This paper proposes a new procedures for assessing the influence of individual or groups of cases when any regressors are included. At first, various influence measures pickout influential cases when one regress-or is deleted. Next find influential subsets by using heuristic approach and perform group deletion. Retaining or removing any regressors may depend on the presence or absence of one or few cases. Then, we can identify the interrelationships that exist among regressors and cases and examine their impact on the fitted regression equation. We conclude with an example using fuel consumption data.