Statistics Dictionary

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Influential Point

An influential point is an outlier that greatly affects the slope of the regression line. One way to test the influence of an outlier is to compute the regression equation with and without the outlier.

This type of analysis is illustrated below. The slope is larger when the outlier is present, so this outlier would be considered an influential point. Sometimes, an influential point will cause the coefficient of determination to be bigger; sometimes, smaller. In this example, the coefficient of determination is smaller when the outlier is present.

Without Outlier
Regression equation: ŷ = 104.78 - 4.10x
Coefficient of determination: R2 = 0.94

With Outlier
Regression equation: ŷ = 97.51 - 3.32x
Coefficient of determination: R2 = 0.55

See also:   AP Statistics Tutorial: Influential Points