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Unformatted text preview: Regression and Efficient Diversification I Imperfect Linear Dependence By definition: i i i e bx a y + + = ) ( i i i bx a y e + = Regression Properties Good estimates of a and b will produce error terms (e): that have an average of zero . This gets the vertical location of the line right that are independent of x . This gets the slope of the line right The formulas for a and b that will produce such error terms are given by (see excel spreadsheet example) x b y a x Var y x Cov b = = ) ( ) , ( Decomposing y i i i e bx a y + + = . with correlated perfectly is that of component The i i x y . of t independen is that of component The i i x y Total Variance of y Rule #3 says: If x and y are random variables and z=ax+by, then y i = a + bx i + e i x i and e i are random variables Cov(x i and e i )=0 Var(y)=b 2 *Var(x i )+Var(e i ) ) , ( 2 ) ( 2 2 2 2 y x abCov b a z Var y x + + = Explanatory Variance Var(y)=b 2 *Var(x i )+Var(e i ) The total variance of y has two components: b...
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This note was uploaded on 03/01/2012 for the course BUS M 410 taught by Professor Brianboyer during the Fall '10 term at BYU.
 Fall '10
 BrianBoyer

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