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Unformatted text preview: Chapter 5: Correlation 5.2: A Numerical Index of Correlation A correlation coefficient is a number that describes the degree of association or strength of a relationship between two variables. The Pearson productmoment correlation coefficient ( r XY or r ) is a measure of the linear relationship between two variables, X and Y. The population correlation coefficient is denoted by ρ .1 ≤ r ≤ 1 r = 1 perfect positive relationship r = 1 perfect negative relationship r = 0 no linear association1 < r < 0 ellipse w/ “downward slope” 0 < r < 1 ellipse w/ “upward slope” Examples 1 5.3: Pearson ProductMoment Correlation Coefficient ( 29 ( 29 ( 29 ( 29   = = ∑ ∑ ∑ n Y Y n X X n Y Y X X S S S r i i i i Y X XY 2 2 Example Compute r using the formula. x y x  xbar y  ybar (x  xbar)^2 (y  ybar)^2 (x  xbar)(y  ybar) 1 21.53 2.25 9 4.5 1 81.5 3 2.25 94.5 3 6 0.5 1 0.25 1 0.5 5 4 2.51 6.25 12.5 Sums 10 20...
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This note was uploaded on 04/15/2008 for the course STATS 2402 taught by Professor Kirk during the Spring '08 term at Baylor.
 Spring '08
 kirk
 Correlation, Correlation Coefficient

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