common 082608 lin regress

# common 082608 lin regress - returns x y xx xy 1 0.2570...

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Linear Regression i i i e bx a y + + = Assume that  e  is distributed normally, with mean zero and standard  deviation  σ . i i i bx a y e - - = 2 2 2 2 2 2 2 2 i i i i i i i x b abx a y bx ay y e + + + - - = + + + - - = 2 2 2 2 2 2 2 2 i i i i i i i x b x ab na y x b y a y e Now, to minimize the sum of the squared error terms, and to get the best  “fit” we take partial deriviatives w res to a and b and set them equal to zero. 0 2 2 2 2 = + + - = i i i x b na y e a 0 2 2 2 2 2 = + + - = i i i i i x b x a y x e b This yields the two equations + = i i x b na y                            1.1700 = 10* a  +  b *(1.1000) + = 2 i i i i x b x a y x                 .3857 =  a *(1.1000) +  b *.4303 So, now we have two equations and two unknowns. We will now do a linear regression, letting x be the Market returns and y be stock PQU

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Unformatted text preview: returns. x y xx xy 1 0.2570 0.4000 0.0660 0.1028 2 0.0800-0.1500 0.0064-0.0120 3-0.1100-0.1500 0.0121 0.0165 4 0.1500 0.3500 0.0225 0.0525 5 0.3250 0.1000 0.1056 0.0325 6 0.1370 0.3000 0.0188 0.0411 7 0.4000 0.4200 0.1600 0.1680 8 0.1000-0.1000 0.0100-0.0100 9-0.1080-0.2500 0.0117 0.0270 10-0.1310 0.2500 0.0172-0.0328 Sum 1.1000 1.1700 0.4303 0.3857 1.1700 = 10* a + b *(1.1000) .3857 = a *(1.1000) + b *.4303 Solving these two equations yields the regression line y = .0256 + . 8309 x...
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common 082608 lin regress - returns x y xx xy 1 0.2570...

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