unr, math/stat 352, spring 2007. definition: corollary:
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UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
2 2
Cov( , )
( )( )
( ) ( )
XYX Y
X YXY
X Y
X Y
E X Y
E X E Y
1 1XY
Definition:
Corollary:
UNR, MATH/STAT 352, Spring 2007
Perfect linear relation Y = -X
Observations
Line Y = -X
UNR, MATH/STAT 352, Spring 2007
Approximate linear relation: Y = -0.8X +
Observations
Line Y = - 0.8X
UNR, MATH/STAT 352, Spring 2007
No linear relation
Observations
Line Y = 0
UNR, MATH/STAT 352, Spring 2007
Observations
Line Y = 0.8X
Approximate linear relation: Y = 0.8X +
UNR, MATH/STAT 352, Spring 2007
Observations
Line Y = X
Perfect linear relation: Y = X
UNR, MATH/STAT 352, Spring 2007
=1
=-1
If = ±1 then Y= ± X + c, c - constant
If -1< then various scenarios are possible…
UNR, MATH/STAT 352, Spring 2007
Some patterns with r = 0
r = 0r = 0r = 0
(a) (b) (c)
From Chance Encounters by C.J. Wild and G.A.F. Seber, © John Wiley & Sons, 2000.
= 0
= 0 = 0 = 0
Some patterns with r = 0.7
r = 0.7 r = 0.7 r = 0.7
r = 0.7r = 0.7r = 0.7
(d) (e) (f)
(g) (h) (i)
From Chance Encounters by C.J. Wild and G.A.F. Seber, © John Wiley & Sons, 2000.
UNR, MATH/STAT 352, Spring 2007
= 0.7
= 0.7= 0.7 = 0.7
= 0.7= 0.7= 0.7