An influential observation in statistics refers to a data point that significantly affects the results of a statistical analysis, particularly in regression models. These observations can have a disproportionate impact on the estimates of parameters (such as regression coefficients), the overall fit of the model, and predictions made by the model.
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An influential observation substantially changes a fitted model or its predictions when removed or perturbed. In a linear regression, influence depends jointly on residual size and regression leverage. Large predictor leverage with a small residual and a large residual at ordinary leverage can have different consequences. Regression diagnostics examine this sensitivity; influence is not synonymous with an invalid observation.