On 2 Mar 2003 at 22:22, Dalby, James WLAP:EX wrote:
Influential observations (for example as defined by leverage) are
defined only by the x values, not the response (y) values. So
influential observations will correspond to outliers in
x-space, but will not necessarily be response outliers. One simple
example is
x
x
x
x
x
x
Where the rightmost observation is an (x)-outlier, but not (assuming
a linear regression model) an atypical value IN THE MODEL. But is is
influential, and, if correct, very valuable (reduces the variance of
estimation of the slope very much).
In the sime-series context the world INLIER is used: This is an
observation which is not an outlier in any of the marginal
distributions, but still atipical of the model, and possibly
erroneous (that is, if you have faith in the model). low sales of
easter eggs in easter would be an inlier.
Kjetil Halvorsen
> Dear EdStat list members:
>
> I have been refreshing my knowledge of outliers and influential observations
> in regression analysis and could use some clarification on the difference
> between the two. I'm aware that some outiers are influential while others
> are not, but I'm wondering whether all influential observations are
> outliers. Is it possible for an influential observation to not be an
> outlier? If you know of a graph that would answer this, please refer me to
> it.
>
> Thank you, James.
>
>
> .
> .
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