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lecture 8 correlation1

# lecture 8 correlation1 - Correlation Two variables are...

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Correlation Two variables are correlated if knowing something about one tells you something about the other Height and Weight (+) Heavy smoking and Life expectancy (-) Height and Life expectancy (uncorrelated) Age and Strength (curvilinear) 1

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Linear Correlation: Pearson’s r A measure of the strength, and direction, of the linear relationship between two variables Takes values ranging from 1 to -1 Values of r close to 1 or -1 indicate a stronger relationship; values close to 0 indicate a weaker relationship Positive values indicate a positive relationship; negative values indicate a negative relationship 2
z Score formula for r r = z x z y n - 1 Where z x and z y are the sample z -transformed scores for the i th individual on the variables x and y , and n = the number of paired observations in the sample (i.e., half the total number of scores) z x = z x = x i - X s x y i - Y s y 3

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Covariance Var(x) =E(x - µ ) 2 =E(x - µ )(x - µ ) = Cov(x, x) Cov(x, y) =E(x - µ x )(y - µ y ) = (x - µ x )(y - µ y ) N Where N = the number of paired observations in the population data set {X,Y} 4
Covariance Positive values of Cov(x, y) indicate that higher values of

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lecture 8 correlation1 - Correlation Two variables are...

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