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400SSII09-HW_5 - SummerSessionII2009 Prof.MikeAguilar...

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Econ 400 – Economic Statistics Prof. Mike Aguilar Summer Session II 2009 UNC at Chapel Hill HW#5 Due: Tuesday 7/21/09 @11:30am Students may work together, but each must turn in their own assignment. Assignments should be typed whenever possible. A hardcopy must be turned into me by the due date above. No late assignments will be accepted. Please show all work carefully. There may be more than one solution to each problem. 1) Consider the model ݕ ൌ ߚ ൅ ߚ ݔ ൅ ݑ where the standard assumptions of the linear regression model apply. a. (2pts) Prove that ሺݔ െ ݔ ҧሻሺݕ െ ݕ തሻ ൌ ∑ ሺݔ െ ݔ ҧሻݕ ௜ୀଵ ሺݕ െ ݕ തሻݔ ௜ୀଵ ௜ୀଵ . b. (2pts) Prove that the OLS estimator of ߚ is unbiased. Note: you may either assume x is fixed, or that x is a random variable, in which case you would need to use a conditional expectation in your proof.
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