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Topic: Influential Observations
Replies: 2   Last Post: Sep 25, 1996 11:38 PM

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Bruce B. Richards

Posts: 6
Registered: 12/6/04
Influential Observations
Posted: Sep 25, 1996 5:39 PM
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To all,

Moore and McCabe define an observation as influential if removing it
would "markedly" change the position of the regression line. They also
point out that points separated in the "x" direction from other
observations are often influential. My question has more to do with
the first half of their definition. What qualifies as being a
"markedly" changed position of the regression line, i.e. are there any
numerical boundaries or guidelines in deciding if a "marked" change
has occurred? Case in point, I gave a set of data with the following
numerical information :

a = ‚10.98
b = 2.124
r = .835
r^2 = .697

From the graph there exist a point all the way to the left and above
the next three pieces of data (I know this description may not help
much, sorry). It is definitely an outlier, but is it influential?
Eliminating it produces the following numerical information :

a = ‚52.62
b = 3.015
r = .924
r^2 = .853

The regression line definitely shifts, but was it a "marked" shift?
Where does one draw the line (pardon the pun)....?
Actual Data :

y x
102.5 51.3
104.5 49.9
100.4 50
95.9 49.2
87 48.5
95 47.8
88.6 47.3
89.2 45.1
78.9 46.3
84.6 42.1
81.7 44.2
72.2 43.5
65.1 42.3
68.1 40.2
70.3 30.2
52.5 34

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