# DMtutorial0s - Tutorial 1 1. Prove the solution of ridge...

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Tutorial 1 1. Prove the solution of ridge regression estimator ˆ β R = min β { n X i =1 ( Y i - X > i β ) 2 + λ p X k =1 β 2 k is ˆ β R = ( n X i =1 X > i X i + λI ) - 1 n X i =1 X i Y i or ˆ β R = ( X > X + λI ) - 1 X > Y. what about ˆ β R = min β { n X i =1 ( Y i - X > i β ) 2 + p X k =1 λ k β 2 k where λ k > 0 , k = 1 , ..., p 2. In Example 1.1 of lecture notes chapter 1 (part 1), after removing x 5 , ﬁt a new linear regression model. Check whether there is other variables that can be removed (using both T statistics and CV method). The estimated model is y = 0 . 1891 - 0 . 3424 x 1 + 0 . 9882 x 2 - 0 . 2191 x 3 - 0 . 7473 x 4 SE (0 . 139) (0 . 149) (0 . 130) (0 . 143) (0 . 114) x 3 with t statistics -1.53, which can be removed. The GCV values of models with (x1, x2, x3, x4), (x1, x2, x3), (x1, x2, x4), (x1, x3, x4), ( x2, x3, x4) are respectively 0.2509600 0.9080486, 0.2720439, 1.1407614, 0.3181061. No variable needs to be removed from the model further.
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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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