DMtutorial6s - Tutorial 6: suggested solutions 1. Suppose...

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Tutorial 6: suggested solutions 1. Suppose we use model Y = ± a 0 + b 0 x 1 + c 0 x 2 + ε 0 , if x 1 + x 2 < 0 , a 1 + b 1 x 1 + c 1 x 2 + ε 1 , if x 1 + x 2 0 . to fit data ( x i 1 , x i 2 , Y i ) , i = 1 , 2 , ..., n . Write the procedure to calculate the (delete-one-out) CV value. CV = n - 1 h X x i 1 + x i 2 < 0 { Y i - ˆ a \ i 0 - ˆ b \ i 0 x i 1 - ˆ c \ i 0 x i 2 } 2 + X x i 1 + x i 2 0 { Y i - ˆ a \ i 1 - ˆ b \ i 1 x i 1 - ˆ c \ i 1 x i 2 } 2 i , where ˆ a \ i 0 ˆ b \ i 0 ˆ c \ i 0 = n X x j 1 + x j 2 < 0 j 6 = i 1 x j 1 x j 2 1 x j 1 x j 2 > o - 1 X x j 1 + x j 2 < 0 j 6 = i 1 x j 1 x j 2 Y j and ˆ a \ i 1 ˆ b \ i 1 ˆ c \ i 1 = n X x j 1 + x j 2 0 j 6 = i 1 x j 1 x j 2 1 x j 1 x j 2 > o - 1 X x j 1 + x j 2 0 j 6 = i 1 x j 1 x j 2 Y j 2. For model Y = 4 x 1 x 2 + ε, find two PPR models for it. (In other word, the representations of PPR model is not unique.) for any nonzero a and b , we have Y = ( ab ) - 1 { ( a x 1 + b x 2 ) 2 - ( a x 1 - b x 2 ) 2 } + ε 3. For data B (the first 3 columns are independent variables, the last one response variable). Find the best model among
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This note was uploaded on 10/04/2010 for the course STAT ST4240 taught by Professor Xiayingcun during the Fall '09 term at National University of Singapore.

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DMtutorial6s - Tutorial 6: suggested solutions 1. Suppose...

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