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midterm-200901 - ECON 301 Econometrics I Mid-semester Test...

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ECON 301 Econometrics I, Mid-semester Test Monday 20 April 2009 (Semester ONE) Department of Economics, Korea University TIME ALLOWED: 80 minutes INSTRUCTIONS: Answer ALL five questions. (Total 100 points.) Do not write questions. Irrelevant answers will not count at best. 1. Consider the simple linear regression model y = β 0 + β 1 x + u (1) where x and y are observable variables. Assume that E ( u | x ) = 0 . [ 20 points total ] (a) Using the notations used in (1), write what denotes each of the following items below. Write “NOT FOUND in (1)” if the right notation is not found in (1) . The first one (item number ‘o’) is an example. [ 1 point each, total 5 points ] o. (Example) The intercept parameter: β 0 i. The control variable: ii. The dependent variable: iii. The disturbance term: iv. The explanatory variable: v. The OLS residual: (b) Express E ( y | x = 4) - E ( y | x = 3) in terms of the parameters in (1). Also express E ( y | x = 1) - E ( y | x = 0) . Are they equal? Explain why they are (or are not) equal. [ 5 points ] (c) Suppose that a sample of data gives n X i =1 ( x i - ¯ x ) 2 = 2000 , n X i =1 ( x i - ¯ x )( y i - ¯ y ) = 200 , n X i =1 ( y i - y ) 2 = 200 , where ¯ x = n - 1 n i =1 x i and ¯ y = n - 1 n i =1 y i . Calculate the OLS estimate of β 1 . [ 5 points ] (d) Using information in part (c) above, and using the fact that b y i = b β 0 + b β 1 x i and ¯ y = b β 0 + b β 1 ¯ x , calculate the R-squared.
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