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Influential Observations
Posted:
Sep 25, 1996 5:39 PM


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 :
LinReg(a+bx) a = ÃÂ10.98 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 :
LinReg(a+bx) a = ÃÂ52.62 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



