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exam2solutions - ISYE 6414 Summer 2009 Solution Exam 2...

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ISYE 6414 - Summer 2009 Solution Exam 2 Problem 1. 1. Y i = β 0 + β 1 X i 1 + β 2 X i 1 X i 2 + i X = 1 X 11 X 11 X 12 1 X 21 X 21 X 22 1 X 31 X 31 X 32 1 X 41 X 41 X 42 b = ˆ β 0 , ˆ β 1 , ˆ β 2 T = ( X 0 X ) - 1 X 0 Y 2. log Y i = β 0 + β 1 X i 1 + β 2 X i 2 + i X = 1 X 11 X 12 1 X 21 X 22 1 X 31 X 32 1 X 41 X 42 b = ˆ β 0 , ˆ β 1 , ˆ β 2 T = ( X 0 X ) - 1 X 0 Y * . Where Y * = (log Y 1 , log Y 2 , log Y 3 , log Y 4 ) T 3. Y i = β 1 X i 1 + β 2 X i 2 + β 3 X 2 i 1 + i X = X 11 X 12 X 2 11 X 21 X 22 X 2 21 X 31 X 32 X 2 31 X 41 X 42 X 2 41 b = ˆ β 1 , ˆ β 2 , ˆ β 3 T = ( X 0 X ) - 1 X 0 Y 4. Y i = β 0 + β 1 X i 1 + β 2 log X i 2 + i X = 1 X 11 log X 12 1 X 21 log X 22 1 X 31 log X 32 1 X 41 log X 42 b = ˆ β 0 , ˆ β 1 , ˆ β 2 T = ( X 0 X ) - 1 X 0 Y * . Where Y * = ( Y 1 , Y 2 , Y 3 , Y 4 ) T 1
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Problem 2. Given three categories, two indicator predictor are used: X 1 and X 2 . From the given matrix ( X 0 X ) - 1 we can deduce that X i 1 = 1 if Y i belongs to the Democrat party and 0 otherwise. Also, X i 2 = 1 if Y i belongs to the Republican party and 0 otherwise. The design
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