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6.TwoAndMoreRandomVariables

# 6.TwoAndMoreRandomVariables - Two and More Random Variables...

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Two and More Random Variables GE 331 / IE 300 G. Köksal UIUC, IESE, 2011

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Outline Measures of linear association between two variables Causal and casual relationships Joint probability distributions Independence vs. correlation Bivariate normal distribution Linear functions of random variables 2
Sample Covariance Often we are interested in relationships between two or more variables. Stock prices of eBay and Amazon GPA and salary Rainfall and harvest Sample covariance is a measure of the linear association between two variables. 3

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Sample Covariance for samples for finite populations 4 ( )( ) 1 i i xy x x y y s n ( )( ) i x i y xy x y N
Correlation Correlation is another measure of linear association and not necessarily causation. Just because two variables are highly correlated, it does not mean that one variable is the cause of the other. 5

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for samples for populations y x xy xy s s s r y x xy xy Correlation Coefficient The coefficient can take on values between -1 and +1.
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