Solution to Tutorial 8
1.
(a)
Hard hat:
E
(
Y
) =
β
0
+
β
2
+
β
1
X
1
Bump hat:
E
(
Y
) =
β
0
+
β
3
+
β
1
X
1
None:
E
(
Y
) =
β
0
+
β
1
X
1
(b)
(1)
H
0
:
β
3
= 0;
H
a
:
β
3
= 0;
(1)
H
0
:
β
3
=
β
2
;
H
a
:
β
3
=
β
2
;
2. (1)
β
3
means the difference in the intercepts between M2 and M4
(2)
β
4
−
β
3
is the difference in the intercepts between M2 and M3
(3) when all the other factors are fixed, the expected increment of
Y
as
X
1
increase
by one unit.
(4)
β
7
= 0 means there is no difference on the effect of
X
1
on the response for M3 and
M4.
(5)
β
5
−
β
6
is difference on the effect of
X
1
on the response for M1 and M2.
3. See
Rcode
4. See
Rcode
5.
a.
X
=
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
1
1
1
1
.
.
.
1
1
1
0
1
0
.
.
.
1
0
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
thus
X X
=
⎛
⎜
⎜
⎝
n
n
1
n
1
n
1
⎞
⎟
⎟
⎠
We have
(
X X
)
−
1
=
⎛
⎜
⎜
⎝
1
n
−
n
1
−
1
n
−
n
1
−
1
n
−
n
1
n
(
n
−
n
1
)
n
1
⎞
⎟
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 XIAYingcun
 Regression Analysis, G protein coupled receptors, M3 Lee, M3 Halftrack, M2 Browning machine gun, M4 Sherman, M2 Medium Tank

Click to edit the document details