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Definition of Influential points

Influential points Definition from Science & Technology Dictionaries & Glossaries
Common Concepts in Statistics
Observations that actually dominate a regression analysis (due to high leverage, high residuals or their combination). The method of ordinary least squares gives equal weight to every observation. However, every observation does not have equal impact on the least squares results. The slope, for example, is influenced most by the observations having values of the independent variable farthest from the mean. An observation is influential if deleting it from the dataset would lead to a substantial change in the fit of the generalized linear model. High-leverage points have the potential to dominate a regression analysis but not necessarily exert an influence (i.e., a point may have high leverage but low influence as measured by Cook statistics). Cook statistics is used to determine the influence of a data point on the model.