CH 5 - Chapter 5: Correlation 5.2: A Numerical Index of...

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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 product-moment 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 .-1 r 1 r = 1 perfect positive relationship r = -1 perfect negative relationship r = 0 no linear association-1 < r < 0 ellipse w/ downward slope 0 < r < 1 ellipse w/ upward slope Examples 1 5.3: Pearson Product-Moment 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 2-1.5-3 2.25 9 4.5 1 8-1.5 3 2.25 9-4.5 3 6 0.5 1 0.25 1 0.5 5 4 2.5-1 6.25 1-2.5 Sums 10 20...
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CH 5 - Chapter 5: Correlation 5.2: A Numerical Index of...

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