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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 proﬁtloss 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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This note was uploaded on 09/01/2011 for the course ISYE 6414 taught by Professor Staff during the Fall '08 term at Georgia Institute of Technology.
 Fall '08
 Staff

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