An influential point in a statistical data set is an observation whose removal produces a substantial change in a fitted model, meaning a model whose coefficients or other parameters have been estimated from the data. In linear regression, influence may be measured by the changes in estimated regression coefficients, fitted values, or residual variance after deleting the observation. A fitted value is the response predicted by the fitted model at the observed values of the independent variables, also called predictor variables.
Influence is distinct from leverage, which quantifies how unusual an observation's values of the independent variables are relative to the other observations. A leverage point therefore has the potential to affect the fit, but it need not be influential if it follows the fitted relationship. Conversely, a point with a large residual may have little influence when it does not have high leverage. An influential point typically combines high leverage with a residual large enough to move the fitted model.
