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In [[regression analysis]], '''partial leverage''' ('''PL''') is a measure of the contribution of the individual [[independent variable]]s to the [[leverage (statistics)|total leverage]] of each observation. That is, if ''h''''i'' is the ''i''th element of the diagonal of the [[hat matrix]], PL is a measure of how ''h''''i'' changes as a variable is added to the regression model. It is computed as:

:<math>
\left(\mathrm{PL}_j\right)_i = \frac{\left(X_{j\bullet[j]}\right)_i^2}{\sum_{k=1}^n\left(X_{j\bullet[j]}\right)_k^2}
</math>

where
:''j'' = index of independent variable
:''i'' = index of observation
:''X''''j''·[''j''] = [[errors and residuals in statistics|residuals]] from regressing ''X''''j'' against the remaining independent variables

Note that the partial leverage is the leverage of the ''i''th point in the [[partial regression plot]] for the ''j''th variable. Data points with large partial leverage for an independent variable can exert undue influence on the selection of that variable in automatic regression model building procedures.

==See also==
* [[Leverage (statistics)|Leverage]]
* [[Partial residual plot]]
* [[Partial regression plot]]
* [[Variance inflation factor]] for a multi-linear fit

==References==
* {{cite book
|title = Modern Regression Methods
|author = Tom Ryan
|publisher = John Wiley
|year = 1997}}
* {{cite book
|title = Applied Linear Statistical Models
|edition = 3rd
|author = Neter, Wasserman, and Kunter
|year = 1990
|publisher = Irwin}}
* {{cite book
|title = Applied Regression Analysis
|edition = 3rd
|author = Draper and Smith
|publisher = John Wiley
|year = 1998}}
* {{cite book
|title = Residuals and Influence in Regression
|author = Cook and Weisberg
|publisher = Chapman and Hall
|year = 1982}}
* {{cite book
|title = Regression Diagnostics
|author = Belsley, Kuh, and Welsch
|publisher = John Wiley
|year = 1980}}
* {{cite journal
|title = Efficient Computing of Regression Diagnostiocs
|author = Paul Velleman
|author2=Roy Welsch
|journal = The American Statistician
|date=November 1981
|volume = 35
|pages = 234–242
|doi = 10.2307/2683296
|issue = 4
|publisher = American Statistical Association
|jstor = 2683296}}

==External links==
* [http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partleve.htm Partial Leverage Plot], [[Dataplot]] manual, Statistical Engineering Division, [[National Institute of Standards and Technology]]

{{NIST-PD}}

[[Category:Regression diagnostics]]

Partial leverage - Revision history

imported>Beland: convert special characters found by Wikipedia:Typo Team/moss (via WP:JWB)