extended form of those measures DSSEIJ, FJ and FJ(I) to deal with the interrelationships that exist among the multiple observations and a subset of variables by monitoring the effects of the simultaneous omission of multiple variables and multiple observations.