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quiz1solution - ISYE6414 Summer 2010 Quiz I solution Dr...

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Unformatted text preview: ISYE6414 Summer 2010 Quiz I solution Dr. Kobi Abayomi June 24, 2010 You are given this data Dem. Rep. z= Indep. Indep. 75 -50 y= 25 -25 If you set up the design matrix the way I have in mind, then (xT x)−1 1/2 -1/2 -1/2 3/2 = -1/2 1/2 where Y is the proﬁt-loss in some investment. 1 1 x= 1 1 -1/2 1/2 3/2 The design matrix I have in mind is 10 0 1 0 0 00 since I’m letting X1 = 1 if Democrat 0 otherwise and X2 = 1 if Republican and 0 otherwise. 1 ˆ Then since β = (xT x)−1 xT y 0 ˆ β = 75 -50 and y T = (75, −50, 0, 0). The interpretation of the coeﬃcients is straightforward: Democrats ˆ are expected to get 75 units of whatever; Republicans lose 50 units; and Independents break even. 2 ...
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quiz1solution - ISYE6414 Summer 2010 Quiz I solution Dr...

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