correl - Correlation Coefficient A measure of the strength...

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Correlation Coefficient A measure of the strength of the linear relationship between 2 quantitative variables
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How To Calculate (x 1 ,y 1 ), (x 2 ,y 2 ), . .. (x n ,y n ) ( 29 ( 29 1 ( 1) 1 2 where is the mean and is the standard deviation of , , , , n i i i x y x x y y n s s x n r x s x x x = - - - = K
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Example: calculating correlation (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ) (1, 3) (1.5, 6) (2.5, 8) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1.67 3 5.67 1.5 1.67 6 5.67 2.5 1.67 8 5.67 (3 1)(.76)(2.52) 1.67, 5.67, .76, 2.52 .9538 x y x y s s r  - - + - - + - -    - = = = = = =
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PROPERTIES scaleless [like demand elasticity in economics (-infinity, 0)] -1 < r < 1 r= -1 only if y = a + bx with slope b<0 r =+1 only if y = a + bx with slope b>0
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Values of r and scatterplots r near +1 r near -1 r near 0 x x y y r near 0
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Correlation: Fuel Consumption vs Car Weight FUEL CONSUMPTION vs CAR WEIGHT 2 3 4 5 6 7 1.5 2.5 3.5 4.5 WEIGHT (1000 lbs) FUEL CONSUMP. (gal/100 miles) r = .9766
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This note was uploaded on 04/21/2009 for the course BUS 350 taught by Professor Reiland during the Spring '08 term at N.C. State.

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correl - Correlation Coefficient A measure of the strength...

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