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Unformatted text preview: Midterm Exam 1 Econ 360  Spring 2010 Professor Mumford Monday, February 22, 2010 [email protected] YOUR NAME: Answer all questions clearly and legibly. Show all of your work in the space provided. Do not use additional sheets or write on the back of the page. Do not refer to your notes, the text book, or any other materials during the exam. There are 100 points possible. Maximum points for each question are noted in parentheses. You have one hour and ten minutes to complete the exam. Good luck! 1. (12 points) Define or explain the following terms: a. (3 points) tstatistic b. (3 points) fitted value c. (3 points) total sum of squares d. (3 points) spurious correlation 2. (12 Points) Consider the simple regression model y = β + β 1 x + u . Suppose you collect a random sample { ( y i ,x i ) ; i = 1 , 2 , 3 } . The values are: y 1 = 5 ,y 2 = 6 ,y 3 = 2 and x 1 = 2 ,x 2 = 1 ,x 3 = 3. Write down the equation for the OLS estimator of β 1 . Fill in the actual numbers and solve for the value of ˆ β 1 . 3. (12 Points) In the multiple linear regression model, explain what σ 2 is. Explain how we estimate it by giving the formula for ˆ σ 2 . Give some intuition as to why, under the Gauss Markov assumptions, ˆ σ 2 is an unbiased estimator of σ 2 (I’m not looking for a formal proof, just an explanation). 4. (12 Points) State any four of the six classical assumptions on the multiple linear regression model. 5. (12 Points) In the multiple linear regression model, show that ˆ β 1 can be expressed as ˆ β 1 = n X i =1 ˆ r i 1 y i n X i =1 (ˆ r i 1 ) 2 where ˆ r i 1 are the residuals from a regression of x 1 on x 2 ,x 3 ,...,x k . 6. (20 Points) Economists have long been interested in trying to establish causal links between features of the school environment and educational outcomes for the students. One of the most important relationships is how the number of students in a class,...
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This note was uploaded on 02/06/2012 for the course ECON 360 taught by Professor Na during the Spring '10 term at Purdue.
 Spring '10
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