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==Correlation==
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==Introduction==
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Covariance and correlation are very similarly related. Correlation is used to identify the relationship of two random variables, X and Y. In order to determine the dependence of the two events, the correlation coefficient,<math> \rho </math>, is calculated as:
  
 
<math> \rho (X,Y) =  \frac{cov(X,Y)}{ \sqrt{var(X)var(Y)} } </math>
 
<math> \rho (X,Y) =  \frac{cov(X,Y)}{ \sqrt{var(X)var(Y)} } </math>
  
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The covariance is defined as: E(X-E[X])(Y-E[X]))
  
===Auto-Correlation===
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If X and Y are independent of each other, that means they are uncorrelated with each other, or cov(X,Y) = 0. However, if X and Y are uncorrelated, that does not mean they are independent of each other. 1, -1, and 0 are the three extreme points <math>p\rho X,Y)</math> can represent. 1 represents that X and Y are linearly dependent of each other. In other words, Y-E[X] is a positive multiple of X-E[X]. -1 represents that X and Y are inversely dependent of each other. In other words, Y-E[X] is a negative multiple of X-E[X].
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==Covariance==
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===Examples===
 
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===Auto-Covariance===
 
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==References==
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[[2013_Spring_ECE_302_Boutin|Back to ECE302 Spring 2013, Prof. Boutin]]
 
[[2013_Spring_ECE_302_Boutin|Back to ECE302 Spring 2013, Prof. Boutin]]

Revision as of 19:04, 30 April 2013


Correlation vs Covariance

Student project for ECE302

by Blue



Introduction

Covariance and correlation are very similarly related. Correlation is used to identify the relationship of two random variables, X and Y. In order to determine the dependence of the two events, the correlation coefficient,$ \rho $, is calculated as:

$ \rho (X,Y) = \frac{cov(X,Y)}{ \sqrt{var(X)var(Y)} } $

The covariance is defined as: E(X-E[X])(Y-E[X]))

If X and Y are independent of each other, that means they are uncorrelated with each other, or cov(X,Y) = 0. However, if X and Y are uncorrelated, that does not mean they are independent of each other. 1, -1, and 0 are the three extreme points $ p\rho X,Y) $ can represent. 1 represents that X and Y are linearly dependent of each other. In other words, Y-E[X] is a positive multiple of X-E[X]. -1 represents that X and Y are inversely dependent of each other. In other words, Y-E[X] is a negative multiple of X-E[X].

Examples

text



References

Back to ECE302 Spring 2013, Prof. Boutin

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood