12-Correlation

# 12-Correlation - Correlation Correlation Yes:Correlation &Y...

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Correlation

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Correlation Can we summarize the  degree of  dependence  between two random  variables in a single number? Yes: Correlation First must find  Covariance
Covariances from a Discrete PDF Step1: Find E[X] and E[Y] Step 2: Find deviations from the means State 1: D 1 =(X 1 -E[X]), (Y 1 -E[Y]) State 2: D =(X 2 -E[X]), (Y 2 -E[Y]) State n: D n = =(X n -E[X]), (Y n -E[Y])

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Method Step 3: Find the  products of the deviations State 1: Prod 1 =(X 1 -E[X])* (Y 1 -E[Y]) State 2: Prod =(X 2 -E[X])* (Y 2 -E[Y]) State n: Prod n = =(X n -E[X])* (Y n -E[Y]) Step 4: Covariance = The expected product of the  deviations: P 1 *Prod 1 +P 2 *Prod 2 +…+P n Prod n
Example Four state model (My answers are in percentage form) Step 1: E[r IBM ]=.65*(18)+.35*(-10)=8.2 E[r M ]=.45*(12)+.55*(-5)=2.65 State 1 State 4 State 2 State 3

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12-Correlation - Correlation Correlation Yes:Correlation &Y...

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