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)= (Xi-c-dy) 2 (Xi-c-dy)=0 (Xi-c-dy)=0 d= (x i-)(y i-)/ ( y i-) 2 b. b.d = (x i-)(y i-)/ ( y i-) 2 . (x i-)(y i-)/ ( x i-) 2 Now given that y i= a+bx i +e i Since a= (y i-)=b 2 (x i-) 2 + e i 2 since (x i-) 2 e i =0 (y i-)=b 2 (x i-) 2 + e i 2 SST=b(SSE)+SSR R 2 =SSE/SST=b 2 (x i-) 2 / ( y i-) 2 Now b= (x i-)(y i-)/ ( x i-) 2 R 2 = (x i-)(y i-)/ ( x i-) 2 ( y i-) 2 =bd<= thus prooved Mphil Advanced Econometrics Solution to Problem Set no 1...
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Lahore School of Economics MPHIL Econometrics I (Winter 2010) Problem Set 1-Q4-Solutions

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