In
regression analysis
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...
, partial leverage (PL) is a measure of the contribution of the individual
independent variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
s to the
total leverage of each observation. That is, if ''h''
''i'' is the ''i''
th element of the diagonal of the
hat matrix
In statistics, the projection matrix (\mathbf), sometimes also called the influence matrix or hat matrix (\mathbf), maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It describes t ...
, PL is a measure of how ''h''
''i'' changes as a variable is added to the regression model. It is computed as:
:
where
:''j'' = index of independent variable
:''i'' = index of observation
:''X''
''j''· 'j''/sub> = 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 In applied statistics, a partial regression plot attempts to show the effect of adding another variable to a model that already has one or more independent variables. Partial regression plots are also referred to as added variable plots, adjusted va ...
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
Leverage or leveraged may refer to:
*Leverage (mechanics), mechanical advantage achieved by using a lever
* ''Leverage'' (album), a 2012 album by Lyriel
*Leverage (dance), a type of dance connection
*Leverage (finance), using given resources to ...
* Partial residual plot
In applied statistics, a partial residual plot is a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the Statistical model, ...
* Partial regression plot In applied statistics, a partial regression plot attempts to show the effect of adding another variable to a model that already has one or more independent variables. Partial regression plots are also referred to as added variable plots, adjusted va ...
* Variance inflation factor
In statistics, the variance inflation factor (VIF) is the ratio (quotient) of the variance of estimating some parameter in a model that includes multiple other terms (parameters) by the variance of a model constructed using only one term. It quant ...
for a multi-linear fit
References
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External links
Partial Leverage Plot
Dataplot manual, Statistical Engineering Division, National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
{{NIST-PD
Regression diagnostics