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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
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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.
 Fall '09
 XIAYingcun

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