note 1_2018.pdf - Econometrics I Spring 2018 Lecture Note 1 Multiple Regression yi 0 1 xi1 2 xi 2 k xik ui i 1 n In matrix form y n1 X nk k1 u n1 y1 x11

note 1_2018.pdf - Econometrics I Spring 2018 Lecture Note 1...

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Econometrics I Spring 2018 1 Dr. Yu-Chen Kuo Lecture Note 1 Multiple Regression i ik k i i i u x x x y ...... 2 2 1 1 0 , n i , ...... , 1 In matrix form: 1 1 1 n k k n n u X y 1 11 12 1 1 1 21 22 2 1 2 k k n n n nk k n y x x x u x x x y x x x u         or ' i i i y x u Sample estimator of is and the residual is denoted by ' i i i e y x ( vs. ' i i i u y x ) Or X y e OLS Estimation: 2 2 ' 1 1 n n i i i i i min e y x   X y X y e e  X y X y ' X X y X X y y y X X X y y y 2
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Econometrics I Spring 2018 2 Dr. Yu-Chen Kuo Note : n x x f y , ...... , 1 1 1 n n f x f y g r a d i e x f f x 1 If 1 1 n n x y a x a a x , then a x y a x x 2 If 1 n k k y A x , Ax y A x x 3 If ' k n n k y x A x , and A is a symmetric matrix. Then ' 2 y x Ax Ax x x , when A is not symmetric, then ' x Ax A A x x   min e e y X y X   X X X y y y 2 FOC 0 2 2 X X y X e e y X X X X X y X o l s 1 X y
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