HW1sols_2008 - HOMEWORK 1 SOLUTIONS Exercise 1 A potential...

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HOMEWORK 1 SOLUTIONS Exercise 1 A potential project This is an open ended question, the main thing is to try and get to ask me in o¢ ce hours. Exercise 2 Test of Covariance Here you need to remember the two results that can be derived X i ^ u i = 0 X i x i ^ u i = 0 Now the question asks you if Cov [ X; ^ u ] can be informative about Cov [ X; u ] . Let±s look at Cov [ X; ^ u ] = E [ X ^ u ] E [ X ] E [ ^ u ] order conditions. So Cov [ X; ^ u ] is always going to be zero. Hence, it cannot tell us anything about Cov [ X; u ] . (NOTE: in this notation ^ u refers to the vector of residuals from OLS estima- tion, while u is the error term in the linear OLS model. Exercise 3 Unbiased? Consistent? First I want to draw the distinction between unbiasedness and consistency. Being unbiased is a statement only about the expectation of the estimator. An estimator is unbiased if, E [ ^ ] = Notice that being unbiased says nothing about the variance and that unbiasedness doesn±t consider
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This homework help was uploaded on 04/18/2008 for the course BIOL_SCI 164 taught by Professor Walsh during the Spring '08 term at Northwestern.

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HW1sols_2008 - HOMEWORK 1 SOLUTIONS Exercise 1 A potential...

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