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Unformatted text preview: Two and More Random Variables GE 331 / IE 300 G. Köksal UIUC, IESE, 2011 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 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 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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This note was uploaded on 01/26/2012 for the course IE IE 300 taught by Professor Zafarani during the Spring '09 term at University of Illinois, Urbana Champaign.
 Spring '09
 Zafarani

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