Key - Problem Set 4 2011

Key - Problem Set 4 2011 - Problem Set 4 Due 3/3/11...

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Problem Due 3/3/ 1. Suppo Unfortun conseque variabilit Some equ a. How w explanati Let’s che and subs 1 a Now, tak E Well hec absolute variable, average, populati distribut amount the para coefficie b. The ap is the est Start wit either a numerat The num Var(a 1 ) < Set 4 /11 ose you estim nately, the tru ences for our ty of a 1 ? uations: 1 a will the estim ion. eck, by dete stitute the t 1 2 1 ii i x Y x ke the expec 11 [] E a ck, that does ely no correl , so our SLM we will find on paramet tion is not o and directio meter β 1 an nts” of X 2 on ppropriate es imator b 1 . C th the two fo common de tor, just mul 1 2 2 2 1 a i x erators are < Var(b 1 ). W mate the foll ue model is: r simple line 1 2 1 i x Y x , mator do on a rmining the rue model f 10 1 i x  ctation, and 1 2 i x x sn’t equal β lation betw M estimator d that we do ter. The cen over the true on of the bia nd the “regr n X 1 . stimator for t Compare the ormulas abo enominator ltiply Var(a 2 2 2 2 i i x x    e the same, b hile biased, owing simp 0 i Y ear model es 1 2 a average? Ex e expected v for Y: 12 2 1 i i X X x using CRM 2 2 1 i i X 1 , unless th een indepen is biased. T o not get th nter of our s e value. The as depends ression the effect of variance fo ove and ask or numerat 1 ) by “1.” 2 1 i x  but clearly t , it appears le linear mod i X  timator, a 1 ? 2 2 1 i x , 1 2 b plain – prov value of the 2 v A 2 and 3, w ere is ndent Thus, on e true ampling e exact upon f X 1 on Y r b 1 to the va k: Is Var(a 1 ) tor. It’s a bit 22 2 2 21 i x x x x
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Key - Problem Set 4 2011 - Problem Set 4 Due 3/3/11...

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