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key35mxmf03 - ECONOMICS 351 ANSWERS to Mid-Term Exam - Fall...

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ECONOMICS 351 ANSWERS to Mid-Term Exam -- Fall 2003 Page 1 of 16 pages QUEEN'S UNIVERSITY AT KINGSTON Department of Economics ECONOMICS 351* - Fall Term 2003 Introductory Econometrics Fall Term 2003 MID-TERM EXAM: ANSWERS M.G. Abbott DATE : Tuesday October 28, 2003. TIME : 80 minutes; 1:00 p.m. - 2:20 p.m. INSTRUCTIONS : The exam consists of FIVE (5) questions. Students are required to answer ALL FIVE (5) questions. Answer all questions in the exam booklets provided. Be sure your name and student number are printed clearly on the front of all exam booklets used. Do not write answers to questions on the front page of the first exam booklet . Please label clearly each of your answers in the exam booklets with the appropriate number and letter. Please write legibly. MARKING : The marks for each question are indicated in parentheses immediately above each question. Total marks for the exam equal 100 . GOOD LUCK! All questions pertain to the simple (two-variable) linear regression model for which the population regression equation can be written in conventional notation as: (1) YX ii =+ + ββ 12 u i where Y i and X i are observable variables, β 1 and β 2 are unknown (constant) regression coefficients, and u i is an unobservable random error term. The Ordinary Least Squares (OLS) sample regression equation corresponding to regression equation (1) is (i = 1, . .., N) (2) + $$ $ u i where β is the OLS estimator of the intercept coefficient $ 1 β 1 , β is the OLS estimator of the slope coefficient β 2 , i is the OLS residual for the i-th sample observation, i 2 1 i Y is the OLS estimated value of Y for the i-th sample observation, and N is sample size (the number of bservations in the sample). $ 2 $ u X ˆ ˆ ˆ β + β = o QUESTIONS : Answer ALL FIVE questions. ECON 351 -- Fall Term 2003: Answers to Mid-Term Exam Page 1 of 16 pages
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ECONOMICS 351 ANSWERS to Mid-Term Exam -- Fall 2003 Page 2 of 16 pages (15 marks) 1. State the Ordinary Least Squares (OLS) estimation criterion. State the OLS normal equations. Derive the OLS normal equations from the OLS estimation criterion. ANSWER : (3 marks) State the Ordinary Least Squares (OLS) estimation criterion. (3 marks) The OLS coefficient estimators are those formulas or expressions for β and that 1 ˆ 2 ˆ β minimize the sum of squared residuals RSS for any given sample of size N. The OLS estimation criterion is therefore: () ( ) = = β β = = β β N 1 i 2 i 2 1 i N 1 i 2 i 2 1 X ˆ ˆ Y u ˆ ˆ , ˆ RSS Minimize { β } j ˆ (4 marks) S t a t e t h e O L S n o r m a l e q u a t i o n s . (4 marks) The first OLS normal equation can be written in any one of the following forms: (N1) i i i i 2 1 i i i i 2 1 i i 2 1 i i Y X ˆ ˆ N Y X ˆ ˆ N 0 X ˆ ˆ N Y = β + β = β β = β β The second OLS normal equation can be written in any one of the following forms: (N2) i i i 2 i i 2 i i 1 i i i 2 i i 2 i i 1 2 i i 2 i i 1 i i i Y X X ˆ X ˆ Y X X ˆ X ˆ 0 X ˆ X ˆ Y X = β + β = β β = β β ECON 351 -- Fall Term 2003: Answers to Mid-Term Exam Page 2 of 16 pages
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ECONOMICS 351
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key35mxmf03 - ECONOMICS 351 ANSWERS to Mid-Term Exam - Fall...

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