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Tutorial 7
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
oneout) CV value.
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.)
3. For
data B
(the ﬁrst 3 columns are independent variables, the last one response
variable). Find the best model among
Linear regression I:
Y
=
a
+
b
x
1
+
ε
Linear regression I:
Y
=
a
+
b
x
1
+
c
x
2
+
ε
Linear regression I:
Y
=
a
+
b
x
1
+
c
x
2
+
d
x
3
+
ε
PPRA:
Y
=
φ
1
(
α
1
x
1
+
α
2
x
2
+
α
3
x
3
) +
ε
PPRB:
Y
=
φ
1
(
α
1
x
1
+
α
2
x
2
+
α
3
x
3
) +
φ
2
(
β
1
x
1
+
β
2
x
2
+
β
3
x
3
) +
ε
PPRC:
Y
=
φ
1
(
α
1
x
1
+
α
2
x
2
+
α
3
x
3
) +
φ
2
(
β
1
x
1
+
β
2
x
2
+
β
3
x
3
)
+
φ
3
(
γ
1
x
1
+
γ
2
x
2
+
γ
3
x
3
) +
ε
PPRD:
Y
=
φ
1
(
α
1
x
1
+
α
3
x
3
) +
ε
PPRE:
Y
=
φ
1
(
α
1
x
1
+
α
3
x
3
) +
φ
2
(
β
1
x
1
+
β
3
x
3
) +
ε
PPRF:
Y
=
φ
1
(
α
1
x
1
+
α
3
x
3
) +
φ
2
(
β
1
x
1
+
β
3
x
3
)
+
φ
3
(
γ
1
x
1
+
γ
3
x
3
) +
ε
4. Consider the Swiss banknotes again. For
training data
apply CART to built the
CART tree. Based on this tree, check the
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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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