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In [[statistics]], high-leverage points are those that are [[outlier]]s with respect to the [[independent variables]]. [[leverage (statistics)|Leverage point]]s are those that cause large changes in the parameter estimates when they are deleted. Although an inflential point will typically have high leverage, a high leverage point is not necessarily an influential point. The [[leverage (statistics)|leverage]] is typically defined as the diagonal of the [[hat matrix]]
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


:<math> H = X(X'X)^{-1}X'. \, </math>
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


'''Partial leverage''' is used to measure the contribution of the individual independent variables to the leverage of each observation. That is, if ''h''<sub>''i''</sub> is the ''i''<sup>th</sup> row of the diagonal of the hat matrix, the partial leverage is a measure of how ''h''<sub>''i''</sub> changes as a variable is added to the regression model.
Registered users will be able to choose between the following three rendering modes:


The partial leverage is computed as:
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


:<math>
<!--'''PNG'''  (currently default in production)
\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 forcemathmode="png">E=mc^2</math>
</math>


where
'''source'''
:''j'' = index of independent variable
:<math forcemathmode="source">E=mc^2</math> -->
:''i'' = index of observation
:''X''<sub>''j''&middot;[''j'']</sub> = [[errors and residuals in statistics|residuals]] from regressing ''X''<sub>''j''</sub> against the remaining independent variables


Note that the partial leverage is the leverage of the ''i''<sup>th</sup> point in the [[partial regression plot]] for the ''j''<sup>th</sup> 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.
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


==See also==
==Demos==
* [[Partial residual plot]]
* [[Partial regression plot]]
* [[Variance inflation factor]] for a multi-linear fit
* [[Scatterplot matrix]]


==External links==
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
* [http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partleve.htm Partial Leverage 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
|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
|coauthor = Roy Welsch
|journal = The American Statistician
|month = November
|year = 1981
|volume = 35
|pages = 234–242
|doi = 10.2307/2683296
|issue = 4
|publisher = American Statistical Association
|jstor = 2683296}}


{{NIST-PD}}
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


[[Category:Regression diagnostics]]
==Test pages ==
 
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]
 
*[[Inputtypes|Inputtypes (private Wikis only)]]
*[[Url2Image|Url2Image (private Wikis only)]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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