- Partial residual plot
In

applied statistics , a**partial residual plot**is agraphical 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 model.**Background**When performing a

linear regression with a singleindependent variable , ascatter plot of theresponse variable against the independent variable provides a good indication of the nature of the relationship. If there is more than one independent variable, things become more complicated. Although it can still be useful to generate scatter plots of the response variable against each of the independent variables, this does not take into account the effect of the other independent variables in the model.**Definition**Partial residual plots are formed as::$mathrm\{Residuals\}\; +\; hat\{eta\}\_iX\_i\; mathrm\{\; versus\; \}\; X\_i$where:Residuals = residuals from the

full model :$hat\{eta\}\_i$ = regression coefficient from the "i"^{th}independent variable in the full model:"X"_{i}= the "i"^{th}independent variablePartial residual plots are widely discussed in the regression diagnostics literature (e.g., see the References section below). Although they can often be useful, they can also fail to indicate the proper relationship. In particular, if "X"

_{i}is highly correlated with any of the other independent variables, the variance indicated by the partial residual plot can be much less than the actual variance. These issues are discussed in more detail in the references given below.**CCPR plot**The CCPR (component and component-plus-residual) plot is a refinement of the partial residual plot, adding:$hat\{eta\}\_iX\_i\; mathrm\{\; versus\; \}\; X\_i$

This is the "component" part of the plot and is intended to show where the "fitted line" would lie.

**ee also***

partial regression plot

*partial leverage plot

*variance inflation factor s for a multi-linear fit.

*scatter plot matrix **External links*** [

*http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partresi.htm Partial Residual Plot*]**References*** cite book

title = Modern Regression Methods

author = Tom Ryan

publisher = John Wiley

year = 1997

* cite book

title = Applied Linear Statistical Models

edition = 3rd ed.

author = Neter, Wasserman, and Kunter

year = 1990

publisher = Irwin

* cite book

title = Applied Regression Analysis

edition = 3rd ed.

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

coauthor = Roy Welsch

journal = The American Statistician

month = November

year = 1981

volume = 35

number = 4

pages = 234-242

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