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# samplequestions1 - All exercises in appendix C and chapters...

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All exercises in appendix C and chapters 1 and 2 of the Wooldridge textbook are good practice exercises. Question 1 Suppose that I run an experiment to measure the effect of classroom temperature on final exam scores. I have a total of 300 students and give them the same final exam. I randomly assign students to one of the three classrooms, each one with different levels of temperature: 10 C (50 F), 20 C (68 F) and 30 C (86 F). Define Y i the grade on the exam (between 0 and 100) and define X i the temperature of the classroom in which the student had to complete the exam (X i =10, or X i =20 or X i =30). Assume the regression model: Y i = β 0 + β 1 X i + ε i (a) What does the term ε i mean? Why will different students have different values of ε i ? (b) Why E( ε i | X i ) = 0 in this regression model? (c) The estimated regression is Ŷ i = 45 + 1.2 X i . What is the predicted grade of students who completed the exam in the cold room (10 C)? What about the other two classrooms (20 C and 30 C)? (d) In light of your conclusions in part (c), discuss the current specification. Is it right and if not, what changes would you make? Question 2 Assume the regression model Y i = α + βX i + ε i (a) Derive the least squares (OLS) estimator of β and verify that it is unbiased. State the assumptions that you are making. (b) Suppose you know that α=4. Derive a formula for the least squares estimator. (c) Suppose that the regression model is such that there is no constant in the model (α=0). What is the ordinary least square estimator of β in this case? Under what conditions is this estimator unbiased? Question 3

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## This note was uploaded on 07/11/2011 for the course ECON 321 taught by Professor Louis during the Fall '09 term at Waterloo.

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samplequestions1 - All exercises in appendix C and chapters...

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