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Unformatted text preview: q q q Statistical methods provide a way of parsimoniously summarizing the strength, pattern, and significance of relationships. q q q q q q q q 0 3 6 9 Age 12 15 Researchers are often interested in complex relationships among variables. 18 Figure: Nearest Neighbor Prediction of Age and Lung Capacity for Smokers and Non-Smokers. Culpepper, SA STAT 400: Statistics and Probability I Definitions Examples Predictions, Best Fit Line 4.1: Distributions of two random variables 4.2: The Correlation Coefficient Definition of Covariance Researchers are interested in how variables relate. e.g., how do differences on one variable relate to differences on another (i.e., how do they covary). Let u (X , Y ) = (X − µX ) (Y − µY ). Note E [u (X , Y )] = E [(X − µX ) (Y − µY )] = E (XY ) − µX µY . In the discrete case, the covariance is defined as, xyf (x , y ) − µX µY σ X ,Y = x (11) y In the continuous case, σX ,Y is, ∞ ∞ −∞ −∞ xyf (x , y ) dxdy − µX µY σ X ,Y = The covariance...
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This note was uploaded on 12/12/2013 for the course STAT 400 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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