Lahore School of Economics MPHIL Econometrics I (Winter 2010) Problem Set 1-Q4-Solutions

Lahore School of Economics MPHIL Econometrics I (Winter 2010) Problem Set 1-Q4-Solutions

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Mphil Advanced Econometrics Solution to Problem Set no 1 Q4.In regression model the variable y is regressed on the variable x with resulting regression line a+bx. Reversing the role of the two variables , x can be regressed on y with the resulting regression line c+dy. a. Derive formulas for the least squares estimates of c and d obtained by regressing x on y. b. Show that bd=R 2 , where b is the conventional least squares estimator and d the slope estimator in a. c. Conclude that in general d≠1/b. Explain this in terms of the criterion functions used to obtain b and d.
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Unformatted text preview: Answer: a. X=c+dy S(c,d)= Ʃ (Xi-c-dy) 2 Ʃ (Xi-c-dy)=0 Ʃ (Xi-c-dy)=0 d= (x Ʃ i-)(y i-)/ ( Ʃ y i-) 2 b. b.d = (x Ʃ i-)(y i-)/ ( Ʃ y i-) 2 . (x Ʃ i-)(y i-)/ ( Ʃ x i-) 2 Now given that y i= a+bx i +e i Since a= Ʃ (y i-)=b 2 (x Ʃ i-) 2 + e Ʃ i 2 since (x Ʃ i-) 2 e i =0 Ʃ (y i-)=b 2 (x Ʃ i-) 2 + e Ʃ i 2 SST=b(SSE)+SSR R 2 =SSE/SST=b 2 (x Ʃ i-) 2 / ( Ʃ y i-) 2 Now b= (x Ʃ i-)(y i-)/ ( Ʃ x i-) 2 R 2 = (x Ʃ i-)(y i-)/ ( Ʃ x i-) 2 ( Ʃ y i-) 2 =bd<= thus prooved Mphil Advanced Econometrics Solution to Problem Set no 1...
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This note was uploaded on 03/23/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.

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Lahore School of Economics MPHIL Econometrics I (Winter 2010) Problem Set 1-Q4-Solutions

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