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Tutorial 6
1. For each of the following regression models, indicate whether it is a general linear
regression model. If not, state whether it can be expressed in the form of a linear
regression model after some suitable transformation
a.
Y
i
=
β
0
+
β
1
X
i
1
+
β
2
log
X
i
2
+
β
3
X
2
i
1
+
ε
i
b.
Y
i
=
ε
i
exp(
β
0
+
β
1
X
i
1
+
β
2
X
2
i
2
)
,w
i
t
h
ε
i
>
0
c.
Y
i
=
β
0
log(
β
1
X
i
1
)+
ε
i
d.
Y
i
=log(
β
1
X
i
1
β
2
log
X
i
2
+
ε
i
e.
Y
i
=[1+exp(
β
0
+
β
1
X
i
1
+
ε
i
]

1
2. Consider the multiple linear regression models
Y
i
=
β
1
X
i
1
+
β
2
X
i
2
+
ε
i
,i
=1
, ..., n
where
ε
i
are uncorrelated with
Eε
i
=0and
2
i
=
σ
2
state the least square criterion
and derive the least squares estimators for
β
1
and
β
2
.
3. Consider the multiple regression models
Y
i
=
β
0
+
β
1
X
i
1
+
β
2
X
2
i
1
+
β
3
X
i
2
+
ε
i
, ..., n
where
ε
i
are uncorrelated with
i
2
i
=
σ
2
. state the least square criterion
and derive the least squares normal equations.
4. An analyst wanted to ±t the regression model
Y
i
=
β
0
+
β
1
X
i
1
+
β
2
X
i
2
+
β
3
X
i
3
+
ε
i
, ..., n
by the least squares estimation when it is known that
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This note was uploaded on 10/04/2010 for the course STAT ST3131 taught by Professor Xiayingcun during the Fall '09 term at National University of Singapore.
 Fall '09
 XIAYingcun
 Linear Regression, Regression Analysis

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