ps5 - Problem Set 5 ECON 837 Prof Simon Woodcock Spring...

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Problem Set 5 ECON 837 Prof. Simon Woodcock, Spring 2006 Due: Monday Feb 27 1. Consider the least squares residual vector e from the regression of y on X with V ar [ y ] = 2 I n : (a) Let e j be any element of e : Show V ar [ e j ] 2 : (b) What is the rank of E [ ee 0 ]? 2. Suppose we have the linear regression model y = X + " with E [ " ] = 0 and E [ "" 0 ] = 2 I n : Suppose X = [ i X 2 ] where i is an n ± vector of ones and X 2 is n ² ( k ± 1) and measured in deviations from means. Show that the least squares estimator of the intercept (the parameter on i ) is uncorrelated with the least squares estimator of the slopes (the parameters on X 2 ). 3. Suppose you estimate the linear regression y = X 1 1 + X 2 2 + " R 2 to be satisfactory, you reject the null hypothesis that all slope coe¢ cients are zero (the F t -statistics on the slope coe¢ cients. (a) What do you think the problem is? Do you suspect any assumptions of the linear
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This note was uploaded on 10/08/2011 for the course PHYS 102 taught by Professor Thewalt during the Spring '09 term at Simon Fraser.

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ps5 - Problem Set 5 ECON 837 Prof Simon Woodcock Spring...

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