Influential observation

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In statistics, an influential observation is an observation for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation.[1] In particular, in regression analysis an influential point is one whose deletion has a large effect on the parameter estimates. [2]

Example[edit]

All four sets are identical when examined using simple summary statistics, but vary considerably when graphed

In Anscombe's Quartet the two datasets on the bottom both contain influential points. If one point were removed, the line would look very different.

Assessment[edit]

Various methods have been proposed for measuring influence [3] In regression, the most direct are:

  1. DFFITS
  2. DFBETA measures the difference in each parameter estimate with and without the influential point. There is a DFBETA for each point and each observation (if there are N points and p variables there are N*P DFBETAs). [4]
  3. Cook's D measures the effect of removing a data point on all the parameters combined. [5]


Outliers, leverage and influence[edit]

An outlier may be defined as a surprising data point. leverage is a measure of how much the estimated value of the dependent variable changes when the point is removed. There is one value of leverage for each data point. [6] Data points with high leverage force the regression line to be close to the point. [5] In Anscombe's quartet, only the bottom right image has a point with high leverage.

See also[edit]


References[edit]

  1. ^ Burt, James E.; Barber, Gerald M.; Rigby, David L. (2009), Elementary Statistics for Geographers, Guilford Press, p. 513, ISBN 9781572304840 .
  2. ^ Everitt, Brian (1998). The Cambridge Dictionary of Statistics. Cambridge, UK New York: Cambridge University Press. ISBN 0521593468. 
  3. ^ stat.ufl.edu/~winner/sta6127/influence.doc.
  4. ^ http://www.albany.edu/faculty/kretheme/PAD705/SupportMat/DFBETA.pdf
  5. ^ a b Everitt, Brian (1998). The Cambridge Dictionary of Statistics. Cambridge, UK New York: Cambridge University Press. ISBN 0521593468. 
  6. ^ http://pages.stern.nyu.edu/~churvich/Undergrad/Handouts2/31-Reg6.pdf