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Leverage


Leverage in linear regression measures how unusual an observation's values of the independent variables are relative to those of the other observations. If X is the full-column-rank design matrix, the projection matrix

 H=X(X^TX)^(-1)X^T

maps the observed response vector to the vector of fitted values. The leverage of observation i is the diagonal entry h_(ii). If X has p columns and n rows, the leverages sum to p and therefore have average p/n. An observation having unusually large leverage is called a leverage point.


See also

Design Matrix, Fitted Value, Influential Point, Leverage Point, Linear Regression, Projection Matrix

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References

Belsley, D. A.; Kuh, E.; and Welsch, R. E. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: Wiley, 1980.

Cite this as:

Weisstein, Eric W. "Leverage." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Leverage.html

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