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Unformatted text preview: STAT 420 Examples for 09/25/2007 Fall 2007 correlation coefficient: & --- = y x s y y s x x n r 1 1 ( ) ( ) ( ) ( ) & & &---- = 2 2 y y x x y y x x r ( )( ) ( ) ( ) 2 2 2 2 & & & & & & &--- = y y n x x n y x y x n r 1. The value of r is always between 1 and + 1. 2. The magnitude of r indicates the strength of a linear relation, whereas its sign indicates the direction. 3. A value of r close to zero means that the linear association is very weak. 4. The value of r does not depend on which of the two variables under study is labeled x and which is labeled y , and is independent of the units in which x and y are measured. 5. r is invariant under linear transformations of x and y . That is, if v = a + b x and w = c + d y , then r x y = r v w if b and d are of the same sign, r x y = r v w if b and d are of the opposite sign. > - < - y x s y y s x x + > - > - y x s y y s x x y <...
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